Properties

Label 570.2.i.f.391.1
Level $570$
Weight $2$
Character 570.391
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 570.391
Dual form 570.2.i.f.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.44949 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.44949 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} -3.00000 q^{11} -1.00000 q^{12} +(-2.44949 - 4.24264i) q^{13} +(0.724745 - 1.25529i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.775255 - 1.34278i) q^{17} +1.00000 q^{18} +(-4.17423 - 1.25529i) q^{19} +1.00000 q^{20} +(-0.724745 + 1.25529i) q^{21} +(1.50000 - 2.59808i) q^{22} +(2.94949 + 5.10867i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.89898 q^{26} -1.00000 q^{27} +(0.724745 + 1.25529i) q^{28} +(-4.67423 - 8.09601i) q^{29} -1.00000 q^{30} -0.898979 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(0.775255 + 1.34278i) q^{34} +(0.724745 - 1.25529i) q^{35} +(-0.500000 + 0.866025i) q^{36} -9.89898 q^{37} +(3.17423 - 2.98735i) q^{38} -4.89898 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.17423 + 3.76588i) q^{41} +(-0.724745 - 1.25529i) q^{42} +(5.89898 - 10.2173i) q^{43} +(1.50000 + 2.59808i) q^{44} +1.00000 q^{45} -5.89898 q^{46} +(0.550510 + 0.953512i) q^{47} +(0.500000 + 0.866025i) q^{48} -4.89898 q^{49} +1.00000 q^{50} +(-0.775255 - 1.34278i) q^{51} +(-2.44949 + 4.24264i) q^{52} +(3.72474 + 6.45145i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{55} -1.44949 q^{56} +(-3.17423 + 2.98735i) q^{57} +9.34847 q^{58} +(3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-6.22474 - 10.7816i) q^{61} +(0.449490 - 0.778539i) q^{62} +(0.724745 + 1.25529i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(-1.50000 - 2.59808i) q^{66} +(3.67423 + 6.36396i) q^{67} -1.55051 q^{68} +5.89898 q^{69} +(0.724745 + 1.25529i) q^{70} +(1.67423 - 2.89986i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.22474 + 9.04952i) q^{73} +(4.94949 - 8.57277i) q^{74} -1.00000 q^{75} +(1.00000 + 4.24264i) q^{76} +4.34847 q^{77} +(2.44949 - 4.24264i) q^{78} +(-3.44949 + 5.97469i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.17423 - 3.76588i) q^{82} +11.7980 q^{83} +1.44949 q^{84} +(0.775255 + 1.34278i) q^{85} +(5.89898 + 10.2173i) q^{86} -9.34847 q^{87} -3.00000 q^{88} +(2.72474 + 4.71940i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(3.55051 + 6.14966i) q^{91} +(2.94949 - 5.10867i) q^{92} +(-0.449490 + 0.778539i) q^{93} -1.10102 q^{94} +(3.17423 - 2.98735i) q^{95} -1.00000 q^{96} +(9.22474 - 15.9777i) q^{97} +(2.44949 - 4.24264i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} + 4q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} + 4q^{7} + 4q^{8} - 2q^{9} - 2q^{10} - 12q^{11} - 4q^{12} - 2q^{14} + 2q^{15} - 2q^{16} + 8q^{17} + 4q^{18} - 2q^{19} + 4q^{20} + 2q^{21} + 6q^{22} + 2q^{23} + 2q^{24} - 2q^{25} - 4q^{27} - 2q^{28} - 4q^{29} - 4q^{30} + 16q^{31} - 2q^{32} - 6q^{33} + 8q^{34} - 2q^{35} - 2q^{36} - 20q^{37} - 2q^{38} - 2q^{40} + 6q^{41} + 2q^{42} + 4q^{43} + 6q^{44} + 4q^{45} - 4q^{46} + 12q^{47} + 2q^{48} + 4q^{50} - 8q^{51} + 10q^{53} + 2q^{54} + 6q^{55} + 4q^{56} + 2q^{57} + 8q^{58} + 12q^{59} + 2q^{60} - 20q^{61} - 8q^{62} - 2q^{63} + 4q^{64} - 6q^{66} - 16q^{68} + 4q^{69} - 2q^{70} - 8q^{71} - 2q^{72} - 16q^{73} + 10q^{74} - 4q^{75} + 4q^{76} - 12q^{77} - 4q^{79} - 2q^{80} - 2q^{81} + 6q^{82} + 8q^{83} - 4q^{84} + 8q^{85} + 4q^{86} - 8q^{87} - 12q^{88} + 6q^{89} - 2q^{90} + 24q^{91} + 2q^{92} + 8q^{93} - 24q^{94} - 2q^{95} - 4q^{96} + 32q^{97} + 6q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) −1.44949 −0.547856 −0.273928 0.961750i \(-0.588323\pi\)
−0.273928 + 0.961750i \(0.588323\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.44949 4.24264i −0.679366 1.17670i −0.975172 0.221449i \(-0.928921\pi\)
0.295806 0.955248i \(-0.404412\pi\)
\(14\) 0.724745 1.25529i 0.193696 0.335492i
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.775255 1.34278i 0.188027 0.325672i −0.756565 0.653918i \(-0.773124\pi\)
0.944592 + 0.328246i \(0.106457\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.17423 1.25529i −0.957635 0.287984i
\(20\) 1.00000 0.223607
\(21\) −0.724745 + 1.25529i −0.158152 + 0.273928i
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 2.94949 + 5.10867i 0.615011 + 1.06523i 0.990383 + 0.138356i \(0.0441818\pi\)
−0.375371 + 0.926874i \(0.622485\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 4.89898 0.960769
\(27\) −1.00000 −0.192450
\(28\) 0.724745 + 1.25529i 0.136964 + 0.237228i
\(29\) −4.67423 8.09601i −0.867984 1.50339i −0.864054 0.503399i \(-0.832082\pi\)
−0.00392972 0.999992i \(-0.501251\pi\)
\(30\) −1.00000 −0.182574
\(31\) −0.898979 −0.161461 −0.0807307 0.996736i \(-0.525725\pi\)
−0.0807307 + 0.996736i \(0.525725\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 0.775255 + 1.34278i 0.132955 + 0.230285i
\(35\) 0.724745 1.25529i 0.122504 0.212184i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −9.89898 −1.62738 −0.813691 0.581298i \(-0.802545\pi\)
−0.813691 + 0.581298i \(0.802545\pi\)
\(38\) 3.17423 2.98735i 0.514929 0.484611i
\(39\) −4.89898 −0.784465
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −2.17423 + 3.76588i −0.339558 + 0.588132i −0.984350 0.176226i \(-0.943611\pi\)
0.644791 + 0.764359i \(0.276944\pi\)
\(42\) −0.724745 1.25529i −0.111831 0.193696i
\(43\) 5.89898 10.2173i 0.899586 1.55813i 0.0715617 0.997436i \(-0.477202\pi\)
0.828024 0.560692i \(-0.189465\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 1.00000 0.149071
\(46\) −5.89898 −0.869757
