Properties

Label 570.2.m.a.37.3
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 37.3
Root \(-1.75036 + 1.75036i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.a.493.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.253765 - 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 - 2.47539i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.253765 - 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 - 2.47539i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.75036 + 1.39149i) q^{10} +2.74367 q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.20178 + 1.20178i) q^{13} +3.50073 q^{14} +(-1.39149 + 1.75036i) q^{15} -1.00000 q^{16} +(-4.87121 - 4.87121i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-1.94007 + 3.90335i) q^{19} +(-2.22162 + 0.253765i) q^{20} +3.50073i q^{21} +(-1.94007 + 1.94007i) q^{22} +(0.0321428 - 0.0321428i) q^{23} -1.00000i q^{24} +(-4.87121 + 1.12754i) q^{25} -1.69957 q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.47539 + 2.47539i) q^{28} -6.50952 q^{29} +(-0.253765 - 2.22162i) q^{30} +6.50952i q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.94007 - 1.94007i) q^{33} +6.88893 q^{34} +(-4.87121 + 6.12754i) q^{35} +1.00000 q^{36} +(-4.58998 + 4.58998i) q^{37} +(-1.38825 - 4.13192i) q^{38} -1.69957i q^{39} +(1.39149 - 1.75036i) q^{40} -5.96665i q^{41} +(-2.47539 - 2.47539i) q^{42} +(5.39582 - 5.39582i) q^{43} -2.74367i q^{44} +(2.22162 - 0.253765i) q^{45} +0.0454567i q^{46} +(3.66743 + 3.66743i) q^{47} +(0.707107 + 0.707107i) q^{48} +5.25508i q^{49} +(2.64717 - 4.24175i) q^{50} +6.88893i q^{51} +(1.20178 - 1.20178i) q^{52} +(-8.97544 - 8.97544i) q^{53} +1.00000i q^{54} +(-0.696246 - 6.09540i) q^{55} -3.50073i q^{56} +(4.13192 - 1.38825i) q^{57} +(4.60292 - 4.60292i) q^{58} -4.42301 q^{59} +(1.75036 + 1.39149i) q^{60} -2.95077 q^{61} +(-4.60292 - 4.60292i) q^{62} +(2.47539 - 2.47539i) q^{63} +1.00000i q^{64} +(2.36493 - 2.97487i) q^{65} +2.74367 q^{66} +(-7.00145 + 7.00145i) q^{67} +(-4.87121 + 4.87121i) q^{68} -0.0454567 q^{69} +(-0.888360 - 7.77729i) q^{70} -5.56594i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-2.19205 + 2.19205i) q^{73} -6.49122i q^{74} +(4.24175 + 2.64717i) q^{75} +(3.90335 + 1.94007i) q^{76} +(-6.79164 - 6.79164i) q^{77} +(1.20178 + 1.20178i) q^{78} +0.225823 q^{79} +(0.253765 + 2.22162i) q^{80} -1.00000 q^{81} +(4.21906 + 4.21906i) q^{82} +(-3.87246 + 3.87246i) q^{83} +3.50073 q^{84} +(-9.58584 + 12.0581i) q^{85} +7.63084i q^{86} +(4.60292 + 4.60292i) q^{87} +(1.94007 + 1.94007i) q^{88} +9.13628 q^{89} +(-1.39149 + 1.75036i) q^{90} -5.94974i q^{91} +(-0.0321428 - 0.0321428i) q^{92} +(4.60292 - 4.60292i) q^{93} -5.18653 q^{94} +(9.16409 + 3.31956i) q^{95} -1.00000 q^{96} +(8.76663 - 8.76663i) q^{97} +(-3.71590 - 3.71590i) q^{98} +2.74367i 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
\(5\) −0.253765 2.22162i −0.113487 0.993539i
\(6\) 1.00000 0.408248
\(7\) −2.47539 2.47539i −0.935608 0.935608i 0.0624406 0.998049i \(-0.480112\pi\)
−0.998049 + 0.0624406i \(0.980112\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.75036 + 1.39149i 0.553513 + 0.440026i
\(11\) 2.74367 0.827247 0.413624 0.910448i \(-0.364263\pi\)
0.413624 + 0.910448i \(0.364263\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 1.20178 + 1.20178i 0.333314 + 0.333314i 0.853844 0.520530i \(-0.174265\pi\)
−0.520530 + 0.853844i \(0.674265\pi\)
\(14\) 3.50073 0.935608
\(15\) −1.39149 + 1.75036i −0.359280 + 0.451942i
\(16\) −1.00000 −0.250000
\(17\) −4.87121 4.87121i −1.18144 1.18144i −0.979371 0.202070i \(-0.935233\pi\)
−0.202070 0.979371i \(-0.564767\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −1.94007 + 3.90335i −0.445082 + 0.895490i
\(20\) −2.22162 + 0.253765i −0.496770 + 0.0567435i
\(21\) 3.50073i 0.763921i
\(22\) −1.94007 + 1.94007i −0.413624 + 0.413624i
\(23\) 0.0321428 0.0321428i 0.00670223 0.00670223i −0.703748 0.710450i \(-0.748491\pi\)
0.710450 + 0.703748i \(0.248491\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −4.87121 + 1.12754i −0.974241 + 0.225508i
\(26\) −1.69957 −0.333314
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −2.47539 + 2.47539i −0.467804 + 0.467804i
\(29\) −6.50952 −1.20879 −0.604394 0.796686i \(-0.706585\pi\)
−0.604394 + 0.796686i \(0.706585\pi\)
\(30\) −0.253765 2.22162i −0.0463309 0.405611i
\(31\) 6.50952i 1.16914i 0.811342 + 0.584572i \(0.198738\pi\)
−0.811342 + 0.584572i \(0.801262\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −1.94007 1.94007i −0.337722 0.337722i
\(34\) 6.88893 1.18144
\(35\) −4.87121 + 6.12754i −0.823384 + 1.03574i
\(36\) 1.00000 0.166667
\(37\) −4.58998 + 4.58998i −0.754589 + 0.754589i −0.975332 0.220743i \(-0.929152\pi\)
0.220743 + 0.975332i \(0.429152\pi\)
\(38\) −1.38825 4.13192i −0.225204 0.670286i
\(39\) 1.69957i 0.272150i
\(40\) 1.39149 1.75036i 0.220013 0.276757i
\(41\) 5.96665i 0.931833i −0.884829 0.465917i \(-0.845725\pi\)
0.884829 0.465917i \(-0.154275\pi\)
\(42\) −2.47539 2.47539i −0.381960 0.381960i
\(43\) 5.39582 5.39582i 0.822855 0.822855i −0.163662 0.986517i \(-0.552331\pi\)
0.986517 + 0.163662i \(0.0523305\pi\)
\(44\) 2.74367i 0.413624i
\(45\) 2.22162 0.253765i 0.331180 0.0378290i
\(46\) 0.0454567i 0.00670223i
\(47\) 3.66743 + 3.66743i 0.534950 + 0.534950i 0.922041 0.387091i \(-0.126520\pi\)
−0.387091 + 0.922041i \(0.626520\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 5.25508i 0.750725i
\(50\) 2.64717 4.24175i 0.374367 0.599875i
\(51\) 6.88893i 0.964643i
