Properties

Label 570.2.m.a.493.6
Level $570$
Weight $2$
Character 570.493
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 493.6
Root \(1.53190 + 1.53190i\) of defining polynomial
Character \(\chi\) \(=\) 570.493
Dual form 570.2.m.a.37.6

$q$-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} +(-4.03490 - 1.64913i) 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} +(-1.64913 + 4.03490i) 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} +(9.09870 - 3.49481i) 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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.985939 0.167105i \(-0.946558\pi\)
0.167105 + 0.985939i \(0.446558\pi\)
\(8\) −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 −0.0920758 + 0.995752i \(0.529350\pi\)
−0.995752 + 0.0920758i \(0.970650\pi\)
\(14\) −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 0.239500 0.970896i \(-0.423016\pi\)
0.970896 0.239500i \(-0.0769836\pi\)
\(18\) 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 0.995202 0.0978397i \(-0.0311932\pi\)
−0.0978397 + 0.995202i \(0.531193\pi\)
\(24\) 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 \(-0.377465\pi\)
0.375518 + 0.926815i \(0.377465\pi\)
\(30\) −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 −0.999813 0.0193530i \(-0.993839\pi\)
−0.0193530 0.999813i \(-0.506161\pi\)
\(38\) −4.03490 1.64913i −0.654546 0.267524i
\(39\) 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 0.315114 0.949054i \(-0.397957\pi\)
−0.949054 + 0.315114i \(0.897957\pi\)
\(44\) 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 −0.429832 0.902909i \(-0.641427\pi\)
0.902909 + 0.429832i \(0.141427\pi\)
\(48\) −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 \(-0.926043\pi\)
0.230259 + 0.973129i \(0.426043\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 12.7039 + 0.389830i 1.71299 + 0.0525647i
\(56\) 3.06380i 0.409417i
\(57\) −1.64913 + 4.03490i −0.218432 + 0.534435i
\(58\) 2.85986 + 2.85986i 0.375518 + 0.375518i
\(59\) 2.39487 0.311786 0.155893 0.987774i \(-0.450175\pi\)
0.155893 + 0.987774i \(0.450175\pi\)
\(60\) −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 \(-0.0724382\pi\)
−0.225612 + 0.974217i \(0.572438\pi\)
\(68\) 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 0.575047 0.818121i \(-0.304984\pi\)
−0.818121 + 0.575047i \(0.804984\pi\)
\(74\) 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 \(-0.576633\pi\)
−0.238431 + 0.971159i \(0.576633\pi\)
\(80\) 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 0.353110 0.935582i \(-0.385124\pi\)
−0.935582 + 0.353110i \(0.885124\pi\)
\(84\) −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 \(-0.457558\pi\)
0.132939 + 0.991124i \(0.457558\pi\)
\(90\) −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
\(95\) 9.09870 3.49481i 0.933507 0.358559i
\(96\) −1.00000 −0.102062
\(97\) −6.22010 6.22010i −0.631555 0.631555i 0.316903 0.948458i \(-0.397357\pi\)
−0.948458 + 0.316903i \(0.897357\pi\)
\(98\) 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 −0.353961 + 0.935260i \(0.615165\pi\)
−0.935260 + 0.353961i \(0.884835\pi\)
\(104\) 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 \(-0.361713\pi\)
−0.907106 + 0.420903i \(0.861713\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 5.95528 0.570412 0.285206 0.958466i \(-0.407938\pi\)
0.285206 + 0.958466i \(0.407938\pi\)
\(110\) 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 \(-0.749124\pi\)
0.709051 + 0.705157i \(0.249124\pi\)
\(114\) −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 \(-0.0331236\pi\)
−0.103873 + 0.994591i \(0.533124\pi\)
\(128\) 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
\(133\) 5.05259 12.3621i 0.438115 1.07193i
\(134\) 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 −0.797228 0.603678i \(-0.793701\pi\)
0.603678 + 0.797228i \(0.293701\pi\)
\(138\) 4.30360 + 4.30360i 0.366347 + 0.366347i
\(139\) 17.4266i 1.47810i 0.673649 + 0.739051i \(0.264726\pi\)
−0.673649 + 0.739051i \(0.735274\pi\)