\(47\) 0.550510 + 0.953512i 0.0803002 + 0.139084i 0.903379 0.428843i \(-0.141079\pi\)
−0.823079 + 0.567927i \(0.807745\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −4.89898 −0.699854
\(50\) 1.00000 0.141421
\(51\) −0.775255 1.34278i −0.108557 0.188027i
\(52\) −2.44949 + 4.24264i −0.339683 + 0.588348i
\(53\) 3.72474 + 6.45145i 0.511633 + 0.886174i 0.999909 + 0.0134852i \(0.00429260\pi\)
−0.488276 + 0.872689i \(0.662374\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 1.50000 2.59808i 0.202260 0.350325i
\(56\) −1.44949 −0.193696
\(57\) −3.17423 + 2.98735i −0.420438 + 0.395684i
\(58\) 9.34847 1.22751
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −6.22474 10.7816i −0.796997 1.38044i −0.921563 0.388228i \(-0.873087\pi\)
0.124566 0.992211i \(-0.460246\pi\)
\(62\) 0.449490 0.778539i 0.0570853 0.0988746i
\(63\) 0.724745 + 1.25529i 0.0913093 + 0.158152i
\(64\) 1.00000 0.125000
\(65\) 4.89898 0.607644
\(66\) −1.50000 2.59808i −0.184637 0.319801i
\(67\) 3.67423 + 6.36396i 0.448879 + 0.777482i 0.998313 0.0580554i \(-0.0184900\pi\)
−0.549434 + 0.835537i \(0.685157\pi\)
\(68\) −1.55051 −0.188027
\(69\) 5.89898 0.710154
\(70\) 0.724745 + 1.25529i 0.0866236 + 0.150036i
\(71\) 1.67423 2.89986i 0.198695 0.344150i −0.749410 0.662106i \(-0.769663\pi\)
0.948106 + 0.317956i \(0.102996\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −5.22474 + 9.04952i −0.611510 + 1.05917i 0.379476 + 0.925202i \(0.376104\pi\)
−0.990986 + 0.133965i \(0.957229\pi\)
\(74\) 4.94949 8.57277i 0.575366 0.996564i
\(75\) −1.00000 −0.115470
\(76\) 1.00000 + 4.24264i 0.114708 + 0.486664i
\(77\) 4.34847 0.495554
\(78\) 2.44949 4.24264i 0.277350 0.480384i
\(79\) −3.44949 + 5.97469i −0.388098 + 0.672205i −0.992194 0.124706i \(-0.960201\pi\)
0.604096 + 0.796912i \(0.293534\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.17423 3.76588i −0.240104 0.415872i
\(83\) 11.7980 1.29499 0.647497 0.762068i \(-0.275816\pi\)
0.647497 + 0.762068i \(0.275816\pi\)
\(84\) 1.44949 0.158152
\(85\) 0.775255 + 1.34278i 0.0840882 + 0.145645i
\(86\) 5.89898 + 10.2173i 0.636103 + 1.10176i
\(87\) −9.34847 −1.00226
\(88\) −3.00000 −0.319801
\(89\) 2.72474 + 4.71940i 0.288822 + 0.500255i 0.973529 0.228564i \(-0.0734030\pi\)
−0.684707 + 0.728819i \(0.740070\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) 3.55051 + 6.14966i 0.372195 + 0.644660i
\(92\) 2.94949 5.10867i 0.307506 0.532615i
\(93\) −0.449490 + 0.778539i −0.0466099 + 0.0807307i
\(94\) −1.10102 −0.113562
\(95\) 3.17423 2.98735i 0.325670 0.306495i
\(96\) −1.00000 −0.102062
\(97\) 9.22474 15.9777i 0.936631 1.62229i 0.164931 0.986305i \(-0.447260\pi\)
0.771699 0.635987i \(-0.219407\pi\)
\(98\) 2.44949 4.24264i 0.247436 0.428571i
\(99\) 1.50000 + 2.59808i 0.150756 + 0.261116i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 0.550510 + 0.953512i 0.0547778 + 0.0948780i 0.892114 0.451810i \(-0.149222\pi\)
−0.837336 + 0.546688i \(0.815888\pi\)
\(102\) 1.55051 0.153523
\(103\) 11.2474 1.10824 0.554122 0.832435i \(-0.313054\pi\)
0.554122 + 0.832435i \(0.313054\pi\)
\(104\) −2.44949 4.24264i −0.240192 0.416025i
\(105\) −0.724745 1.25529i −0.0707279 0.122504i
\(106\) −7.44949 −0.723558
\(107\) −2.65153 −0.256333 −0.128167 0.991753i \(-0.540909\pi\)
−0.128167 + 0.991753i \(0.540909\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −0.674235 + 1.16781i −0.0645800 + 0.111856i −0.896508 0.443028i \(-0.853904\pi\)
0.831928 + 0.554884i \(0.187237\pi\)
\(110\) 1.50000 + 2.59808i 0.143019 + 0.247717i
\(111\) −4.94949 + 8.57277i −0.469785 + 0.813691i
\(112\) 0.724745 1.25529i 0.0684820 0.118614i
\(113\) −9.55051 −0.898436 −0.449218 0.893422i \(-0.648297\pi\)
−0.449218 + 0.893422i \(0.648297\pi\)
\(114\) −1.00000 4.24264i −0.0936586 0.397360i
\(115\) −5.89898 −0.550083
\(116\) −4.67423 + 8.09601i −0.433992 + 0.751696i
\(117\) −2.44949 + 4.24264i −0.226455 + 0.392232i
\(118\) 3.00000 + 5.19615i 0.276172 + 0.478345i
\(119\) −1.12372 + 1.94635i −0.103012 + 0.178421i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) −2.00000 −0.181818
\(122\) 12.4495 1.12712
\(123\) 2.17423 + 3.76588i 0.196044 + 0.339558i
\(124\) 0.449490 + 0.778539i 0.0403654 + 0.0699149i
\(125\) 1.00000 0.0894427
\(126\) −1.44949 −0.129131
\(127\) 0.174235 + 0.301783i 0.0154608 + 0.0267789i 0.873652 0.486551i \(-0.161745\pi\)
−0.858191 + 0.513330i \(0.828412\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −5.89898 10.2173i −0.519376 0.899586i
\(130\) −2.44949 + 4.24264i −0.214834 + 0.372104i
\(131\) 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) 3.00000 0.261116
\(133\) 6.05051 + 1.81954i 0.524646 + 0.157774i
\(134\) −7.34847 −0.634811
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 0.775255 1.34278i 0.0664776 0.115143i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) −2.94949 + 5.10867i −0.251077 + 0.434879i
\(139\) 7.34847 + 12.7279i 0.623289 + 1.07957i 0.988869 + 0.148788i \(0.0475373\pi\)
−0.365580 + 0.930780i \(0.619129\pi\)
\(140\) −1.44949 −0.122504
\(141\) 1.10102 0.0927227
\(142\) 1.67423 + 2.89986i 0.140499 + 0.243351i
\(143\) 7.34847 + 12.7279i 0.614510 + 1.06436i
\(144\) 1.00000 0.0833333
\(145\) 9.34847 0.776348
\(146\) −5.22474 9.04952i −0.432403 0.748944i
\(147\) −2.44949 + 4.24264i −0.202031 + 0.349927i
\(148\) 4.94949 + 8.57277i 0.406846 + 0.704677i
\(149\) −6.77526 + 11.7351i −0.555051 + 0.961376i 0.442849 + 0.896596i \(0.353968\pi\)
−0.997900 + 0.0647795i \(0.979366\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −4.65153 −0.378536 −0.189268 0.981925i \(-0.560612\pi\)