\(52\) 1.20178 1.20178i 0.166657 0.166657i
\(53\) −8.97544 8.97544i −1.23287 1.23287i −0.962856 0.270015i \(-0.912971\pi\)
−0.270015 0.962856i \(-0.587029\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −0.696246 6.09540i −0.0938818 0.821903i
\(56\) 3.50073i 0.467804i
\(57\) 4.13192 1.38825i 0.547286 0.183878i
\(58\) 4.60292 4.60292i 0.604394 0.604394i
\(59\) −4.42301 −0.575826 −0.287913 0.957657i \(-0.592961\pi\)
−0.287913 + 0.957657i \(0.592961\pi\)
\(60\) 1.75036 + 1.39149i 0.225971 + 0.179640i
\(61\) −2.95077 −0.377808 −0.188904 0.981996i \(-0.560493\pi\)
−0.188904 + 0.981996i \(0.560493\pi\)
\(62\) −4.60292 4.60292i −0.584572 0.584572i
\(63\) 2.47539 2.47539i 0.311869 0.311869i
\(64\) 1.00000i 0.125000i
\(65\) 2.36493 2.97487i 0.293334 0.368987i
\(66\) 2.74367 0.337722
\(67\) −7.00145 + 7.00145i −0.855363 + 0.855363i −0.990788 0.135424i \(-0.956760\pi\)
0.135424 + 0.990788i \(0.456760\pi\)
\(68\) −4.87121 + 4.87121i −0.590721 + 0.590721i
\(69\) −0.0454567 −0.00547235
\(70\) −0.888360 7.77729i −0.106179 0.929564i
\(71\) 5.56594i 0.660556i −0.943884 0.330278i \(-0.892858\pi\)
0.943884 0.330278i \(-0.107142\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −2.19205 + 2.19205i −0.256560 + 0.256560i −0.823653 0.567094i \(-0.808068\pi\)
0.567094 + 0.823653i \(0.308068\pi\)
\(74\) 6.49122i 0.754589i
\(75\) 4.24175 + 2.64717i 0.489795 + 0.305669i
\(76\) 3.90335 + 1.94007i 0.447745 + 0.222541i
\(77\) −6.79164 6.79164i −0.773979 0.773979i
\(78\) 1.20178 + 1.20178i 0.136075 + 0.136075i
\(79\) 0.225823 0.0254070 0.0127035 0.999919i \(-0.495956\pi\)
0.0127035 + 0.999919i \(0.495956\pi\)
\(80\) 0.253765 + 2.22162i 0.0283717 + 0.248385i
\(81\) −1.00000 −0.111111
\(82\) 4.21906 + 4.21906i 0.465917 + 0.465917i
\(83\) −3.87246 + 3.87246i −0.425058 + 0.425058i −0.886941 0.461883i \(-0.847174\pi\)
0.461883 + 0.886941i \(0.347174\pi\)
\(84\) 3.50073 0.381960
\(85\) −9.58584 + 12.0581i −1.03973 + 1.30789i
\(86\) 7.63084i 0.822855i
\(87\) 4.60292 + 4.60292i 0.493485 + 0.493485i
\(88\) 1.94007 + 1.94007i 0.206812 + 0.206812i
\(89\) 9.13628 0.968444 0.484222 0.874945i \(-0.339103\pi\)
0.484222 + 0.874945i \(0.339103\pi\)
\(90\) −1.39149 + 1.75036i −0.146675 + 0.184504i
\(91\) 5.94974i 0.623703i
\(92\) −0.0321428 0.0321428i −0.00335112 0.00335112i
\(93\) 4.60292 4.60292i 0.477301 0.477301i
\(94\) −5.18653 −0.534950
\(95\) 9.16409 + 3.31956i 0.940216 + 0.340580i
\(96\) −1.00000 −0.102062
\(97\) 8.76663 8.76663i 0.890117 0.890117i −0.104417 0.994534i \(-0.533298\pi\)
0.994534 + 0.104417i \(0.0332976\pi\)
\(98\) −3.71590 3.71590i −0.375363 0.375363i
\(99\) 2.74367i 0.275749i
\(100\) 1.12754 + 4.87121i 0.112754 + 0.487121i
\(101\) 11.2650 1.12091 0.560455 0.828185i \(-0.310626\pi\)
0.560455 + 0.828185i \(0.310626\pi\)
\(102\) −4.87121 4.87121i −0.482321 0.482321i
\(103\) −0.762447 0.762447i −0.0751262 0.0751262i 0.668545 0.743671i \(-0.266917\pi\)
−0.743671 + 0.668545i \(0.766917\pi\)
\(104\) 1.69957i 0.166657i
\(105\) 7.77729 0.888360i 0.758986 0.0866951i
\(106\) 12.6932 1.23287
\(107\) 13.5351 13.5351i 1.30849 1.30849i 0.385985 0.922505i \(-0.373861\pi\)
0.922505 0.385985i \(-0.126139\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 4.37207 0.418768 0.209384 0.977833i \(-0.432854\pi\)
0.209384 + 0.977833i \(0.432854\pi\)
\(110\) 4.80242 + 3.81777i 0.457892 + 0.364011i
\(111\) 6.49122 0.616119
\(112\) 2.47539 + 2.47539i 0.233902 + 0.233902i
\(113\) −6.95599 6.95599i −0.654365 0.654365i 0.299676 0.954041i \(-0.403121\pi\)
−0.954041 + 0.299676i \(0.903121\pi\)
\(114\) −1.94007 + 3.90335i −0.181704 + 0.365582i
\(115\) −0.0795658 0.0632524i −0.00741955 0.00589832i
\(116\) 6.50952i 0.604394i
\(117\) −1.20178 + 1.20178i −0.111105 + 0.111105i
\(118\) 3.12754 3.12754i 0.287913 0.287913i
\(119\) 24.1162i 2.21073i
\(120\) −2.22162 + 0.253765i −0.202805 + 0.0231654i
\(121\) −3.47228 −0.315662
\(122\) 2.08651 2.08651i 0.188904 0.188904i
\(123\) −4.21906 + 4.21906i −0.380419 + 0.380419i
\(124\) 6.50952 0.584572
\(125\) 3.74110 + 10.5359i 0.334614 + 0.942355i
\(126\) 3.50073i 0.311869i
\(127\) −13.7136 + 13.7136i −1.21689 + 1.21689i −0.248173 + 0.968716i \(0.579830\pi\)
−0.968716 + 0.248173i \(0.920170\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −7.63084 −0.671858
\(130\) 0.431292 + 3.77581i 0.0378268 + 0.331161i
\(131\) 8.01380 0.700169 0.350085 0.936718i \(-0.386153\pi\)
0.350085 + 0.936718i \(0.386153\pi\)
\(132\) −1.94007 + 1.94007i −0.168861 + 0.168861i
\(133\) 14.4647 4.85988i 1.25425 0.421405i
\(134\) 9.90155i 0.855363i
\(135\) −1.75036 1.39149i −0.150647 0.119760i
\(136\) 6.88893i 0.590721i
\(137\) −12.6299 12.6299i −1.07905 1.07905i −0.996595 0.0824532i \(-0.973725\pi\)
−0.0824532 0.996595i \(-0.526275\pi\)
\(138\) 0.0321428 0.0321428i 0.00273617 0.00273617i
\(139\) 10.3499i 0.877869i −0.898519 0.438934i \(-0.855356\pi\)
0.898519 0.438934i \(-0.144644\pi\)
\(140\) 6.12754 + 4.87121i 0.517871 + 0.411692i
\(141\) 5.18653i 0.436785i
\(142\) 3.93571 + 3.93571i 0.330278 + 0.330278i
\(143\) 3.29729 + 3.29729i 0.275733 + 0.275733i
\(144\) 1.00000i 0.0833333i
\(145\) 1.65189 + 14.4617i 0.137182 + 1.20098i
\(146\) 3.10002i 0.256560i
\(147\) 3.71590 3.71590i 0.306482 0.306482i
\(148\) 4.58998 + 4.58998i 0.377294 + 0.377294i
\(149\) 9.07466i 0.743425i 0.928348 + 0.371712i \(0.121229\pi\)
−0.928348 + 0.371712i \(0.878771\pi\)
\(150\) −4.87121 + 1.12754i −0.397732 + 0.0920631i
\(151\) 1.75287i 0.142647i 0.997453 + 0.0713234i \(0.0227222\pi\)