\(140\) 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 \(0.0234691\pi\)
−0.997283 + 0.0736637i \(0.976531\pi\)
\(150\) 4.99059 + 0.306570i 0.407480 + 0.0250314i
\(151\) 8.62201i 0.701649i 0.936441 + 0.350825i \(0.114099\pi\)
−0.936441 + 0.350825i \(0.885901\pi\)
\(152\) 1.64913 4.03490i 0.133762 0.327273i
\(153\) −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 −0.324076 0.946031i \(-0.605053\pi\)
0.946031 + 0.324076i \(0.105053\pi\)
\(158\) −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 0.944408 0.328776i \(-0.106636\pi\)
−0.328776 + 0.944408i \(0.606636\pi\)
\(164\) −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 −0.873779 0.486323i \(-0.838338\pi\)
−0.486323 0.873779i \(-0.661662\pi\)
\(168\) −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 \(-0.748141\pi\)
0.711225 + 0.702965i \(0.248141\pi\)
\(174\) 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 \(-0.616141\pi\)
−0.356825 + 0.934171i \(0.616141\pi\)
\(180\) −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
\(190\) 8.90495 + 3.96255i 0.646033 + 0.287474i
\(191\) 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 \(-0.729956\pi\)
0.750203 + 0.661207i \(0.229956\pi\)
\(194\) 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 −0.475308 0.879819i \(-0.657663\pi\)
0.879819 + 0.475308i \(0.157663\pi\)
\(198\) −4.01921 + 4.01921i −0.285633 + 0.285633i
\(199\) 3.89894i 0.276389i 0.990405 + 0.138194i \(0.0441299\pi\)
−0.990405 + 0.138194i \(0.955870\pi\)
\(200\) −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 \(-0.894486\pi\)
0.325445 + 0.945561i \(0.394486\pi\)
\(224\) 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 \(-0.289531\pi\)
−0.789251 + 0.614071i \(0.789531\pi\)
\(228\) −4.03490 1.64913i −0.267217 0.109216i
\(229\) 4.94601i 0.326841i 0.986556 + 0.163421i \(0.0522528\pi\)
−0.986556 + 0.163421i \(0.947747\pi\)
\(230\) 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 −0.977871 0.209210i \(-0.932911\pi\)
−0.209210 0.977871i \(-0.567089\pi\)
\(234\) 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 \(-0.927485\pi\)
0.974163 0.225846i \(-0.0725147\pi\)
\(240\) 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
\(247\) 9.14747 22.3810i 0.582039 1.42407i
\(248\) −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 \(-0.374783\pi\)
−0.923619 + 0.383313i \(0.874783\pi\)
\(258\) −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 0.899819 0.436264i \(-0.143699\pi\)
−0.436264 + 0.899819i \(0.643699\pi\)
\(264\) 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 \(-0.713432\pi\)
−0.621391 + 0.783500i \(0.713432\pi\)
\(270\) −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 −0.00844603 0.999964i \(-0.502688\pi\)
0.999964 + 0.00844603i \(0.00268849\pi\)
\(278\) −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 0.379946 0.925009i \(-0.375943\pi\)
−0.925009 + 0.379946i \(0.875943\pi\)
\(284\) −6.51556 −0.386628
\(285\) 3.96255 8.90495i 0.234721 0.527484i
\(286\) 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 \(-0.588983\pi\)
0.961180 + 0.275921i \(0.0889827\pi\)
\(294\) 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 \(-0.151889\pi\)
−0.459269 + 0.888297i \(0.651889\pi\)
\(308\) 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 0.569460 0.822019i \(-0.307152\pi\)
−0.822019 + 0.569460i \(0.807152\pi\)
\(314\) 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 0.988128 + 0.153632i \(0.0490971\pi\)
0.153632 + 0.988128i \(0.450903\pi\)
\(318\) −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
\(323\) −11.6391 + 28.4773i −0.647619 + 1.58452i
\(324\) 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 \(-0.301826\pi\)
−0.812375 + 0.583135i \(0.801826\pi\)
\(338\) 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
\(342\) −1.64913 + 4.03490i −0.0891746 + 0.218182i
\(343\) −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 −0.0131194 + 0.999914i \(0.504176\pi\)
−0.999914 + 0.0131194i \(0.995824\pi\)
\(348\) 2.85986 + 2.85986i 0.153305 + 0.153305i
\(349\) 3.34923i 0.179280i −0.995974 0.0896401i \(-0.971428\pi\)