−0.189268 + 0.981925i \(0.560612\pi\)
\(152\) −4.17423 1.25529i −0.338575 0.101818i
\(153\) −1.55051 −0.125351
\(154\) −2.17423 + 3.76588i −0.175205 + 0.303464i
\(155\) 0.449490 0.778539i 0.0361039 0.0625338i
\(156\) 2.44949 + 4.24264i 0.196116 + 0.339683i
\(157\) −10.3990 + 18.0116i −0.829929 + 1.43748i 0.0681644 + 0.997674i \(0.478286\pi\)
−0.898093 + 0.439805i \(0.855048\pi\)
\(158\) −3.44949 5.97469i −0.274427 0.475321i
\(159\) 7.44949 0.590783
\(160\) 1.00000 0.0790569
\(161\) −4.27526 7.40496i −0.336937 0.583593i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 16.6969 1.30781 0.653903 0.756579i \(-0.273131\pi\)
0.653903 + 0.756579i \(0.273131\pi\)
\(164\) 4.34847 0.339558
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) −5.89898 + 10.2173i −0.457850 + 0.793019i
\(167\) 4.84847 + 8.39780i 0.375186 + 0.649841i 0.990355 0.138554i \(-0.0442456\pi\)
−0.615169 + 0.788395i \(0.710912\pi\)
\(168\) −0.724745 + 1.25529i −0.0559153 + 0.0968481i
\(169\) −5.50000 + 9.52628i −0.423077 + 0.732791i
\(170\) −1.55051 −0.118919
\(171\) 1.00000 + 4.24264i 0.0764719 + 0.324443i
\(172\) −11.7980 −0.899586
\(173\) 2.27526 3.94086i 0.172984 0.299618i −0.766477 0.642271i \(-0.777992\pi\)
0.939462 + 0.342653i \(0.111326\pi\)
\(174\) 4.67423 8.09601i 0.354353 0.613757i
\(175\) 0.724745 + 1.25529i 0.0547856 + 0.0948914i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) −5.44949 −0.408457
\(179\) −20.7980 −1.55451 −0.777256 0.629184i \(-0.783389\pi\)
−0.777256 + 0.629184i \(0.783389\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −8.57321 14.8492i −0.637242 1.10374i −0.986035 0.166536i \(-0.946742\pi\)
0.348793 0.937200i \(-0.386591\pi\)
\(182\) −7.10102 −0.526363
\(183\) −12.4495 −0.920293
\(184\) 2.94949 + 5.10867i 0.217439 + 0.376616i
\(185\) 4.94949 8.57277i 0.363894 0.630282i
\(186\) −0.449490 0.778539i −0.0329582 0.0570853i
\(187\) −2.32577 + 4.02834i −0.170077 + 0.294582i
\(188\) 0.550510 0.953512i 0.0401501 0.0695420i
\(189\) 1.44949 0.105435
\(190\) 1.00000 + 4.24264i 0.0725476 + 0.307794i
\(191\) −3.79796 −0.274811 −0.137405 0.990515i \(-0.543876\pi\)
−0.137405 + 0.990515i \(0.543876\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 10.6742 18.4883i 0.768348 1.33082i −0.170110 0.985425i \(-0.554412\pi\)
0.938458 0.345393i \(-0.112254\pi\)
\(194\) 9.22474 + 15.9777i 0.662298 + 1.14713i
\(195\) 2.44949 4.24264i 0.175412 0.303822i
\(196\) 2.44949 + 4.24264i 0.174964 + 0.303046i
\(197\) 6.55051 0.466705 0.233352 0.972392i \(-0.425030\pi\)
0.233352 + 0.972392i \(0.425030\pi\)
\(198\) −3.00000 −0.213201
\(199\) −3.22474 5.58542i −0.228596 0.395940i 0.728796 0.684731i \(-0.240080\pi\)
−0.957392 + 0.288791i \(0.906747\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 7.34847 0.518321
\(202\) −1.10102 −0.0774675
\(203\) 6.77526 + 11.7351i 0.475530 + 0.823642i
\(204\) −0.775255 + 1.34278i −0.0542787 + 0.0940135i
\(205\) −2.17423 3.76588i −0.151855 0.263021i
\(206\) −5.62372 + 9.74058i −0.391823 + 0.678658i
\(207\) 2.94949 5.10867i 0.205004 0.355077i
\(208\) 4.89898 0.339683
\(209\) 12.5227 + 3.76588i 0.866214 + 0.260492i
\(210\) 1.44949 0.100024
\(211\) 13.1742 22.8184i 0.906952 1.57089i 0.0886760 0.996061i \(-0.471736\pi\)
0.818276 0.574826i \(-0.194930\pi\)
\(212\) 3.72474 6.45145i 0.255817 0.443087i
\(213\) −1.67423 2.89986i −0.114717 0.198695i
\(214\) 1.32577 2.29629i 0.0906275 0.156971i
\(215\) 5.89898 + 10.2173i 0.402307 + 0.696816i
\(216\) −1.00000 −0.0680414
\(217\) 1.30306 0.0884576
\(218\) −0.674235 1.16781i −0.0456649 0.0790940i
\(219\) 5.22474 + 9.04952i 0.353056 + 0.611510i
\(220\) −3.00000 −0.202260
\(221\) −7.59592 −0.510957
\(222\) −4.94949 8.57277i −0.332188 0.575366i
\(223\) 1.72474 2.98735i 0.115497 0.200047i −0.802481 0.596678i \(-0.796487\pi\)
0.917978 + 0.396630i \(0.129820\pi\)
\(224\) 0.724745 + 1.25529i 0.0484241 + 0.0838729i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 4.77526 8.27098i 0.317645 0.550178i
\(227\) −11.3485 −0.753224 −0.376612 0.926371i \(-0.622911\pi\)
−0.376612 + 0.926371i \(0.622911\pi\)
\(228\) 4.17423 + 1.25529i 0.276445 + 0.0831339i
\(229\) 8.69694 0.574710 0.287355 0.957824i \(-0.407224\pi\)
0.287355 + 0.957824i \(0.407224\pi\)
\(230\) 2.94949 5.10867i 0.194484 0.336855i
\(231\) 2.17423 3.76588i 0.143054 0.247777i
\(232\) −4.67423 8.09601i −0.306879 0.531529i
\(233\) 13.8990 24.0737i 0.910552 1.57712i 0.0972668 0.995258i \(-0.468990\pi\)
0.813286 0.581865i \(-0.197677\pi\)
\(234\) −2.44949 4.24264i −0.160128 0.277350i
\(235\) −1.10102 −0.0718227
\(236\) −6.00000 −0.390567
\(237\) 3.44949 + 5.97469i 0.224068 + 0.388098i
\(238\) −1.12372 1.94635i −0.0728402 0.126163i
\(239\) −29.7980 −1.92747 −0.963735 0.266862i \(-0.914013\pi\)
−0.963735 + 0.266862i \(0.914013\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −3.34847 5.79972i −0.215694 0.373593i 0.737793 0.675027i \(-0.235868\pi\)
−0.953487 + 0.301434i \(0.902535\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −6.22474 + 10.7816i −0.398498 + 0.690220i
\(245\) 2.44949 4.24264i 0.156492 0.271052i
\(246\) −4.34847 −0.277248
\(247\) 4.89898 + 20.7846i 0.311715 + 1.32249i
\(248\) −0.898979 −0.0570853
\(249\) 5.89898 10.2173i 0.373833 0.647497i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 1.10102 + 1.90702i 0.0694958 + 0.120370i 0.898679 0.438606i \(-0.144528\pi\)
−0.829184 + 0.558976i \(0.811194\pi\)
\(252\) 0.724745 1.25529i 0.0456546 0.0790761i
\(253\) −8.84847 15.3260i −0.556298 0.963537i
\(254\) −0.348469 −0.0218649
\(255\) 1.55051 0.0970967