−0.997453 + 0.0713234i \(0.977278\pi\)
\(152\) −4.13192 + 1.38825i −0.335143 + 0.112602i
\(153\) 4.87121 4.87121i 0.393814 0.393814i
\(154\) 9.60483 0.773979
\(155\) 14.4617 1.65189i 1.16159 0.132683i
\(156\) −1.69957 −0.136075
\(157\) 7.20733 + 7.20733i 0.575207 + 0.575207i 0.933579 0.358372i \(-0.116668\pi\)
−0.358372 + 0.933579i \(0.616668\pi\)
\(158\) −0.159681 + 0.159681i −0.0127035 + 0.0127035i
\(159\) 12.6932i 1.00664i
\(160\) −1.75036 1.39149i −0.138378 0.110007i
\(161\) −0.159132 −0.0125413
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 9.60292 9.60292i 0.752159 0.752159i −0.222723 0.974882i \(-0.571494\pi\)
0.974882 + 0.222723i \(0.0714945\pi\)
\(164\) −5.96665 −0.465917
\(165\) −3.81777 + 4.80242i −0.297213 + 0.373868i
\(166\) 5.47649i 0.425058i
\(167\) −12.9013 + 12.9013i −0.998336 + 0.998336i −0.999999 0.00166271i \(-0.999471\pi\)
0.00166271 + 0.999999i \(0.499471\pi\)
\(168\) −2.47539 + 2.47539i −0.190980 + 0.190980i
\(169\) 10.1114i 0.777804i
\(170\) −1.74817 15.3046i −0.134078 1.17381i
\(171\) −3.90335 1.94007i −0.298497 0.148361i
\(172\) −5.39582 5.39582i −0.411427 0.411427i
\(173\) −0.271593 0.271593i −0.0206488 0.0206488i 0.696707 0.717356i \(-0.254648\pi\)
−0.717356 + 0.696707i \(0.754648\pi\)
\(174\) −6.50952 −0.493485
\(175\) 14.8492 + 9.26703i 1.12249 + 0.700521i
\(176\) −2.74367 −0.206812
\(177\) 3.12754 + 3.12754i 0.235080 + 0.235080i
\(178\) −6.46033 + 6.46033i −0.484222 + 0.484222i
\(179\) −16.1543 −1.20743 −0.603715 0.797200i \(-0.706314\pi\)
−0.603715 + 0.797200i \(0.706314\pi\)
\(180\) −0.253765 2.22162i −0.0189145 0.165590i
\(181\) 16.1980i 1.20399i −0.798501 0.601994i \(-0.794373\pi\)
0.798501 0.601994i \(-0.205627\pi\)
\(182\) 4.20710 + 4.20710i 0.311851 + 0.311851i
\(183\) 2.08651 + 2.08651i 0.154239 + 0.154239i
\(184\) 0.0454567 0.00335112
\(185\) 11.3620 + 9.03243i 0.835349 + 0.664078i
\(186\) 6.50952i 0.477301i
\(187\) −13.3650 13.3650i −0.977344 0.977344i
\(188\) 3.66743 3.66743i 0.267475 0.267475i
\(189\) −3.50073 −0.254640
\(190\) −8.82727 + 4.13270i −0.640398 + 0.299818i
\(191\) 14.6162 1.05759 0.528795 0.848750i \(-0.322644\pi\)
0.528795 + 0.848750i \(0.322644\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −6.20432 6.20432i −0.446597 0.446597i 0.447625 0.894221i \(-0.352270\pi\)
−0.894221 + 0.447625i \(0.852270\pi\)
\(194\) 12.3979i 0.890117i
\(195\) −3.77581 + 0.431292i −0.270392 + 0.0308855i
\(196\) 5.25508 0.375363
\(197\) −9.77456 9.77456i −0.696408 0.696408i 0.267226 0.963634i \(-0.413893\pi\)
−0.963634 + 0.267226i \(0.913893\pi\)
\(198\) −1.94007 1.94007i −0.137875 0.137875i
\(199\) 7.77253i 0.550980i −0.961304 0.275490i \(-0.911160\pi\)
0.961304 0.275490i \(-0.0888401\pi\)
\(200\) −4.24175 2.64717i −0.299937 0.187183i
\(201\) 9.90155 0.698401
\(202\) −7.96556 + 7.96556i −0.560455 + 0.560455i
\(203\) 16.1136 + 16.1136i 1.13095 + 1.13095i
\(204\) 6.88893 0.482321
\(205\) −13.2556 + 1.51412i −0.925813 + 0.105751i
\(206\) 1.07826 0.0751262
\(207\) 0.0321428 + 0.0321428i 0.00223408 + 0.00223408i
\(208\) −1.20178 1.20178i −0.0833285 0.0833285i
\(209\) −5.32290 + 10.7095i −0.368193 + 0.740792i
\(210\) −4.87121 + 6.12754i −0.336145 + 0.422840i
\(211\) 7.91902i 0.545168i −0.962132 0.272584i \(-0.912122\pi\)
0.962132 0.272584i \(-0.0878783\pi\)
\(212\) −8.97544 + 8.97544i −0.616436 + 0.616436i
\(213\) −3.93571 + 3.93571i −0.269671 + 0.269671i
\(214\) 19.1416i 1.30849i
\(215\) −13.3567 10.6182i −0.910922 0.724156i
\(216\) 1.00000 0.0680414
\(217\) 16.1136 16.1136i 1.09386 1.09386i
\(218\) −3.09152 + 3.09152i −0.209384 + 0.209384i
\(219\) 3.10002 0.209480
\(220\) −6.09540 + 0.696246i −0.410951 + 0.0469409i
\(221\) 11.7082i 0.787582i
\(222\) −4.58998 + 4.58998i −0.308059 + 0.308059i
\(223\) 14.3643 + 14.3643i 0.961907 + 0.961907i 0.999301 0.0373940i \(-0.0119057\pi\)
−0.0373940 + 0.999301i \(0.511906\pi\)
\(224\) −3.50073 −0.233902
\(225\) −1.12754 4.87121i −0.0751692 0.324747i
\(226\) 9.83726 0.654365
\(227\) 15.0385 15.0385i 0.998139 0.998139i −0.00185921 0.999998i \(-0.500592\pi\)
0.999998 + 0.00185921i \(0.000591804\pi\)
\(228\) −1.38825 4.13192i −0.0919391 0.273643i
\(229\) 2.69570i 0.178137i −0.996026 0.0890683i \(-0.971611\pi\)
0.996026 0.0890683i \(-0.0283890\pi\)
\(230\) 0.100988 0.0115353i 0.00665893 0.000760616i
\(231\) 9.60483i 0.631951i
\(232\) −4.60292 4.60292i −0.302197 0.302197i
\(233\) −12.4775 + 12.4775i −0.817426 + 0.817426i −0.985734 0.168309i \(-0.946169\pi\)
0.168309 + 0.985734i \(0.446169\pi\)
\(234\) 1.69957i 0.111105i
\(235\) 7.21698 9.07831i 0.470784 0.592204i
\(236\) 4.42301i 0.287913i
\(237\) −0.159681 0.159681i −0.0103724 0.0103724i
\(238\) −17.0528 17.0528i −1.10537 1.10537i
\(239\) 27.2150i 1.76039i −0.474613 0.880195i \(-0.657412\pi\)
0.474613 0.880195i \(-0.342588\pi\)
\(240\) 1.39149 1.75036i 0.0898200 0.112985i
\(241\) 25.1111i 1.61755i −0.588120 0.808774i \(-0.700132\pi\)
0.588120 0.808774i \(-0.299868\pi\)
\(242\) 2.45527 2.45527i 0.157831 0.157831i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 2.95077i 0.188904i
\(245\) 11.6748 1.33355i 0.745875 0.0851975i
\(246\) 5.96665i 0.380419i
\(247\) −7.02251 + 2.35944i −0.446831 + 0.150127i
\(248\) −4.60292 + 4.60292i −0.292286 + 0.292286i
\(249\) 5.47649 0.347058
\(250\) −10.0953 4.80461i −0.638485 0.303870i
\(251\) −2.30195 −0.145298 −0.0726489 0.997358i \(-0.523145\pi\)
−0.0726489 + 0.997358i \(0.523145\pi\)
\(252\) −2.47539 2.47539i −0.155935 0.155935i
