Properties

Label 78.2.i.b.43.1
Level $78$
Weight $2$
Character 78.43
Analytic conductor $0.623$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.43
Dual form 78.2.i.b.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.866025 + 1.50000i) q^{10} +(-1.09808 - 0.633975i) q^{11} +1.00000 q^{12} +(1.59808 + 3.23205i) q^{13} -1.26795 q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.59808 + 4.50000i) q^{17} +1.00000i q^{18} +(-4.09808 + 2.36603i) q^{19} +(1.50000 - 0.866025i) q^{20} -1.26795i q^{21} +(0.633975 + 1.09808i) q^{22} +(-4.09808 + 7.09808i) q^{23} +(-0.866025 - 0.500000i) q^{24} +2.00000 q^{25} +(0.232051 - 3.59808i) q^{26} -1.00000 q^{27} +(1.09808 + 0.633975i) q^{28} +(1.50000 - 2.59808i) q^{29} +(0.866025 + 1.50000i) q^{30} -9.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09808 + 0.633975i) q^{33} -5.19615i q^{34} +(-1.09808 - 1.90192i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.59808 - 1.50000i) q^{37} +4.73205 q^{38} +(3.59808 + 0.232051i) q^{39} -1.73205 q^{40} +(5.59808 + 3.23205i) q^{41} +(-0.633975 + 1.09808i) q^{42} +(-2.09808 - 3.63397i) q^{43} -1.26795i q^{44} +(-1.50000 + 0.866025i) q^{45} +(7.09808 - 4.09808i) q^{46} -4.73205i q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.69615 + 4.66987i) q^{49} +(-1.73205 - 1.00000i) q^{50} +5.19615 q^{51} +(-2.00000 + 3.00000i) q^{52} +3.00000 q^{53} +(0.866025 + 0.500000i) q^{54} +(-1.09808 + 1.90192i) q^{55} +(-0.633975 - 1.09808i) q^{56} +4.73205i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-12.0000 + 6.92820i) q^{59} -1.73205i q^{60} +(-7.59808 - 13.1603i) q^{61} +(-4.73205 + 8.19615i) q^{62} +(-1.09808 - 0.633975i) q^{63} -1.00000 q^{64} +(5.59808 - 2.76795i) q^{65} +1.26795 q^{66} +(6.29423 + 3.63397i) q^{67} +(-2.59808 + 4.50000i) q^{68} +(4.09808 + 7.09808i) q^{69} +2.19615i q^{70} +(1.90192 - 1.09808i) q^{71} +(-0.866025 + 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 + 2.59808i) q^{74} +(1.00000 - 1.73205i) q^{75} +(-4.09808 - 2.36603i) q^{76} -1.60770 q^{77} +(-3.00000 - 2.00000i) q^{78} +8.39230 q^{79} +(1.50000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.23205 - 5.59808i) q^{82} -5.66025i q^{83} +(1.09808 - 0.633975i) q^{84} +(7.79423 - 4.50000i) q^{85} +4.19615i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.633975 + 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} +1.73205 q^{90} +(3.80385 + 2.53590i) q^{91} -8.19615 q^{92} +(-8.19615 - 4.73205i) q^{93} +(-2.36603 + 4.09808i) q^{94} +(4.09808 + 7.09808i) q^{95} -1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(4.66987 - 2.69615i) q^{98} +1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 4 q^{13} - 12 q^{14} - 6 q^{15} - 2 q^{16} - 6 q^{19} + 6 q^{20} + 6 q^{22} - 6 q^{23} + 8 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{33} + 6 q^{35} + 2 q^{36} + 12 q^{38} + 4 q^{39} + 12 q^{41} - 6 q^{42} + 2 q^{43} - 6 q^{45} + 18 q^{46} + 2 q^{48} + 10 q^{49} - 8 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 48 q^{59} - 20 q^{61} - 12 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{65} + 12 q^{66} - 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} + 4 q^{75} - 6 q^{76} - 48 q^{77} - 12 q^{78} - 8 q^{79} + 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{84} - 6 q^{87} - 6 q^{88} - 12 q^{89} + 36 q^{91} - 12 q^{92} - 12 q^{93} - 6 q^{94} + 6 q^{95} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.73205i 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 1.09808 0.633975i 0.415034 0.239620i −0.277916 0.960605i \(-0.589644\pi\)