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.89898 13.6814i −0.492725 0.853424i 0.507240 0.861805i \(-0.330666\pi\)
−0.999965 + 0.00838040i \(0.997332\pi\)
\(258\) 11.7980 0.734509
\(259\) 14.3485 0.891570
\(260\) −2.44949 4.24264i −0.151911 0.263117i
\(261\) −4.67423 + 8.09601i −0.289328 + 0.501131i
\(262\) 1.50000 + 2.59808i 0.0926703 + 0.160510i
\(263\) −5.05051 + 8.74774i −0.311428 + 0.539409i −0.978672 0.205431i \(-0.934141\pi\)
0.667244 + 0.744839i \(0.267474\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) −7.44949 −0.457619
\(266\) −4.60102 + 4.33013i −0.282107 + 0.265497i
\(267\) 5.44949 0.333503
\(268\) 3.67423 6.36396i 0.224440 0.388741i
\(269\) 12.1237 20.9989i 0.739197 1.28033i −0.213661 0.976908i \(-0.568539\pi\)
0.952858 0.303418i \(-0.0981279\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) 7.44949 12.9029i 0.452524 0.783795i −0.546018 0.837774i \(-0.683857\pi\)
0.998542 + 0.0539785i \(0.0171903\pi\)
\(272\) 0.775255 + 1.34278i 0.0470067 + 0.0814181i
\(273\) 7.10102 0.429773
\(274\) −12.0000 −0.724947
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) −2.94949 5.10867i −0.177538 0.307506i
\(277\) −12.8990 −0.775025 −0.387512 0.921865i \(-0.626666\pi\)
−0.387512 + 0.921865i \(0.626666\pi\)
\(278\) −14.6969 −0.881464
\(279\) 0.449490 + 0.778539i 0.0269102 + 0.0466099i
\(280\) 0.724745 1.25529i 0.0433118 0.0750182i
\(281\) −7.17423 12.4261i −0.427979 0.741281i 0.568714 0.822535i \(-0.307441\pi\)
−0.996693 + 0.0812537i \(0.974108\pi\)
\(282\) −0.550510 + 0.953512i −0.0327824 + 0.0567808i
\(283\) 6.34847 10.9959i 0.377377 0.653637i −0.613302 0.789848i \(-0.710159\pi\)
0.990680 + 0.136211i \(0.0434927\pi\)
\(284\) −3.34847 −0.198695
\(285\) −1.00000 4.24264i −0.0592349 0.251312i
\(286\) −14.6969 −0.869048
\(287\) 3.15153 5.45861i 0.186029 0.322212i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 7.29796 + 12.6404i 0.429292 + 0.743555i
\(290\) −4.67423 + 8.09601i −0.274481 + 0.475414i
\(291\) −9.22474 15.9777i −0.540764 0.936631i
\(292\) 10.4495 0.611510
\(293\) −11.4495 −0.668886 −0.334443 0.942416i \(-0.608548\pi\)
−0.334443 + 0.942416i \(0.608548\pi\)
\(294\) −2.44949 4.24264i −0.142857 0.247436i
\(295\) 3.00000 + 5.19615i 0.174667 + 0.302532i
\(296\) −9.89898 −0.575366
\(297\) 3.00000 0.174078
\(298\) −6.77526 11.7351i −0.392480 0.679795i
\(299\) 14.4495 25.0273i 0.835636 1.44736i
\(300\) 0.500000 + 0.866025i 0.0288675 + 0.0500000i
\(301\) −8.55051 + 14.8099i −0.492843 + 0.853629i
\(302\) 2.32577 4.02834i 0.133833 0.231805i
\(303\) 1.10102 0.0632520
\(304\) 3.17423 2.98735i 0.182055 0.171336i
\(305\) 12.4495 0.712856
\(306\) 0.775255 1.34278i 0.0443184 0.0767617i
\(307\) 5.12372 8.87455i 0.292426 0.506497i −0.681957 0.731393i \(-0.738871\pi\)
0.974383 + 0.224895i \(0.0722040\pi\)
\(308\) −2.17423 3.76588i −0.123889 0.214581i
\(309\) 5.62372 9.74058i 0.319923 0.554122i
\(310\) 0.449490 + 0.778539i 0.0255293 + 0.0442180i
\(311\) −9.79796 −0.555591 −0.277796 0.960640i \(-0.589604\pi\)
−0.277796 + 0.960640i \(0.589604\pi\)
\(312\) −4.89898 −0.277350
\(313\) −15.7980 27.3629i −0.892953 1.54664i −0.836317 0.548246i \(-0.815296\pi\)
−0.0566362 0.998395i \(-0.518038\pi\)
\(314\) −10.3990 18.0116i −0.586848 1.01645i
\(315\) −1.44949 −0.0816695
\(316\) 6.89898 0.388098
\(317\) −4.72474 8.18350i −0.265368 0.459631i 0.702292 0.711889i \(-0.252160\pi\)
−0.967660 + 0.252258i \(0.918827\pi\)
\(318\) −3.72474 + 6.45145i −0.208873 + 0.361779i
\(319\) 14.0227 + 24.2880i 0.785121 + 1.35987i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −1.32577 + 2.29629i −0.0739970 + 0.128167i
\(322\) 8.55051 0.476501
\(323\) −4.92168 + 4.63191i −0.273850 + 0.257726i
\(324\) 1.00000 0.0555556
\(325\) −2.44949 + 4.24264i −0.135873 + 0.235339i
\(326\) −8.34847 + 14.4600i −0.462379 + 0.800864i
\(327\) 0.674235 + 1.16781i 0.0372853 + 0.0645800i
\(328\) −2.17423 + 3.76588i −0.120052 + 0.207936i
\(329\) −0.797959 1.38211i −0.0439929 0.0761979i
\(330\) 3.00000 0.165145
\(331\) 18.3485 1.00852 0.504262 0.863551i \(-0.331765\pi\)
0.504262 + 0.863551i \(0.331765\pi\)
\(332\) −5.89898 10.2173i −0.323749 0.560749i
\(333\) 4.94949 + 8.57277i 0.271230 + 0.469785i
\(334\) −9.69694 −0.530593
\(335\) −7.34847 −0.401490
\(336\) −0.724745 1.25529i −0.0395381 0.0684820i
\(337\) 13.2474 22.9453i 0.721635 1.24991i −0.238710 0.971091i \(-0.576724\pi\)
0.960344 0.278817i \(-0.0899422\pi\)
\(338\) −5.50000 9.52628i −0.299161 0.518161i
\(339\) −4.77526 + 8.27098i −0.259356 + 0.449218i
\(340\) 0.775255 1.34278i 0.0420441 0.0728225i
\(341\) 2.69694 0.146047
\(342\) −4.17423 1.25529i −0.225717 0.0678786i
\(343\) 17.2474 0.931275
\(344\) 5.89898 10.2173i 0.318052 0.550882i
\(345\) −2.94949 + 5.10867i −0.158795 + 0.275041i
\(346\) 2.27526 + 3.94086i 0.122318 + 0.211862i
\(347\) −5.89898 + 10.2173i −0.316674 + 0.548495i −0.979792 0.200020i \(-0.935899\pi\)
0.663118 + 0.748515i \(0.269233\pi\)
\(348\) 4.67423 + 8.09601i 0.250565 + 0.433992i
\(349\) −20.0454 −1.07301 −0.536503 0.843898i \(-0.680255\pi\)
−0.536503 + 0.843898i \(0.680255\pi\)
\(350\) −1.44949 −0.0774785
\(351\) 2.44949 + 4.24264i 0.130744 + 0.226455i
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) −35.3485 −1.88141 −0.940705 0.339227i \(-0.889835\pi\)
−0.940705 + 0.339227i \(0.889835\pi\)
\(354\) 6.00000 0.318896
\(355\) 1.67423 + 2.89986i 0.0888591 + 0.153909i
\(356\) 2.72474 4.71940i 0.144411 0.250128i
\(357\) 1.12372 + 1.94635i 0.0594738 + 0.103012i
\(358\) 10.3990 18.0116i 0.549603 0.951941i