\(253\) 0.0881891 0.0881891i 0.00554440 0.00554440i
\(254\) 19.3940i 1.21689i
\(255\) 15.3046 1.74817i 0.958411 0.109474i
\(256\) 1.00000 0.0625000
\(257\) −15.7752 + 15.7752i −0.984032 + 0.984032i −0.999874 0.0158429i \(-0.994957\pi\)
0.0158429 + 0.999874i \(0.494957\pi\)
\(258\) 5.39582 5.39582i 0.335929 0.335929i
\(259\) 22.7240 1.41200
\(260\) −2.97487 2.36493i −0.184494 0.146667i
\(261\) 6.50952i 0.402929i
\(262\) −5.66661 + 5.66661i −0.350085 + 0.350085i
\(263\) −1.21906 + 1.21906i −0.0751702 + 0.0751702i −0.743692 0.668522i \(-0.766927\pi\)
0.668522 + 0.743692i \(0.266927\pi\)
\(264\) 2.74367i 0.168861i
\(265\) −17.6624 + 22.2177i −1.08499 + 1.36482i
\(266\) −6.79164 + 13.6646i −0.416422 + 0.837828i
\(267\) −6.46033 6.46033i −0.395366 0.395366i
\(268\) 7.00145 + 7.00145i 0.427682 + 0.427682i
\(269\) 7.58430 0.462423 0.231211 0.972904i \(-0.425731\pi\)
0.231211 + 0.972904i \(0.425731\pi\)
\(270\) 2.22162 0.253765i 0.135204 0.0154436i
\(271\) −25.6741 −1.55959 −0.779795 0.626036i \(-0.784676\pi\)
−0.779795 + 0.626036i \(0.784676\pi\)
\(272\) 4.87121 + 4.87121i 0.295360 + 0.295360i
\(273\) −4.20710 + 4.20710i −0.254626 + 0.254626i
\(274\) 17.8614 1.07905
\(275\) −13.3650 + 3.09359i −0.805939 + 0.186551i
\(276\) 0.0454567i 0.00273617i
\(277\) −21.7414 21.7414i −1.30631 1.30631i −0.924056 0.382257i \(-0.875147\pi\)
−0.382257 0.924056i \(-0.624853\pi\)
\(278\) 7.31850 + 7.31850i 0.438934 + 0.438934i
\(279\) −6.50952 −0.389715
\(280\) −7.77729 + 0.888360i −0.464782 + 0.0530897i
\(281\) 21.9050i 1.30674i −0.757037 0.653372i \(-0.773354\pi\)
0.757037 0.653372i \(-0.226646\pi\)
\(282\) 3.66743 + 3.66743i 0.218392 + 0.218392i
\(283\) 15.7217 15.7217i 0.934557 0.934557i −0.0634298 0.997986i \(-0.520204\pi\)
0.997986 + 0.0634298i \(0.0202039\pi\)
\(284\) −5.56594 −0.330278
\(285\) −4.13270 8.82727i −0.244800 0.522883i
\(286\) −4.66307 −0.275733
\(287\) −14.7698 + 14.7698i −0.871831 + 0.871831i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 30.4573i 1.79161i
\(290\) −11.3940 9.05790i −0.669080 0.531898i
\(291\) −12.3979 −0.726777
\(292\) 2.19205 + 2.19205i 0.128280 + 0.128280i
\(293\) 8.25768 + 8.25768i 0.482419 + 0.482419i 0.905903 0.423484i \(-0.139193\pi\)
−0.423484 + 0.905903i \(0.639193\pi\)
\(294\) 5.25508i 0.306482i
\(295\) 1.12240 + 9.82625i 0.0653488 + 0.572106i
\(296\) −6.49122 −0.377294
\(297\) 1.94007 1.94007i 0.112574 0.112574i
\(298\) −6.41675 6.41675i −0.371712 0.371712i
\(299\) 0.0772571 0.00446790
\(300\) 2.64717 4.24175i 0.152835 0.244898i
\(301\) −26.7135 −1.53974
\(302\) −1.23947 1.23947i −0.0713234 0.0713234i
\(303\) −7.96556 7.96556i −0.457609 0.457609i
\(304\) 1.94007 3.90335i 0.111270 0.223872i
\(305\) 0.748802 + 6.55550i 0.0428763 + 0.375367i
\(306\) 6.88893i 0.393814i
\(307\) 22.1239 22.1239i 1.26268 1.26268i 0.312887 0.949790i \(-0.398704\pi\)
0.949790 0.312887i \(-0.101296\pi\)
\(308\) −6.79164 + 6.79164i −0.386990 + 0.386990i
\(309\) 1.07826i 0.0613403i
\(310\) −9.05790 + 11.3940i −0.514454 + 0.647137i
\(311\) 3.22108 0.182651 0.0913254 0.995821i \(-0.470890\pi\)
0.0913254 + 0.995821i \(0.470890\pi\)
\(312\) 1.20178 1.20178i 0.0680374 0.0680374i
\(313\) −14.9801 + 14.9801i −0.846724 + 0.846724i −0.989723 0.142999i \(-0.954326\pi\)
0.142999 + 0.989723i \(0.454326\pi\)
\(314\) −10.1927 −0.575207
\(315\) −6.12754 4.87121i −0.345248 0.274461i
\(316\) 0.225823i 0.0127035i
\(317\) 13.3317 13.3317i 0.748782 0.748782i −0.225468 0.974251i \(-0.572391\pi\)
0.974251 + 0.225468i \(0.0723911\pi\)
\(318\) −8.97544 8.97544i −0.503318 0.503318i
\(319\) −17.8600 −0.999966
\(320\) 2.22162 0.253765i 0.124192 0.0141859i
\(321\) −19.1416 −1.06838
\(322\) 0.112523 0.112523i 0.00627066 0.00627066i
\(323\) 28.4645 9.56356i 1.58381 0.532131i
\(324\) 1.00000i 0.0555556i
\(325\) −7.20918 4.49907i −0.399893 0.249563i
\(326\) 13.5806i 0.752159i
\(327\) −3.09152 3.09152i −0.170961 0.170961i
\(328\) 4.21906 4.21906i 0.232958 0.232958i
\(329\) 18.1566i 1.00101i
\(330\) −0.696246 6.09540i −0.0383271 0.335540i
\(331\) 6.73163i 0.370004i 0.982738 + 0.185002i \(0.0592292\pi\)
−0.982738 + 0.185002i \(0.940771\pi\)
\(332\) 3.87246 + 3.87246i 0.212529 + 0.212529i
\(333\) −4.58998 4.58998i −0.251530 0.251530i
\(334\) 18.2453i 0.998336i
\(335\) 17.3313 + 13.7779i 0.946910 + 0.752765i
\(336\) 3.50073i 0.190980i
\(337\) −14.1501 + 14.1501i −0.770806 + 0.770806i −0.978247 0.207441i \(-0.933486\pi\)
0.207441 + 0.978247i \(0.433486\pi\)
\(338\) 7.14987 + 7.14987i 0.388902 + 0.388902i
\(339\) 9.83726i 0.534287i
\(340\) 12.0581 + 9.58584i 0.653943 + 0.519865i
\(341\) 17.8600i 0.967171i
\(342\) 4.13192 1.38825i 0.223429 0.0750680i
\(343\) −4.31936 + 4.31936i −0.233224 + 0.233224i
\(344\) 7.63084 0.411427
\(345\) 0.0115353 + 0.100988i 0.000621040 + 0.00543700i
\(346\) 0.384091 0.0206488
\(347\) 6.84109 + 6.84109i 0.367249 + 0.367249i 0.866473 0.499224i \(-0.166382\pi\)
−0.499224 + 0.866473i \(0.666382\pi\)
\(348\) 4.60292 4.60292i 0.246743 0.246743i
\(349\) 33.2298i 1.77875i −0.457181 0.889374i \(-0.651141\pi\)
0.457181 0.889374i \(-0.348859\pi\)
\(350\) −17.0528 + 3.94720i −0.911508 + 0.210987i
\(351\) 1.69957 0.0907166
\(352\) 1.94007 1.94007i 0.103406 0.103406i
\(353\) 25.3639 25.3639i 1.34999 1.34999i 0.464318 0.885668i \(-0.346299\pi\)
0.885668 0.464318i \(-0.153701\pi\)
\(354\) −4.42301 −0.235080
\(355\) −12.3654 + 1.41244i −0.656288 + 0.0749645i
\(356\) 9.13628i 0.484222i
\(357\) 17.0528 17.0528i 0.902528 0.902528i