0.995974 0.0896401i \(-0.0285717\pi\)
\(350\) −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 0.983876 + 0.178852i \(0.0572382\pi\)
0.178852 + 0.983876i \(0.442762\pi\)
\(354\) 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 \(-0.956005\pi\)
0.990464 0.137775i \(-0.0439950\pi\)
\(360\) −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 −0.602770 0.797915i \(-0.705936\pi\)
0.797915 + 0.602770i \(0.205936\pi\)
\(368\) −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 \(-0.540915\pi\)
0.991750 + 0.128185i \(0.0409150\pi\)
\(374\) −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 \(-0.321184\pi\)
0.532683 + 0.846315i \(0.321184\pi\)
\(380\) 3.49481 + 9.09870i 0.179280 + 0.466753i
\(381\) 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 \(-0.761079\pi\)
0.682071 + 0.731286i \(0.261079\pi\)
\(384\) 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 \(0.393810\pi\)
−0.327452 + 0.944868i \(0.606190\pi\)
\(390\) 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 −0.401117 0.916027i \(-0.631378\pi\)
0.916027 + 0.401117i \(0.131378\pi\)
\(398\) −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 \(-0.467620\pi\)
0.101549 + 0.994831i \(0.467620\pi\)
\(410\) 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
\(418\) 22.9344 + 9.37367i 1.12176 + 0.458481i
\(419\) 11.2890i 0.551504i 0.961229 + 0.275752i \(0.0889268\pi\)
−0.961229 + 0.275752i \(0.911073\pi\)
\(420\) 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 −0.0229344 + 0.999737i \(0.507301\pi\)
−0.999737 + 0.0229344i \(0.992699\pi\)
\(434\) 12.3914i 0.594806i
\(435\) −6.58798 + 6.19570i −0.315869 + 0.297061i
\(436\) 5.95528i 0.285206i
\(437\) −24.5572 10.0369i −1.17473 0.480131i
\(438\) −2.07682 2.07682i −0.0992345 0.0992345i
\(439\) −27.9747 −1.33516 −0.667580 0.744538i \(-0.732670\pi\)
−0.667580 + 0.744538i \(0.732670\pi\)
\(440\) −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 0.363554 0.931573i \(-0.381563\pi\)
−0.931573 + 0.363554i \(0.881563\pi\)
\(444\) 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 \(-0.493996\pi\)
0.0188602 + 0.999822i \(0.493996\pi\)
\(450\) 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 −0.997945 0.0640788i \(-0.979589\pi\)
0.0640788 + 0.997945i \(0.479589\pi\)
\(458\) −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 0.944342 0.328965i \(-0.106700\pi\)
−0.328965 + 0.944342i \(0.606700\pi\)
\(464\) −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 −0.118115 0.993000i \(-0.537685\pi\)
0.993000 + 0.118115i \(0.0376852\pi\)
\(468\) −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
\(475\) −20.5754 + 7.18692i −0.944065 + 0.329759i
\(476\) −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 \(0.0481413\pi\)
−0.988585 + 0.150665i \(0.951859\pi\)
\(480\) 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 \(-0.212920\pi\)
−0.620129 + 0.784499i \(0.712920\pi\)
\(488\) 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 \(-0.899107\pi\)
0.950186 0.311684i \(-0.100893\pi\)
\(500\) 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 0.985033 0.172365i \(-0.0551408\pi\)
−0.172365 + 0.985033i \(0.555141\pi\)
\(504\) −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 \(-0.254030\pi\)
0.698097 + 0.716003i \(0.254030\pi\)
\(510\) −11.4963 + 10.8118i −0.509066 + 0.478754i
\(511\) 8.99859 0.398074
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 4.03490 + 1.64913i 0.178145 + 0.0728107i
\(514\) 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 0.445544 0.895260i \(-0.353010\pi\)
0.895260 0.445544i \(-0.146990\pi\)
\(524\) 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
\(532\) 12.3621 + 5.05259i 0.535965 + 0.219058i
\(533\) −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 0.982450 + 0.186527i \(0.0597231\pi\)
0.186527 + 0.982450i \(0.440277\pi\)
\(548\) −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 0.356350 0.934353i \(-0.384021\pi\)
0.934353 0.356350i \(-0.115979\pi\)
\(558\) 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 \(-0.657396\pi\)