\(359\) −13.2247 + 22.9059i −0.697975 + 1.20893i 0.271192 + 0.962525i \(0.412582\pi\)
−0.969167 + 0.246403i \(0.920751\pi\)
\(360\) 1.00000 0.0527046
\(361\) 15.8485 + 10.4798i 0.834130 + 0.551568i
\(362\) 17.1464 0.901196
\(363\) −1.00000 + 1.73205i −0.0524864 + 0.0909091i
\(364\) 3.55051 6.14966i 0.186097 0.322330i
\(365\) −5.22474 9.04952i −0.273476 0.473674i
\(366\) 6.22474 10.7816i 0.325373 0.563562i
\(367\) −10.4495 18.0990i −0.545459 0.944763i −0.998578 0.0533125i \(-0.983022\pi\)
0.453119 0.891450i \(-0.350311\pi\)
\(368\) −5.89898 −0.307506
\(369\) 4.34847 0.226372
\(370\) 4.94949 + 8.57277i 0.257312 + 0.445677i
\(371\) −5.39898 9.35131i −0.280301 0.485496i
\(372\) 0.898979 0.0466099
\(373\) −3.89898 −0.201882 −0.100941 0.994892i \(-0.532185\pi\)
−0.100941 + 0.994892i \(0.532185\pi\)
\(374\) −2.32577 4.02834i −0.120262 0.208301i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0.550510 + 0.953512i 0.0283904 + 0.0491736i
\(377\) −22.8990 + 39.6622i −1.17936 + 2.04271i
\(378\) −0.724745 + 1.25529i −0.0372769 + 0.0645654i
\(379\) −6.69694 −0.343999 −0.171999 0.985097i \(-0.555023\pi\)
−0.171999 + 0.985097i \(0.555023\pi\)
\(380\) −4.17423 1.25529i −0.214134 0.0643953i
\(381\) 0.348469 0.0178526
\(382\) 1.89898 3.28913i 0.0971602 0.168286i
\(383\) −15.2474 + 26.4094i −0.779108 + 1.34946i 0.153348 + 0.988172i \(0.450994\pi\)
−0.932456 + 0.361283i \(0.882339\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) −2.17423 + 3.76588i −0.110809 + 0.191927i
\(386\) 10.6742 + 18.4883i 0.543304 + 0.941031i
\(387\) −11.7980 −0.599724
\(388\) −18.4495 −0.936631
\(389\) 11.5732 + 20.0454i 0.586785 + 1.01634i 0.994650 + 0.103300i \(0.0329401\pi\)
−0.407865 + 0.913042i \(0.633727\pi\)
\(390\) 2.44949 + 4.24264i 0.124035 + 0.214834i
\(391\) 9.14643 0.462555
\(392\) −4.89898 −0.247436
\(393\) −1.50000 2.59808i −0.0756650 0.131056i
\(394\) −3.27526 + 5.67291i −0.165005 + 0.285797i
\(395\) −3.44949 5.97469i −0.173563 0.300619i
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) −5.74745 + 9.95487i −0.288456 + 0.499621i −0.973441 0.228936i \(-0.926475\pi\)
0.684985 + 0.728557i \(0.259809\pi\)
\(398\) 6.44949 0.323284
\(399\) 4.60102 4.33013i 0.230339 0.216777i
\(400\) 1.00000 0.0500000
\(401\) 1.89898 3.28913i 0.0948305 0.164251i −0.814707 0.579872i \(-0.803102\pi\)
0.909538 + 0.415621i \(0.136436\pi\)
\(402\) −3.67423 + 6.36396i −0.183254 + 0.317406i
\(403\) 2.20204 + 3.81405i 0.109691 + 0.189991i
\(404\) 0.550510 0.953512i 0.0273889 0.0474390i
\(405\) −0.500000 0.866025i −0.0248452 0.0430331i
\(406\) −13.5505 −0.672501
\(407\) 29.6969 1.47202
\(408\) −0.775255 1.34278i −0.0383808 0.0664776i
\(409\) 4.74745 + 8.22282i 0.234746 + 0.406592i 0.959199 0.282732i \(-0.0912408\pi\)
−0.724453 + 0.689325i \(0.757907\pi\)
\(410\) 4.34847 0.214756
\(411\) 12.0000 0.591916
\(412\) −5.62372 9.74058i −0.277061 0.479884i
\(413\) −4.34847 + 7.53177i −0.213974 + 0.370614i
\(414\) 2.94949 + 5.10867i 0.144960 + 0.251077i
\(415\) −5.89898 + 10.2173i −0.289570 + 0.501549i
\(416\) −2.44949 + 4.24264i −0.120096 + 0.208013i
\(417\) 14.6969 0.719712
\(418\) −9.52270 + 8.96204i −0.465771 + 0.438348i
\(419\) 21.8990 1.06984 0.534918 0.844904i \(-0.320343\pi\)
0.534918 + 0.844904i \(0.320343\pi\)
\(420\) −0.724745 + 1.25529i −0.0353639 + 0.0612521i
\(421\) 9.32577 16.1527i 0.454510 0.787234i −0.544150 0.838988i \(-0.683148\pi\)
0.998660 + 0.0517536i \(0.0164811\pi\)
\(422\) 13.1742 + 22.8184i 0.641312 + 1.11078i
\(423\) 0.550510 0.953512i 0.0267667 0.0463613i
\(424\) 3.72474 + 6.45145i 0.180890 + 0.313310i
\(425\) −1.55051 −0.0752108
\(426\) 3.34847 0.162234
\(427\) 9.02270 + 15.6278i 0.436639 + 0.756281i
\(428\) 1.32577 + 2.29629i 0.0640833 + 0.110996i
\(429\) 14.6969 0.709575
\(430\) −11.7980 −0.568948
\(431\) −5.32577 9.22450i −0.256533 0.444328i 0.708778 0.705432i \(-0.249247\pi\)
−0.965311 + 0.261104i \(0.915914\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −1.67423 2.89986i −0.0804586 0.139358i 0.822988 0.568058i \(-0.192305\pi\)
−0.903447 + 0.428700i \(0.858972\pi\)
\(434\) −0.651531 + 1.12848i −0.0312745 + 0.0541690i
\(435\) 4.67423 8.09601i 0.224112 0.388174i
\(436\) 1.34847 0.0645800
\(437\) −5.89898 25.0273i −0.282186 1.19722i
\(438\) −10.4495 −0.499296
\(439\) −1.67423 + 2.89986i −0.0799069 + 0.138403i −0.903210 0.429200i \(-0.858796\pi\)
0.823303 + 0.567603i \(0.192129\pi\)
\(440\) 1.50000 2.59808i 0.0715097 0.123858i
\(441\) 2.44949 + 4.24264i 0.116642 + 0.202031i
\(442\) 3.79796 6.57826i 0.180650 0.312896i
\(443\) −0.876276 1.51775i −0.0416331 0.0721107i 0.844458 0.535622i \(-0.179923\pi\)
−0.886091 + 0.463511i \(0.846589\pi\)
\(444\) 9.89898 0.469785
\(445\) −5.44949 −0.258331
\(446\) 1.72474 + 2.98735i 0.0816690 + 0.141455i
\(447\) 6.77526 + 11.7351i 0.320459 + 0.555051i
\(448\) −1.44949 −0.0684820
\(449\) 8.75255 0.413058 0.206529 0.978440i \(-0.433783\pi\)
0.206529 + 0.978440i \(0.433783\pi\)
\(450\) −0.500000 0.866025i −0.0235702 0.0408248i
\(451\) 6.52270 11.2977i 0.307142 0.531986i
\(452\) 4.77526 + 8.27098i 0.224609 + 0.389034i
\(453\) −2.32577 + 4.02834i −0.109274 + 0.189268i
\(454\) 5.67423 9.82806i 0.266305 0.461254i
\(455\) −7.10102 −0.332901
\(456\) −3.17423 + 2.98735i −0.148647 + 0.139895i
\(457\) −12.0454 −0.563460 −0.281730 0.959494i \(-0.590908\pi\)
−0.281730 + 0.959494i \(0.590908\pi\)
\(458\) −4.34847 + 7.53177i −0.203191 + 0.351936i
\(459\) −0.775255 + 1.34278i −0.0361858 + 0.0626757i
\(460\) 2.94949 + 5.10867i 0.137521 + 0.238193i
\(461\) 13.8990 24.0737i 0.647340 1.12123i −0.336416 0.941714i \(-0.609215\pi\)