\(358\) 11.4228 11.4228i 0.603715 0.603715i
\(359\) 9.12994i 0.481860i 0.970543 + 0.240930i \(0.0774524\pi\)
−0.970543 + 0.240930i \(0.922548\pi\)
\(360\) 1.75036 + 1.39149i 0.0922522 + 0.0733377i
\(361\) −11.4723 15.1455i −0.603804 0.797133i
\(362\) 11.4537 + 11.4537i 0.601994 + 0.601994i
\(363\) 2.45527 + 2.45527i 0.128868 + 0.128868i
\(364\) −5.94974 −0.311851
\(365\) 5.42616 + 4.31363i 0.284018 + 0.225786i
\(366\) −2.95077 −0.154239
\(367\) 12.9778 + 12.9778i 0.677435 + 0.677435i 0.959419 0.281984i \(-0.0909926\pi\)
−0.281984 + 0.959419i \(0.590993\pi\)
\(368\) −0.0321428 + 0.0321428i −0.00167556 + 0.00167556i
\(369\) 5.96665 0.310611
\(370\) −14.4210 + 1.64724i −0.749713 + 0.0856360i
\(371\) 44.4354i 2.30697i
\(372\) −4.60292 4.60292i −0.238651 0.238651i
\(373\) −6.92570 6.92570i −0.358599 0.358599i 0.504697 0.863296i \(-0.331604\pi\)
−0.863296 + 0.504697i \(0.831604\pi\)
\(374\) 18.9009 0.977344
\(375\) 4.80461 10.0953i 0.248109 0.521321i
\(376\) 5.18653i 0.267475i
\(377\) −7.82301 7.82301i −0.402906 0.402906i
\(378\) 2.47539 2.47539i 0.127320 0.127320i
\(379\) −22.4882 −1.15514 −0.577570 0.816341i \(-0.695999\pi\)
−0.577570 + 0.816341i \(0.695999\pi\)
\(380\) 3.31956 9.16409i 0.170290 0.470108i
\(381\) 19.3940 0.993586
\(382\) −10.3352 + 10.3352i −0.528795 + 0.528795i
\(383\) −14.9680 14.9680i −0.764830 0.764830i 0.212361 0.977191i \(-0.431885\pi\)
−0.977191 + 0.212361i \(0.931885\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −13.3650 + 16.8119i −0.681142 + 0.856816i
\(386\) 8.77423 0.446597
\(387\) 5.39582 + 5.39582i 0.274285 + 0.274285i
\(388\) −8.76663 8.76663i −0.445058 0.445058i
\(389\) 10.1897i 0.516639i 0.966060 + 0.258319i \(0.0831687\pi\)
−0.966060 + 0.258319i \(0.916831\pi\)
\(390\) 2.36493 2.97487i 0.119753 0.150638i
\(391\) −0.313148 −0.0158366
\(392\) −3.71590 + 3.71590i −0.187681 + 0.187681i
\(393\) −5.66661 5.66661i −0.285843 0.285843i
\(394\) 13.8233 0.696408
\(395\) −0.0573058 0.501693i −0.00288337 0.0252429i
\(396\) 2.74367 0.137875
\(397\) 14.9493 + 14.9493i 0.750284 + 0.750284i 0.974532 0.224248i \(-0.0719927\pi\)
−0.224248 + 0.974532i \(0.571993\pi\)
\(398\) 5.49601 + 5.49601i 0.275490 + 0.275490i
\(399\) −13.6646 6.79164i −0.684083 0.340007i
\(400\) 4.87121 1.12754i 0.243560 0.0563769i
\(401\) 17.1894i 0.858400i −0.903210 0.429200i \(-0.858796\pi\)
0.903210 0.429200i \(-0.141204\pi\)
\(402\) −7.00145 + 7.00145i −0.349201 + 0.349201i
\(403\) −7.82301 + 7.82301i −0.389692 + 0.389692i
\(404\) 11.2650i 0.560455i
\(405\) 0.253765 + 2.22162i 0.0126097 + 0.110393i
\(406\) −22.7880 −1.13095
\(407\) −12.5934 + 12.5934i −0.624231 + 0.624231i
\(408\) −4.87121 + 4.87121i −0.241161 + 0.241161i
\(409\) 23.9489 1.18420 0.592099 0.805865i \(-0.298299\pi\)
0.592099 + 0.805865i \(0.298299\pi\)
\(410\) 8.30250 10.4438i 0.410031 0.515782i
\(411\) 17.8614i 0.881039i
\(412\) −0.762447 + 0.762447i −0.0375631 + 0.0375631i
\(413\) 10.9487 + 10.9487i 0.538748 + 0.538748i
\(414\) −0.0454567 −0.00223408
\(415\) 9.58584 + 7.62045i 0.470550 + 0.374073i
\(416\) 1.69957 0.0833285
\(417\) −7.31850 + 7.31850i −0.358388 + 0.358388i
\(418\) −3.80890 11.3366i −0.186299 0.554492i
\(419\) 21.4134i 1.04611i −0.852298 0.523056i \(-0.824792\pi\)
0.852298 0.523056i \(-0.175208\pi\)
\(420\) −0.888360 7.77729i −0.0433475 0.379493i
\(421\) 1.72609i 0.0841246i 0.999115 + 0.0420623i \(0.0133928\pi\)
−0.999115 + 0.0420623i \(0.986607\pi\)
\(422\) 5.59960 + 5.59960i 0.272584 + 0.272584i
\(423\) −3.66743 + 3.66743i −0.178317 + 0.178317i
\(424\) 12.6932i 0.616436i
\(425\) 29.2211 + 18.2362i 1.41743 + 0.884585i
\(426\) 5.56594i 0.269671i
\(427\) 7.30430 + 7.30430i 0.353480 + 0.353480i
\(428\) −13.5351 13.5351i −0.654245 0.654245i
\(429\) 4.66307i 0.225135i
\(430\) 16.9528 1.93644i 0.817539 0.0933833i
\(431\) 29.5770i 1.42467i 0.701838 + 0.712337i \(0.252363\pi\)
−0.701838 + 0.712337i \(0.747637\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 18.7711 + 18.7711i 0.902081 + 0.902081i 0.995616 0.0935354i \(-0.0298168\pi\)
−0.0935354 + 0.995616i \(0.529817\pi\)
\(434\) 22.7880i 1.09386i
\(435\) 9.05790 11.3940i 0.434293 0.546301i
\(436\) 4.37207i 0.209384i
\(437\) 0.0631054 + 0.187824i 0.00301874 + 0.00898482i
\(438\) −2.19205 + 2.19205i −0.104740 + 0.104740i
\(439\) −8.66125 −0.413379 −0.206690 0.978407i \(-0.566269\pi\)
−0.206690 + 0.978407i \(0.566269\pi\)
\(440\) 3.81777 4.80242i 0.182005 0.228946i
\(441\) −5.25508 −0.250242
\(442\) 8.27898 + 8.27898i 0.393791 + 0.393791i
\(443\) −19.5669 + 19.5669i −0.929652 + 0.929652i −0.997683 0.0680315i \(-0.978328\pi\)
0.0680315 + 0.997683i \(0.478328\pi\)
\(444\) 6.49122i 0.308059i
\(445\) −2.31847 20.2974i −0.109906 0.962187i
\(446\) −20.3142 −0.961907
\(447\) 6.41675 6.41675i 0.303502 0.303502i
\(448\) 2.47539 2.47539i 0.116951 0.116951i
\(449\) −21.3429 −1.00724 −0.503618 0.863927i \(-0.667998\pi\)
−0.503618 + 0.863927i \(0.667998\pi\)
\(450\) 4.24175 + 2.64717i 0.199958 + 0.124789i
\(451\) 16.3705i 0.770857i
\(452\) −6.95599 + 6.95599i −0.327182 + 0.327182i
\(453\) 1.23947 1.23947i 0.0582353 0.0582353i
\(454\) 21.2676i 0.998139i
\(455\) −13.2181 + 1.50983i −0.619673 + 0.0707821i
\(456\) 3.90335 + 1.94007i 0.182791 + 0.0908520i
\(457\) 21.3371 + 21.3371i 0.998110 + 0.998110i 0.999998 0.00188859i \(-0.000601157\pi\)
−0.00188859 + 0.999998i \(0.500601\pi\)
\(458\) 1.90615 + 1.90615i 0.0890683 + 0.0890683i
\(459\) −6.88893 −0.321548
\(460\) −0.0632524 + 0.0795658i −0.00294916 + 0.00370977i