0.880218 + 0.474570i \(0.157396\pi\)
\(564\) 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 \(-0.413038\pi\)
0.269814 + 0.962913i \(0.413038\pi\)
\(570\) 9.09870 3.49481i 0.381103 0.146381i
\(571\) 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 −0.978200 0.207667i \(-0.933413\pi\)
0.207667 + 0.978200i \(0.433413\pi\)
\(578\) 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 0.0734236 0.997301i \(-0.476607\pi\)
0.997301 0.0734236i \(-0.0233925\pi\)
\(588\) 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 0.807516 0.589845i \(-0.200811\pi\)
−0.589845 + 0.807516i \(0.700811\pi\)
\(594\) 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 \(-0.554792\pi\)
−0.171287 + 0.985221i \(0.554792\pi\)
\(600\) −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 \(-0.353972\pi\)
−0.896601 + 0.442838i \(0.853972\pi\)
\(608\) 4.03490 + 1.64913i 0.163637 + 0.0668809i
\(609\) 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 0.990917 + 0.134477i \(0.0429355\pi\)
0.134477 + 0.990917i \(0.457065\pi\)
\(614\) 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 −0.877808 0.479012i \(-0.840995\pi\)
0.479012 + 0.877808i \(0.340995\pi\)
\(618\) −13.0842 + 13.0842i −0.526322 + 0.526322i
\(619\) 13.1404i 0.528156i 0.964501 + 0.264078i \(0.0850676\pi\)
−0.964501 + 0.264078i \(0.914932\pi\)
\(620\) 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
\(627\) 9.37367 22.9344i 0.374348 0.915913i
\(628\) 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 0.658805 0.752314i \(-0.271062\pi\)
−0.752314 + 0.658805i \(0.771062\pi\)
\(644\) 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 −0.727834 0.685753i \(-0.759473\pi\)
0.685753 + 0.727834i \(0.259473\pi\)
\(648\) 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 0.284723 0.958610i \(-0.408099\pi\)
−0.958610 + 0.284723i \(0.908099\pi\)
\(654\) 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 \(-0.273606\pi\)
0.652773 + 0.757554i \(0.273606\pi\)
\(660\) 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
\(665\) −12.1405 + 27.2830i −0.470787 + 1.05799i
\(666\) −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 \(-0.642428\pi\)
0.901553 + 0.432668i \(0.142428\pi\)
\(674\) 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 −0.997443 0.0714633i \(-0.977233\pi\)
−0.0714633 0.997443i \(-0.522767\pi\)
\(678\) 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 \(-0.903833\pi\)
0.297543 + 0.954709i \(0.403833\pi\)
\(684\) −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
\(703\) 35.3747 + 14.4582i 1.33418 + 0.545302i
\(704\) 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 \(0.149758\pi\)
−0.891351 + 0.453313i \(0.850242\pi\)
\(710\) 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 \(-0.924066\pi\)
0.971681 0.236298i \(-0.0759340\pi\)
\(720\) 0.0685835 2.23502i 0.00255596 0.0832941i
\(721\) 56.6919i 2.11132i
\(722\) 18.9992 0.178653i 0.707076 0.00664878i
\(723\) 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 −0.440719 0.897645i \(-0.645276\pi\)
0.897645 + 0.440719i \(0.145276\pi\)
\(728\) 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 0.679853 0.733348i \(-0.262044\pi\)
−0.733348 + 0.679853i \(0.762044\pi\)
\(734\) 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 \(0.0508412\pi\)
−0.987271 + 0.159044i \(0.949159\pi\)
\(740\) −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 \(-0.909223\pi\)
0.281333 + 0.959610i \(0.409223\pi\)
\(744\) −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 −0.938154 0.346217i \(-0.887466\pi\)
0.346217 + 0.938154i \(0.387466\pi\)
\(758\) 14.6657 + 14.6657i 0.532683 + 0.532683i
\(759\) −34.5941 −1.25569
\(760\) −3.96255 + 8.90495i −0.143737 + 0.323017i
\(761\) 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 \(-0.993506\pi\)
0.999792 0.0203986i \(-0.00649352\pi\)
\(770\) −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 \(-0.801602\pi\)
0.583707 + 0.811964i \(0.301602\pi\)
\(774\) −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
\(779\) −10.7779