0.983756 0.179512i \(-0.0574519\pi\)
\(462\) 2.17423 + 3.76588i 0.101155 + 0.175205i
\(463\) −15.6515 −0.727388 −0.363694 0.931518i \(-0.618485\pi\)
−0.363694 + 0.931518i \(0.618485\pi\)
\(464\) 9.34847 0.433992
\(465\) −0.449490 0.778539i −0.0208446 0.0361039i
\(466\) 13.8990 + 24.0737i 0.643858 + 1.11519i
\(467\) −40.2474 −1.86243 −0.931215 0.364471i \(-0.881250\pi\)
−0.931215 + 0.364471i \(0.881250\pi\)
\(468\) 4.89898 0.226455
\(469\) −5.32577 9.22450i −0.245921 0.425948i
\(470\) 0.550510 0.953512i 0.0253931 0.0439822i
\(471\) 10.3990 + 18.0116i 0.479160 + 0.829929i
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) −17.6969 + 30.6520i −0.813706 + 1.40938i
\(474\) −6.89898 −0.316881
\(475\) 1.00000 + 4.24264i 0.0458831 + 0.194666i
\(476\) 2.24745 0.103012
\(477\) 3.72474 6.45145i 0.170544 0.295391i
\(478\) 14.8990 25.8058i 0.681463 1.18033i
\(479\) −5.02270 8.69958i −0.229493 0.397494i 0.728165 0.685402i \(-0.240374\pi\)
−0.957658 + 0.287908i \(0.907040\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) 24.2474 + 41.9978i 1.10559 + 1.91494i
\(482\) 6.69694 0.305037
\(483\) −8.55051 −0.389062
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 9.22474 + 15.9777i 0.418874 + 0.725511i
\(486\) −1.00000 −0.0453609
\(487\) −28.1464 −1.27544 −0.637718 0.770270i \(-0.720122\pi\)
−0.637718 + 0.770270i \(0.720122\pi\)
\(488\) −6.22474 10.7816i −0.281781 0.488059i
\(489\) 8.34847 14.4600i 0.377531 0.653903i
\(490\) 2.44949 + 4.24264i 0.110657 + 0.191663i
\(491\) 7.60102 13.1654i 0.343029 0.594144i −0.641964 0.766734i \(-0.721880\pi\)
0.984994 + 0.172590i \(0.0552137\pi\)
\(492\) 2.17423 3.76588i 0.0980221 0.169779i
\(493\) −14.4949 −0.652817
\(494\) −20.4495 6.14966i −0.920066 0.276686i
\(495\) −3.00000 −0.134840
\(496\) 0.449490 0.778539i 0.0201827 0.0349574i
\(497\) −2.42679 + 4.20332i −0.108856 + 0.188545i
\(498\) 5.89898 + 10.2173i 0.264340 + 0.457850i
\(499\) −5.27526 + 9.13701i −0.236153 + 0.409029i −0.959607 0.281344i \(-0.909220\pi\)
0.723454 + 0.690372i \(0.242553\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 9.69694 0.433227
\(502\) −2.20204 −0.0982819
\(503\) −1.15153 1.99451i −0.0513442 0.0889308i 0.839211 0.543806i \(-0.183017\pi\)
−0.890555 + 0.454875i \(0.849684\pi\)
\(504\) 0.724745 + 1.25529i 0.0322827 + 0.0559153i
\(505\) −1.10102 −0.0489948
\(506\) 17.6969 0.786725
\(507\) 5.50000 + 9.52628i 0.244264 + 0.423077i
\(508\) 0.174235 0.301783i 0.00773041 0.0133895i
\(509\) 1.44949 + 2.51059i 0.0642475 + 0.111280i 0.896360 0.443327i \(-0.146202\pi\)
−0.832112 + 0.554607i \(0.812869\pi\)
\(510\) −0.775255 + 1.34278i −0.0343289 + 0.0594594i
\(511\) 7.57321 13.1172i 0.335019 0.580270i
\(512\) 1.00000 0.0441942
\(513\) 4.17423 + 1.25529i 0.184297 + 0.0554226i
\(514\) 15.7980 0.696818
\(515\) −5.62372 + 9.74058i −0.247811 + 0.429221i
\(516\) −5.89898 + 10.2173i −0.259688 + 0.449793i
\(517\) −1.65153 2.86054i −0.0726342 0.125806i
\(518\) −7.17423 + 12.4261i −0.315218 + 0.545973i
\(519\) −2.27526 3.94086i −0.0998726 0.172984i
\(520\) 4.89898 0.214834
\(521\) 1.10102 0.0482366 0.0241183 0.999709i \(-0.492322\pi\)
0.0241183 + 0.999709i \(0.492322\pi\)
\(522\) −4.67423 8.09601i −0.204586 0.354353i
\(523\) −1.57321 2.72489i −0.0687918 0.119151i 0.829578 0.558391i \(-0.188581\pi\)
−0.898370 + 0.439240i \(0.855248\pi\)
\(524\) −3.00000 −0.131056
\(525\) 1.44949 0.0632609
\(526\) −5.05051 8.74774i −0.220213 0.381420i
\(527\) −0.696938 + 1.20713i −0.0303591 + 0.0525835i
\(528\) −1.50000 2.59808i −0.0652791 0.113067i
\(529\) −5.89898 + 10.2173i −0.256477 + 0.444232i
\(530\) 3.72474 6.45145i 0.161793 0.280233i
\(531\) −6.00000 −0.260378
\(532\) −1.44949 6.14966i −0.0628434 0.266622i
\(533\) 21.3031 0.922738
\(534\) −2.72474 + 4.71940i −0.117911 + 0.204228i
\(535\) 1.32577 2.29629i 0.0573178 0.0992774i
\(536\) 3.67423 + 6.36396i 0.158703 + 0.274881i
\(537\) −10.3990 + 18.0116i −0.448749 + 0.777256i
\(538\) 12.1237 + 20.9989i 0.522691 + 0.905327i
\(539\) 14.6969 0.633042
\(540\) −1.00000 −0.0430331
\(541\) −9.55051 16.5420i −0.410609 0.711195i 0.584348 0.811503i \(-0.301350\pi\)
−0.994956 + 0.100308i \(0.968017\pi\)
\(542\) 7.44949 + 12.9029i 0.319983 + 0.554227i
\(543\) −17.1464 −0.735824
\(544\) −1.55051 −0.0664776
\(545\) −0.674235 1.16781i −0.0288810 0.0500234i
\(546\) −3.55051 + 6.14966i −0.151948 + 0.263181i
\(547\) 1.65153 + 2.86054i 0.0706144 + 0.122308i 0.899171 0.437598i \(-0.144171\pi\)
−0.828556 + 0.559906i \(0.810837\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) −6.22474 + 10.7816i −0.265666 + 0.460146i
\(550\) −3.00000 −0.127920
\(551\) 9.34847 + 39.6622i 0.398258 + 1.68967i
\(552\) 5.89898 0.251077
\(553\) 5.00000 8.66025i 0.212622 0.368271i
\(554\) 6.44949 11.1708i 0.274013 0.474604i
\(555\) −4.94949 8.57277i −0.210094 0.363894i
\(556\) 7.34847 12.7279i 0.311645 0.539784i
\(557\) 9.17423 + 15.8902i 0.388725 + 0.673291i 0.992278 0.124031i \(-0.0395824\pi\)
−0.603553 + 0.797323i \(0.706249\pi\)
\(558\) −0.898979 −0.0380568
\(559\) −57.7980 −2.44459
\(560\) 0.724745 + 1.25529i 0.0306261 + 0.0530459i
\(561\) 2.32577 + 4.02834i 0.0981939 + 0.170077i
\(562\) 14.3485 0.605254
\(563\) 29.3939 1.23880 0.619402 0.785074i \(-0.287375\pi\)
0.619402 + 0.785074i \(0.287375\pi\)
\(564\) −0.550510 0.953512i −0.0231807 0.0401501i
\(565\) 4.77526 8.27098i 0.200896 0.347963i
\(566\) 6.34847 + 10.9959i 0.266846 + 0.462191i
\(567\) 0.724745 1.25529i 0.0304364 0.0527174i
\(568\) 1.67423 2.89986i 0.0702493 0.121675i
\(569\) −7.44949 −0.312299 −0.156149 0.987733i \(-0.549908\pi\)