\(461\) 0.603474 0.0281066 0.0140533 0.999901i \(-0.495527\pi\)
0.0140533 + 0.999901i \(0.495527\pi\)
\(462\) −6.79164 6.79164i −0.315976 0.315976i
\(463\) −13.8679 + 13.8679i −0.644495 + 0.644495i −0.951657 0.307162i \(-0.900621\pi\)
0.307162 + 0.951657i \(0.400621\pi\)
\(464\) 6.50952 0.302197
\(465\) −11.3940 9.05790i −0.528385 0.420050i
\(466\) 17.6458i 0.817426i
\(467\) 5.10843 + 5.10843i 0.236390 + 0.236390i 0.815353 0.578964i \(-0.196543\pi\)
−0.578964 + 0.815353i \(0.696543\pi\)
\(468\) 1.20178 + 1.20178i 0.0555523 + 0.0555523i
\(469\) 34.6626 1.60057
\(470\) 1.31616 + 11.5225i 0.0607098 + 0.531494i
\(471\) 10.1927i 0.469655i
\(472\) −3.12754 3.12754i −0.143957 0.143957i
\(473\) 14.8043 14.8043i 0.680705 0.680705i
\(474\) 0.225823 0.0103724
\(475\) 5.04929 21.2015i 0.231677 0.972793i
\(476\) 24.1162 1.10537
\(477\) 8.97544 8.97544i 0.410957 0.410957i
\(478\) 19.2439 + 19.2439i 0.880195 + 0.880195i
\(479\) 0.676761i 0.0309220i 0.999880 + 0.0154610i \(0.00492158\pi\)
−0.999880 + 0.0154610i \(0.995078\pi\)
\(480\) 0.253765 + 2.22162i 0.0115827 + 0.101403i
\(481\) −11.0323 −0.503030
\(482\) 17.7562 + 17.7562i 0.808774 + 0.808774i
\(483\) 0.112523 + 0.112523i 0.00511997 + 0.00511997i
\(484\) 3.47228i 0.157831i
\(485\) −21.7008 17.2515i −0.985383 0.783350i
\(486\) −1.00000 −0.0453609
\(487\) 2.31334 2.31334i 0.104828 0.104828i −0.652748 0.757575i \(-0.726384\pi\)
0.757575 + 0.652748i \(0.226384\pi\)
\(488\) −2.08651 2.08651i −0.0944519 0.0944519i
\(489\) −13.5806 −0.614135
\(490\) −7.31236 + 9.19829i −0.330339 + 0.415536i
\(491\) −0.0138034 −0.000622939 −0.000311469 1.00000i \(-0.500099\pi\)
−0.000311469 1.00000i \(0.500099\pi\)
\(492\) 4.21906 + 4.21906i 0.190210 + 0.190210i
\(493\) 31.7092 + 31.7092i 1.42811 + 1.42811i
\(494\) 3.29729 6.63403i 0.148352 0.298479i
\(495\) 6.09540 0.696246i 0.273968 0.0312939i
\(496\) 6.50952i 0.292286i
\(497\) −13.7779 + 13.7779i −0.618021 + 0.618021i
\(498\) −3.87246 + 3.87246i −0.173529 + 0.173529i
\(499\) 19.0461i 0.852619i 0.904577 + 0.426309i \(0.140187\pi\)
−0.904577 + 0.426309i \(0.859813\pi\)
\(500\) 10.5359 3.74110i 0.471178 0.167307i
\(501\) 18.2453 0.815138
\(502\) 1.62772 1.62772i 0.0726489 0.0726489i
\(503\) −15.5475 + 15.5475i −0.693230 + 0.693230i −0.962941 0.269711i \(-0.913072\pi\)
0.269711 + 0.962941i \(0.413072\pi\)
\(504\) 3.50073 0.155935
\(505\) −2.85866 25.0266i −0.127209 1.11367i
\(506\) 0.124718i 0.00554440i
\(507\) −7.14987 + 7.14987i −0.317537 + 0.317537i
\(508\) 13.7136 + 13.7136i 0.608444 + 0.608444i
\(509\) −4.08859 −0.181224 −0.0906118 0.995886i \(-0.528882\pi\)
−0.0906118 + 0.995886i \(0.528882\pi\)
\(510\) −9.58584 + 12.0581i −0.424468 + 0.533943i
\(511\) 10.8523 0.480078
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 1.38825 + 4.13192i 0.0612928 + 0.182429i
\(514\) 22.3095i 0.984032i
\(515\) −1.50039 + 1.88735i −0.0661150 + 0.0831667i
\(516\) 7.63084i 0.335929i
\(517\) 10.0622 + 10.0622i 0.442536 + 0.442536i
\(518\) −16.0683 + 16.0683i −0.705999 + 0.705999i
\(519\) 0.384091i 0.0168597i
\(520\) 3.77581 0.431292i 0.165580 0.0189134i
\(521\) 29.8730i 1.30876i 0.756166 + 0.654380i \(0.227070\pi\)
−0.756166 + 0.654380i \(0.772930\pi\)
\(522\) 4.60292 + 4.60292i 0.201465 + 0.201465i
\(523\) 20.1935 + 20.1935i 0.883001 + 0.883001i 0.993839 0.110837i \(-0.0353532\pi\)
−0.110837 + 0.993839i \(0.535353\pi\)
\(524\) 8.01380i 0.350085i
\(525\) −3.94720 17.0528i −0.172270 0.744243i
\(526\) 1.72400i 0.0751702i
\(527\) 31.7092 31.7092i 1.38127 1.38127i
\(528\) 1.94007 + 1.94007i 0.0844306 + 0.0844306i
\(529\) 22.9979i 0.999910i
\(530\) −3.22108 28.1995i −0.139915 1.22491i
\(531\) 4.42301i 0.191942i
\(532\) −4.85988 14.4647i −0.210703 0.627125i
\(533\) 7.17060 7.17060i 0.310593 0.310593i
\(534\) 9.13628 0.395366
\(535\) −33.5047 26.6352i −1.44853 1.15154i
\(536\) −9.90155 −0.427682
\(537\) 11.4228 + 11.4228i 0.492932 + 0.492932i
\(538\) −5.36291 + 5.36291i −0.231211 + 0.231211i
\(539\) 14.4182i 0.621035i
\(540\) −1.39149 + 1.75036i −0.0598800 + 0.0753236i
\(541\) −25.3583 −1.09024 −0.545120 0.838358i \(-0.683516\pi\)
−0.545120 + 0.838358i \(0.683516\pi\)
\(542\) 18.1543 18.1543i 0.779795 0.779795i
\(543\) −11.4537 + 11.4537i −0.491526 + 0.491526i
\(544\) −6.88893 −0.295360
\(545\) −1.10948 9.71308i −0.0475247 0.416063i
\(546\) 5.94974i 0.254626i
\(547\) 13.3457 13.3457i 0.570622 0.570622i −0.361680 0.932302i \(-0.617797\pi\)
0.932302 + 0.361680i \(0.117797\pi\)
\(548\) −12.6299 + 12.6299i −0.539524 + 0.539524i
\(549\) 2.95077i 0.125936i
\(550\) 7.26297 11.6380i 0.309694 0.496245i
\(551\) 12.6289 25.4089i 0.538009 1.08246i
\(552\) −0.0321428 0.0321428i −0.00136809 0.00136809i
\(553\) −0.558998 0.558998i −0.0237710 0.0237710i
\(554\) 30.7470 1.30631
\(555\) −1.64724 14.4210i −0.0699215 0.612138i
\(556\) −10.3499 −0.438934
\(557\) −8.05867 8.05867i −0.341457 0.341457i 0.515458 0.856915i \(-0.327622\pi\)
−0.856915 + 0.515458i \(0.827622\pi\)
\(558\) 4.60292 4.60292i 0.194857 0.194857i
\(559\) 12.9692 0.548538
\(560\) 4.87121 6.12754i 0.205846 0.258936i
\(561\) 18.9009i 0.797998i
\(562\) 15.4892 + 15.4892i 0.653372 + 0.653372i
\(563\) −28.6648 28.6648i −1.20808 1.20808i −0.971648 0.236430i \(-0.924022\pi\)
−0.236430 0.971648i \(-0.575978\pi\)
\(564\) −5.18653 −0.218392
\(565\) −13.6884 + 17.2188i −0.575875 + 0.724399i
\(566\) 22.2338i 0.934557i
\(567\) 2.47539 + 2.47539i 0.103956 + 0.103956i
\(568\) 3.93571 3.93571i 0.165139 0.165139i
\(569\) 8.54540 0.358242 0.179121 0.983827i \(-0.442675\pi\)
0.179121 + 0.983827i \(0.442675\pi\)
\(570\) 9.16409 + 3.31956i 0.383841 + 0.139041i
\(571\) 45.4169 1.90064 0.950320 0.311275i \(-0.100756\pi\)
0.950320 + 0.311275i \(0.100756\pi\)
\(572\) 3.29729 3.29729i 0.137867 0.137867i
\(573\) −10.3352 10.3352i −0.431759 0.431759i
\(574\) 20.8876i 0.871831i
\(575\) −0.120332 + 0.192816i −0.00501819 + 0.00804100i
\(576\) −1.00000 −0.0416667
\(577\) 12.1650 + 12.1650i 0.506437 + 0.506437i 0.913431 0.406994i \(-0.133423\pi\)
−0.406994 + 0.913431i \(0.633423\pi\)
\(578\) −21.5366 21.5366i −0.895803 0.895803i
\(579\) 8.77423i 0.364645i
\(580\) 14.4617 1.65189i 0.600489 0.0685908i
\(581\) 19.1717 0.795375
\(582\) 8.76663 8.76663i 0.363389 0.363389i
\(583\) −24.6256 24.6256i −1.01989 1.01989i
\(584\) −3.10002 −0.128280
\(585\) 2.97487 + 2.36493i 0.122996 + 0.0977779i
\(586\) −11.6781 −0.482419
\(587\) −5.32968 5.32968i −0.219980 0.219980i 0.588510 0.808490i \(-0.299715\pi\)
−0.808490 + 0.588510i \(0.799715\pi\)
\(588\) −3.71590 3.71590i −0.153241 0.153241i
\(589\) −25.4089 12.6289i −1.04696 0.520365i
\(590\) −7.74186 6.15455i −0.318728 0.253379i
\(591\) 13.8233i 0.568615i
\(592\) 4.58998 4.58998i 0.188647 0.188647i
\(593\) −1.80818 + 1.80818i −0.0742529 + 0.0742529i −0.743258 0.669005i \(-0.766720\pi\)
0.669005 + 0.743258i \(0.266720\pi\)
\(594\) 2.74367i 0.112574i
\(595\) 53.5772 6.11985i 2.19645 0.250889i
\(596\) 9.07466 0.371712
\(597\) −5.49601 + 5.49601i −0.224937 + 0.224937i
\(598\) −0.0546290 + 0.0546290i −0.00223395 + 0.00223395i
\(599\) −25.3131 −1.03426 −0.517132 0.855906i \(-0.673000\pi\)
−0.517132 + 0.855906i \(0.673000\pi\)
\(600\) 1.12754 + 4.87121i 0.0460315 + 0.198866i
\(601\) 18.5367i 0.756126i −0.925780 0.378063i \(-0.876590\pi\)
0.925780 0.378063i \(-0.123410\pi\)
\(602\) 18.8893 18.8893i 0.769870 0.769870i
\(603\) −7.00145 7.00145i −0.285121 0.285121i
\(604\) 1.75287 0.0713234
\(605\) 0.881142 + 7.71409i 0.0358235 + 0.313622i
\(606\) 11.2650 0.457609
\(607\) 11.5164 11.5164i 0.467435 0.467435i −0.433647 0.901083i \(-0.642774\pi\)
0.901083 + 0.433647i \(0.142774\pi\)
\(608\) 1.38825 + 4.13192i 0.0563010 + 0.167571i
\(609\) 22.7880i 0.923418i
\(610\) −5.16492 4.10596i −0.209122 0.166245i
\(611\) 8.81490i 0.356613i
\(612\) −4.87121 4.87121i −0.196907 0.196907i
\(613\) −7.66890 + 7.66890i −0.309744 + 0.309744i −0.844810 0.535066i \(-0.820287\pi\)
0.535066 + 0.844810i \(0.320287\pi\)
\(614\) 31.2879i 1.26268i
\(615\) 10.4438 + 8.30250i 0.421134 + 0.334789i
\(616\) 9.60483i 0.386990i
\(617\) 33.2792 + 33.2792i 1.33977 + 1.33977i 0.896278 + 0.443492i \(0.146260\pi\)
0.443492 + 0.896278i \(0.353740\pi\)
\(618\) −0.762447 0.762447i −0.0306701 0.0306701i
\(619\) 3.87513i 0.155755i −0.996963 0.0778774i \(-0.975186\pi\)
0.996963 0.0778774i \(-0.0248143\pi\)
\(620\) −1.65189 14.4617i −0.0663413 0.580795i
\(621\) 0.0454567i 0.00182412i
\(622\) −2.27765 + 2.27765i −0.0913254 + 0.0913254i
\(623\) −22.6158 22.6158i −0.906084 0.906084i
\(624\) 1.69957i 0.0680374i
\(625\) 22.4573 10.9849i 0.898293 0.439398i
\(626\) 21.1850i 0.846724i
\(627\) 11.3366 3.80890i 0.452741 0.152113i
\(628\) 7.20733 7.20733i 0.287604 0.287604i
\(629\) 44.7175 1.78300
\(630\) 7.77729 0.888360i 0.309855 0.0353931i
\(631\) 1.80965 0.0720412 0.0360206 0.999351i \(-0.488532\pi\)
0.0360206 + 0.999351i \(0.488532\pi\)
\(632\) 0.159681 + 0.159681i 0.00635176 + 0.00635176i
\(633\) −5.59960 + 5.59960i −0.222564 + 0.222564i
\(634\) 18.8539i 0.748782i
\(635\) 33.9466 + 26.9865i 1.34713 + 1.07093i
\(636\) 12.6932 0.503318
\(637\) −6.31545 + 6.31545i −0.250227 + 0.250227i
\(638\) 12.6289 12.6289i 0.499983 0.499983i
\(639\) 5.56594 0.220185
\(640\) −1.39149 + 1.75036i −0.0550033 + 0.0691892i
\(641\) 6.61503i 0.261278i −0.991430 0.130639i \(-0.958297\pi\)
0.991430 0.130639i \(-0.0417029\pi\)
\(642\) 13.5351 13.5351i 0.534189 0.534189i
\(643\) −30.3608 + 30.3608i −1.19731 + 1.19731i −0.222347 + 0.974968i \(0.571372\pi\)
−0.974968 + 0.222347i \(0.928628\pi\)
\(644\) 0.159132i 0.00627066i
\(645\) 1.93644 + 16.9528i 0.0762472 + 0.667518i
\(646\) −13.3650 + 26.8899i −0.525838 + 1.05797i
\(647\) 5.83884 + 5.83884i 0.229549 + 0.229549i 0.812504 0.582956i \(-0.198104\pi\)
−0.582956 + 0.812504i \(0.698104\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −12.1353 −0.476351
\(650\) 8.27898 1.91633i 0.324728 0.0751648i
\(651\) −22.7880 −0.893133
\(652\) −9.60292 9.60292i −0.376080 0.376080i
\(653\) −19.7797 + 19.7797i −0.774039 + 0.774039i −0.978810 0.204771i \(-0.934355\pi\)
0.204771 + 0.978810i \(0.434355\pi\)
\(654\) 4.37207 0.170961
\(655\) −2.03362 17.8036i −0.0794601 0.695646i
\(656\) 5.96665i 0.232958i
\(657\) −2.19205 2.19205i −0.0855198 0.0855198i
\(658\) 12.8387 + 12.8387i 0.500503 + 0.500503i
\(659\) −8.44761 −0.329072 −0.164536 0.986371i \(-0.552613\pi\)
−0.164536 + 0.986371i \(0.552613\pi\)
\(660\) 4.80242 + 3.81777i 0.186934 + 0.148607i
\(661\) 23.8283i 0.926814i −0.886146 0.463407i \(-0.846627\pi\)
0.886146 0.463407i \(-0.153373\pi\)
\(662\) −4.75998 4.75998i −0.185002 0.185002i
\(663\) −8.27898 + 8.27898i −0.321529 + 0.321529i
\(664\) −5.47649 −0.212529
\(665\) −14.4675 30.9019i −0.561024 1.19832i
\(666\) 6.49122 0.251530
\(667\) −0.209234 + 0.209234i −0.00810157 + 0.00810157i
\(668\) 12.9013 + 12.9013i 0.499168 + 0.499168i
\(669\) 20.3142i 0.785393i
\(670\) −21.9975 + 2.51266i −0.849837 + 0.0970726i
\(671\) −8.09594 −0.312540
\(672\) 2.47539 + 2.47539i 0.0954901 + 0.0954901i