−0.156149 + 0.987733i \(0.549908\pi\)
\(570\) 4.17423 + 1.25529i 0.174839 + 0.0525785i
\(571\) −8.20204 −0.343245 −0.171622 0.985163i \(-0.554901\pi\)
−0.171622 + 0.985163i \(0.554901\pi\)
\(572\) 7.34847 12.7279i 0.307255 0.532181i
\(573\) −1.89898 + 3.28913i −0.0793310 + 0.137405i
\(574\) 3.15153 + 5.45861i 0.131542 + 0.227838i
\(575\) 2.94949 5.10867i 0.123002 0.213046i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 11.1464 0.464032 0.232016 0.972712i \(-0.425468\pi\)
0.232016 + 0.972712i \(0.425468\pi\)
\(578\) −14.5959 −0.607110
\(579\) −10.6742 18.4883i −0.443606 0.768348i
\(580\) −4.67423 8.09601i −0.194087 0.336169i
\(581\) −17.1010 −0.709470
\(582\) 18.4495 0.764756
\(583\) −11.1742 19.3543i −0.462790 0.801575i
\(584\) −5.22474 + 9.04952i −0.216201 + 0.374472i
\(585\) −2.44949 4.24264i −0.101274 0.175412i
\(586\) 5.72474 9.91555i 0.236487 0.409608i
\(587\) 16.2474 28.1414i 0.670604 1.16152i −0.307129 0.951668i \(-0.599368\pi\)
0.977733 0.209852i \(-0.0672983\pi\)
\(588\) 4.89898 0.202031
\(589\) 3.75255 + 1.12848i 0.154621 + 0.0464984i
\(590\) −6.00000 −0.247016
\(591\) 3.27526 5.67291i 0.134726 0.233352i
\(592\) 4.94949 8.57277i 0.203423 0.352339i
\(593\) 17.5732 + 30.4377i 0.721645 + 1.24993i 0.960340 + 0.278832i \(0.0899472\pi\)
−0.238695 + 0.971095i \(0.576719\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) −1.12372 1.94635i −0.0460682 0.0797925i
\(596\) 13.5505 0.555051
\(597\) −6.44949 −0.263960
\(598\) 14.4495 + 25.0273i 0.590884 + 1.02344i
\(599\) −12.6742 21.9524i −0.517855 0.896951i −0.999785 0.0207416i \(-0.993397\pi\)
0.481930 0.876210i \(-0.339936\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 19.0000 0.775026 0.387513 0.921864i \(-0.373334\pi\)
0.387513 + 0.921864i \(0.373334\pi\)
\(602\) −8.55051 14.8099i −0.348493 0.603607i
\(603\) 3.67423 6.36396i 0.149626 0.259161i
\(604\) 2.32577 + 4.02834i 0.0946341 + 0.163911i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) −0.550510 + 0.953512i −0.0223630 + 0.0387338i
\(607\) 29.4495 1.19532 0.597659 0.801750i \(-0.296098\pi\)
0.597659 + 0.801750i \(0.296098\pi\)
\(608\) 1.00000 + 4.24264i 0.0405554 + 0.172062i
\(609\) 13.5505 0.549094
\(610\) −6.22474 + 10.7816i −0.252033 + 0.436533i
\(611\) 2.69694 4.67123i 0.109106 0.188978i
\(612\) 0.775255 + 1.34278i 0.0313378 + 0.0542787i
\(613\) −5.74745 + 9.95487i −0.232137 + 0.402074i −0.958437 0.285305i \(-0.907905\pi\)
0.726300 + 0.687378i \(0.241239\pi\)
\(614\) 5.12372 + 8.87455i 0.206777 + 0.358148i
\(615\) −4.34847 −0.175347
\(616\) 4.34847 0.175205
\(617\) −7.79796 13.5065i −0.313934 0.543750i 0.665276 0.746597i \(-0.268314\pi\)
−0.979210 + 0.202848i \(0.934980\pi\)
\(618\) 5.62372 + 9.74058i 0.226219 + 0.391823i
\(619\) 23.0454 0.926273 0.463137 0.886287i \(-0.346724\pi\)
0.463137 + 0.886287i \(0.346724\pi\)
\(620\) −0.898979 −0.0361039
\(621\) −2.94949 5.10867i −0.118359 0.205004i
\(622\) 4.89898 8.48528i 0.196431 0.340229i
\(623\) −3.94949 6.84072i −0.158233 0.274068i
\(624\) 2.44949 4.24264i 0.0980581 0.169842i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 31.5959 1.26283
\(627\) 9.52270 8.96204i 0.380300 0.357909i
\(628\) 20.7980 0.829929
\(629\) −7.67423 + 13.2922i −0.305992 + 0.529993i
\(630\) 0.724745 1.25529i 0.0288745 0.0500121i
\(631\) 13.1237 + 22.7310i 0.522447 + 0.904905i 0.999659 + 0.0261167i \(0.00831416\pi\)
−0.477212 + 0.878788i \(0.658353\pi\)
\(632\) −3.44949 + 5.97469i −0.137213 + 0.237660i
\(633\) −13.1742 22.8184i −0.523629 0.906952i
\(634\) 9.44949 0.375287
\(635\) −0.348469 −0.0138286
\(636\) −3.72474 6.45145i −0.147696 0.255817i
\(637\) 12.0000 + 20.7846i 0.475457 + 0.823516i
\(638\) −28.0454 −1.11033
\(639\) −3.34847 −0.132463
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 5.65153 9.78874i 0.223222 0.386632i −0.732563 0.680700i \(-0.761676\pi\)
0.955785 + 0.294068i \(0.0950092\pi\)
\(642\) −1.32577 2.29629i −0.0523238 0.0906275i
\(643\) −10.1237 + 17.5348i −0.399241 + 0.691505i −0.993632 0.112670i \(-0.964060\pi\)
0.594392 + 0.804176i \(0.297393\pi\)
\(644\) −4.27526 + 7.40496i −0.168469 + 0.291796i
\(645\) 11.7980 0.464544
\(646\) −1.55051 6.57826i −0.0610040 0.258818i
\(647\) 0.101021 0.00397153 0.00198576 0.999998i \(-0.499368\pi\)
0.00198576 + 0.999998i \(0.499368\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −9.00000 + 15.5885i −0.353281 + 0.611900i
\(650\) −2.44949 4.24264i −0.0960769 0.166410i
\(651\) 0.651531 1.12848i 0.0255355 0.0442288i
\(652\) −8.34847 14.4600i −0.326951 0.566296i
\(653\) −40.3485 −1.57896 −0.789479 0.613778i \(-0.789649\pi\)
−0.789479 + 0.613778i \(0.789649\pi\)
\(654\) −1.34847 −0.0527293
\(655\) 1.50000 + 2.59808i 0.0586098 + 0.101515i
\(656\) −2.17423 3.76588i −0.0848896 0.147033i
\(657\) 10.4495 0.407673
\(658\) 1.59592 0.0622154
\(659\) −11.2980 19.5686i −0.440106 0.762286i 0.557591 0.830116i \(-0.311726\pi\)
−0.997697 + 0.0678299i \(0.978392\pi\)
\(660\) −1.50000 + 2.59808i −0.0583874 + 0.101130i
\(661\) 6.89898 + 11.9494i 0.268339 + 0.464777i 0.968433 0.249274i \(-0.0801919\pi\)
−0.700094 + 0.714051i \(0.746859\pi\)
\(662\) −9.17423 + 15.8902i −0.356567 + 0.617592i
\(663\) −3.79796 + 6.57826i −0.147501 + 0.255478i
\(664\) 11.7980 0.457850
\(665\) −4.60102 + 4.33013i −0.178420 + 0.167915i
\(666\) −9.89898 −0.383578
\(667\) 27.5732 47.7582i 1.06764 1.84921i
\(668\) 4.84847 8.39780i 0.187593 0.324920i
\(669\) −1.72474 2.98735i −0.0666825 0.115497i
\(670\) 3.67423 6.36396i 0.141948 0.245861i
\(671\) 18.6742 + 32.3447i 0.720911 + 1.24865i
\(672\) 1.44949 0.0559153