\(673\) 31.9422 + 31.9422i 1.23128 + 1.23128i 0.963471 + 0.267812i \(0.0863005\pi\)
0.267812 + 0.963471i \(0.413700\pi\)
\(674\) 20.0113i 0.770806i
\(675\) −2.64717 + 4.24175i −0.101890 + 0.163265i
\(676\) −10.1114 −0.388902
\(677\) 11.7115 11.7115i 0.450111 0.450111i −0.445280 0.895391i \(-0.646896\pi\)
0.895391 + 0.445280i \(0.146896\pi\)
\(678\) −6.95599 6.95599i −0.267143 0.267143i
\(679\) −43.4016 −1.66560
\(680\) −15.3046 + 1.74817i −0.586904 + 0.0670391i
\(681\) −21.2676 −0.814977
\(682\) −12.6289 12.6289i −0.483586 0.483586i
\(683\) 3.55375 + 3.55375i 0.135981 + 0.135981i 0.771821 0.635840i \(-0.219346\pi\)
−0.635840 + 0.771821i \(0.719346\pi\)
\(684\) −1.94007 + 3.90335i −0.0741803 + 0.149248i
\(685\) −24.8539 + 31.2640i −0.949619 + 1.19453i
\(686\) 6.10850i 0.233224i
\(687\) −1.90615 + 1.90615i −0.0727240 + 0.0727240i
\(688\) −5.39582 + 5.39582i −0.205714 + 0.205714i
\(689\) 21.5730i 0.821867i
\(690\) −0.0795658 0.0632524i −0.00302902 0.00240798i
\(691\) 9.74241 0.370619 0.185309 0.982680i \(-0.440671\pi\)
0.185309 + 0.982680i \(0.440671\pi\)
\(692\) −0.271593 + 0.271593i −0.0103244 + 0.0103244i
\(693\) 6.79164 6.79164i 0.257993 0.257993i
\(694\) −9.67476 −0.367249
\(695\) −22.9936 + 2.62644i −0.872197 + 0.0996267i
\(696\) 6.50952i 0.246743i
\(697\) −29.0648 + 29.0648i −1.10091 + 1.10091i
\(698\) 23.4970 + 23.4970i 0.889374 + 0.889374i
\(699\) 17.6458 0.667425
\(700\) 9.26703 14.8492i 0.350261 0.561247i
\(701\) −10.3224 −0.389873 −0.194936 0.980816i \(-0.562450\pi\)
−0.194936 + 0.980816i \(0.562450\pi\)
\(702\) −1.20178 + 1.20178i −0.0453583 + 0.0453583i
\(703\) −9.01143 26.8212i −0.339873 1.01158i
\(704\) 2.74367i 0.103406i
\(705\) −11.5225 + 1.31616i −0.433963 + 0.0495694i
\(706\) 35.8700i 1.34999i
\(707\) −27.8852 27.8852i −1.04873 1.04873i
\(708\) 3.12754 3.12754i 0.117540 0.117540i
\(709\) 10.3223i 0.387663i −0.981035 0.193831i \(-0.937909\pi\)
0.981035 0.193831i \(-0.0620915\pi\)
\(710\) 7.74492 9.74241i 0.290662 0.365626i
\(711\) 0.225823i 0.00846901i
\(712\) 6.46033 + 6.46033i 0.242111 + 0.242111i
\(713\) 0.209234 + 0.209234i 0.00783587 + 0.00783587i
\(714\) 24.1162i 0.902528i
\(715\) 6.48859 8.16206i 0.242660 0.305244i
\(716\) 16.1543i 0.603715i
\(717\) −19.2439 + 19.2439i −0.718676 + 0.718676i
\(718\) −6.45584 6.45584i −0.240930 0.240930i
\(719\) 34.9029i 1.30166i 0.759224 + 0.650830i \(0.225579\pi\)
−0.759224 + 0.650830i \(0.774421\pi\)
\(720\) −2.22162 + 0.253765i −0.0827950 + 0.00945725i
\(721\) 3.77470i 0.140577i
\(722\) 18.8216 + 2.59737i 0.700468 + 0.0966642i
\(723\) −17.7562 + 17.7562i −0.660361 + 0.660361i
\(724\) −16.1980 −0.601994
\(725\) 31.7092 7.33973i 1.17765 0.272591i
\(726\) −3.47228 −0.128868
\(727\) 12.8595 + 12.8595i 0.476932 + 0.476932i 0.904149 0.427217i \(-0.140506\pi\)
−0.427217 + 0.904149i \(0.640506\pi\)
\(728\) 4.20710 4.20710i 0.155926 0.155926i
\(729\) 1.00000i 0.0370370i
\(730\) −6.88707 + 0.786675i −0.254902 + 0.0291162i
\(731\) −52.5683 −1.94431
\(732\) 2.08651 2.08651i 0.0771197 0.0771197i
\(733\) 11.1047 11.1047i 0.410162 0.410162i −0.471633 0.881795i \(-0.656335\pi\)
0.881795 + 0.471633i \(0.156335\pi\)
\(734\) −18.3534 −0.677435
\(735\) −9.19829 7.31236i −0.339284 0.269720i
\(736\) 0.0454567i 0.00167556i
\(737\) −19.2097 + 19.2097i −0.707597 + 0.707597i
\(738\) −4.21906 + 4.21906i −0.155306 + 0.155306i
\(739\) 18.1001i 0.665823i −0.942958 0.332911i \(-0.891969\pi\)
0.942958 0.332911i \(-0.108031\pi\)
\(740\) 9.03243 11.3620i 0.332039 0.417675i
\(741\) 6.63403 + 3.29729i 0.243707 + 0.121129i
\(742\) −31.4205 31.4205i −1.15348 1.15348i
\(743\) −26.9208 26.9208i −0.987630 0.987630i 0.0122949 0.999924i \(-0.496086\pi\)
−0.999924 + 0.0122949i \(0.996086\pi\)
\(744\) 6.50952 0.238651
\(745\) 20.1605 2.30283i 0.738622 0.0843690i
\(746\) 9.79442 0.358599
\(747\) −3.87246 3.87246i −0.141686 0.141686i
\(748\) −13.3650 + 13.3650i −0.488672 + 0.488672i
\(749\) −67.0093 −2.44847
\(750\) 3.74110 + 10.5359i 0.136606 + 0.384715i
\(751\) 9.91849i 0.361931i −0.983489 0.180965i \(-0.942078\pi\)
0.983489 0.180965i \(-0.0579222\pi\)
\(752\) −3.66743 3.66743i −0.133737 0.133737i
\(753\) 1.62772 + 1.62772i 0.0593176 + 0.0593176i
\(754\) 11.0634 0.402906
\(755\) 3.89422 0.444817i 0.141725 0.0161886i
\(756\) 3.50073i 0.127320i
\(757\) 3.01763 + 3.01763i 0.109678 + 0.109678i 0.759816 0.650138i \(-0.225289\pi\)
−0.650138 + 0.759816i \(0.725289\pi\)
\(758\) 15.9015 15.9015i 0.577570 0.577570i
\(759\) −0.124718 −0.00452699
\(760\) 4.13270 + 8.82727i 0.149909 + 0.320199i
\(761\) −11.1416 −0.403881 −0.201941 0.979398i \(-0.564725\pi\)
−0.201941 + 0.979398i \(0.564725\pi\)
\(762\) −13.7136 + 13.7136i −0.496793 + 0.496793i
\(763\) −10.8226 10.8226i −0.391803 0.391803i
\(764\) 14.6162i 0.528795i
\(765\) −12.0581 9.58584i −0.435962 0.346577i
\(766\) 21.1680 0.764830
\(767\) −5.31548 5.31548i −0.191931 0.191931i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 32.8840i 1.18583i 0.805266 + 0.592913i \(0.202022\pi\)
−0.805266 + 0.592913i \(0.797978\pi\)
\(770\) −2.43737 21.3383i −0.0878366 0.768979i
\(771\) 22.3095 0.803458
\(772\) −6.20432 + 6.20432i −0.223298 + 0.223298i
\(773\) 31.2573 + 31.2573i 1.12425 + 1.12425i 0.991096 + 0.133152i \(0.0425098\pi\)
0.133152 + 0.991096i \(0.457490\pi\)
\(774\) −7.63084 −0.274285
\(775\) −7.33973 31.7092i −0.263651 1.13903i
\(776\) 12.3979 0.445058
\(777\) −16.0683 16.0683i −0.576446 0.576446i
\(778\) −7.20521 7.20521i −0.258319 0.258319i