\(673\) −40.4949 −1.56096 −0.780482 0.625179i \(-0.785026\pi\)
−0.780482 + 0.625179i \(0.785026\pi\)
\(674\) 13.2474 + 22.9453i 0.510273 + 0.883818i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 11.0000 0.423077
\(677\) 29.9444 1.15086 0.575428 0.817852i \(-0.304835\pi\)
0.575428 + 0.817852i \(0.304835\pi\)
\(678\) −4.77526 8.27098i −0.183393 0.317645i
\(679\) −13.3712 + 23.1596i −0.513139 + 0.888782i
\(680\) 0.775255 + 1.34278i 0.0297297 + 0.0514933i
\(681\) −5.67423 + 9.82806i −0.217437 + 0.376612i
\(682\) −1.34847 + 2.33562i −0.0516356 + 0.0894354i
\(683\) −17.7526 −0.679282 −0.339641 0.940555i \(-0.610306\pi\)
−0.339641 + 0.940555i \(0.610306\pi\)
\(684\) 3.17423 2.98735i 0.121370 0.114224i
\(685\) −12.0000 −0.458496
\(686\) −8.62372 + 14.9367i −0.329255 + 0.570287i
\(687\) 4.34847 7.53177i 0.165904 0.287355i
\(688\) 5.89898 + 10.2173i 0.224896 + 0.389532i
\(689\) 18.2474 31.6055i 0.695172 1.20407i
\(690\) −2.94949 5.10867i −0.112285 0.194484i
\(691\) −31.4495 −1.19639 −0.598197 0.801349i \(-0.704116\pi\)
−0.598197 + 0.801349i \(0.704116\pi\)
\(692\) −4.55051 −0.172984
\(693\) −2.17423 3.76588i −0.0825923 0.143054i
\(694\) −5.89898 10.2173i −0.223922 0.387845i
\(695\) −14.6969 −0.557487
\(696\) −9.34847 −0.354353
\(697\) 3.37117 + 5.83904i 0.127692 + 0.221170i
\(698\) 10.0227 17.3598i 0.379365 0.657079i
\(699\) −13.8990 24.0737i −0.525708 0.910552i
\(700\) 0.724745 1.25529i 0.0273928 0.0474457i
\(701\) −2.10102 + 3.63907i −0.0793544 + 0.137446i −0.902972 0.429700i \(-0.858619\pi\)
0.823617 + 0.567146i \(0.191953\pi\)
\(702\) −4.89898 −0.184900
\(703\) 41.3207 + 12.4261i 1.55844 + 0.468661i
\(704\) −3.00000 −0.113067
\(705\) −0.550510 + 0.953512i −0.0207334 + 0.0359113i
\(706\) 17.6742 30.6127i 0.665179 1.15212i
\(707\) −0.797959 1.38211i −0.0300103 0.0519794i
\(708\) −3.00000 + 5.19615i −0.112747 + 0.195283i
\(709\) −22.4722 38.9230i −0.843961 1.46178i −0.886521 0.462689i \(-0.846885\pi\)
0.0425596 0.999094i \(-0.486449\pi\)
\(710\) −3.34847 −0.125666
\(711\) 6.89898 0.258732
\(712\) 2.72474 + 4.71940i 0.102114 + 0.176867i
\(713\) −2.65153 4.59259i −0.0993006 0.171994i
\(714\) −2.24745 −0.0841087
\(715\) −14.6969 −0.549634
\(716\) 10.3990 + 18.0116i 0.388628 + 0.673124i
\(717\) −14.8990 + 25.8058i −0.556413 + 0.963735i
\(718\) −13.2247 22.9059i −0.493543 0.854842i
\(719\) 17.3485 30.0484i 0.646989 1.12062i −0.336850 0.941558i \(-0.609361\pi\)
0.983838 0.179059i \(-0.0573053\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) −16.3031 −0.607158
\(722\) −17.0000 + 8.48528i −0.632674 + 0.315789i
\(723\) −6.69694 −0.249062
\(724\) −8.57321 + 14.8492i −0.318621 + 0.551868i
\(725\) −4.67423 + 8.09601i −0.173597 + 0.300678i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −4.10102 + 7.10318i −0.152098 + 0.263442i −0.931999 0.362462i \(-0.881936\pi\)
0.779900 + 0.625904i \(0.215270\pi\)
\(728\) 3.55051 + 6.14966i 0.131591 + 0.227922i
\(729\) 1.00000 0.0370370
\(730\) 10.4495 0.386753
\(731\) −9.14643 15.8421i −0.338293 0.585940i
\(732\) 6.22474 + 10.7816i 0.230073 + 0.398498i
\(733\) −2.59592 −0.0958824 −0.0479412 0.998850i \(-0.515266\pi\)
−0.0479412 + 0.998850i \(0.515266\pi\)
\(734\) 20.8990 0.771395
\(735\) −2.44949 4.24264i −0.0903508 0.156492i
\(736\) 2.94949 5.10867i 0.108720 0.188308i
\(737\) −11.0227 19.0919i −0.406027 0.703259i
\(738\) −2.17423 + 3.76588i −0.0800347 + 0.138624i
\(739\) −18.9722 + 32.8608i −0.697903 + 1.20880i 0.271289 + 0.962498i \(0.412550\pi\)
−0.969192 + 0.246306i \(0.920783\pi\)
\(740\) −9.89898 −0.363894
\(741\) 20.4495 + 6.14966i 0.751231 + 0.225914i
\(742\) 10.7980 0.396406
\(743\) 9.84847 17.0580i 0.361305 0.625799i −0.626871 0.779123i \(-0.715665\pi\)
0.988176 + 0.153324i \(0.0489979\pi\)
\(744\) −0.449490 + 0.778539i −0.0164791 + 0.0285426i
\(745\) −6.77526 11.7351i −0.248226 0.429940i
\(746\) 1.94949 3.37662i 0.0713759 0.123627i
\(747\) −5.89898 10.2173i −0.215832 0.373833i
\(748\) 4.65153 0.170077
\(749\) 3.84337 0.140434
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) 22.4949 + 38.9623i 0.820850 + 1.42175i 0.905050 + 0.425306i \(0.139833\pi\)
−0.0841993 + 0.996449i \(0.526833\pi\)
\(752\) −1.10102 −0.0401501
\(753\) 2.20204 0.0802468
\(754\) −22.8990 39.6622i −0.833932 1.44441i
\(755\) 2.32577 4.02834i 0.0846433 0.146606i
\(756\) −0.724745 1.25529i −0.0263587 0.0456546i
\(757\) 2.19694 3.80521i 0.0798491 0.138303i −0.823336 0.567555i \(-0.807889\pi\)
0.903185 + 0.429252i \(0.141223\pi\)
\(758\) 3.34847 5.79972i 0.121622 0.210655i
\(759\) −17.6969 −0.642358
\(760\) 3.17423 2.98735i 0.115142 0.108362i
\(761\) 21.4495 0.777543 0.388772 0.921334i \(-0.372899\pi\)
0.388772 + 0.921334i \(0.372899\pi\)
\(762\) −0.174235 + 0.301783i −0.00631185 + 0.0109325i
\(763\) 0.977296 1.69273i 0.0353805 0.0612808i
\(764\) 1.89898 + 3.28913i 0.0687027 + 0.118997i
\(765\) 0.775255 1.34278i 0.0280294 0.0485484i
\(766\) −15.2474 26.4094i −0.550913 0.954209i
\(767\) −29.3939 −1.06135
\(768\) −1.00000 −0.0360844
\(769\) 16.8990 + 29.2699i 0.609393 + 1.05550i 0.991341 + 0.131315i \(0.0419201\pi\)
−0.381948 + 0.924184i \(0.624747\pi\)
\(770\) −2.17423 3.76588i −0.0783540 0.135713i
\(771\) −15.7980 −0.568950
\(772\) −21.3485 −0.768348
\(773\) 22.5227 + 39.0105i 0.810085 + 1.40311i 0.912804 + 0.408399i \(0.133913\pi\)
−0.102718 + 0.994710i \(0.532754\pi\)
\(774\) 5.89898 10.2173i 0.212034 0.367254i
\(775\) 0.449490 + 0.778539i 0.0161461 + 0.0279659i
\(776\) 9.22474 15.9777i 0.331149 0.573567i
\(777\) 7.17423 12.4261i 0.257374 0.445785i
\(778\)