0.692950 + 0.720985i \(0.256311\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.866025 + 1.50000i −0.273861 + 0.474342i
\(11\) −1.09808 0.633975i −0.331082 0.191151i 0.325239 0.945632i \(-0.394555\pi\)
−0.656322 + 0.754481i \(0.727889\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.59808 + 3.23205i 0.443227 + 0.896410i
\(14\) −1.26795 −0.338874
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.59808 + 4.50000i 0.630126 + 1.09141i 0.987526 + 0.157459i \(0.0503301\pi\)
−0.357400 + 0.933952i \(0.616337\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −4.09808 + 2.36603i −0.940163 + 0.542803i −0.890011 0.455938i \(-0.849304\pi\)
−0.0501517 + 0.998742i \(0.515970\pi\)
\(20\) 1.50000 0.866025i 0.335410 0.193649i
\(21\) 1.26795i 0.276689i
\(22\) 0.633975 + 1.09808i 0.135164 + 0.234111i
\(23\) −4.09808 + 7.09808i −0.854508 + 1.48005i 0.0225928 + 0.999745i \(0.492808\pi\)
−0.877101 + 0.480306i \(0.840525\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 2.00000 0.400000
\(26\) 0.232051 3.59808i 0.0455089 0.705641i
\(27\) −1.00000 −0.192450
\(28\) 1.09808 + 0.633975i 0.207517 + 0.119810i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0.866025 + 1.50000i 0.158114 + 0.273861i
\(31\) 9.46410i 1.69980i −0.526942 0.849901i \(-0.676661\pi\)
0.526942 0.849901i \(-0.323339\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −1.09808 + 0.633975i −0.191151 + 0.110361i
\(34\) 5.19615i 0.891133i
\(35\) −1.09808 1.90192i −0.185609 0.321484i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −2.59808 1.50000i −0.427121 0.246598i 0.270998 0.962580i \(-0.412646\pi\)
−0.698119 + 0.715981i \(0.745980\pi\)
\(38\) 4.73205 0.767640
\(39\) 3.59808 + 0.232051i 0.576153 + 0.0371579i
\(40\) −1.73205 −0.273861
\(41\) 5.59808 + 3.23205i 0.874273 + 0.504762i 0.868766 0.495223i \(-0.164914\pi\)
0.00550690 + 0.999985i \(0.498247\pi\)
\(42\) −0.633975 + 1.09808i −0.0978244 + 0.169437i
\(43\) −2.09808 3.63397i −0.319954 0.554176i 0.660524 0.750805i \(-0.270334\pi\)
−0.980478 + 0.196629i \(0.937001\pi\)
\(44\) 1.26795i 0.191151i
\(45\) −1.50000 + 0.866025i −0.223607 + 0.129099i
\(46\) 7.09808 4.09808i 1.04655 0.604228i
\(47\) 4.73205i 0.690241i −0.938558 0.345120i \(-0.887838\pi\)
0.938558 0.345120i \(-0.112162\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −2.69615 + 4.66987i −0.385165 + 0.667125i
\(50\) −1.73205 1.00000i −0.244949 0.141421i
\(51\) 5.19615 0.727607
\(52\) −2.00000 + 3.00000i −0.277350 + 0.416025i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) −1.09808 + 1.90192i −0.148065 + 0.256455i
\(56\) −0.633975 1.09808i −0.0847184 0.146737i
\(57\) 4.73205i 0.626775i
\(58\) −2.59808 + 1.50000i −0.341144 + 0.196960i
\(59\) −12.0000 + 6.92820i −1.56227 + 0.901975i −0.565240 + 0.824927i \(0.691216\pi\)
−0.997027 + 0.0770484i \(0.975450\pi\)
\(60\) 1.73205i 0.223607i
\(61\) −7.59808 13.1603i −0.972834 1.68500i −0.686905 0.726747i \(-0.741031\pi\)
−0.285929 0.958251i \(-0.592302\pi\)
\(62\) −4.73205 + 8.19615i −0.600971 + 1.04091i
\(63\) −1.09808 0.633975i −0.138345 0.0798733i
\(64\) −1.00000 −0.125000
\(65\) 5.59808 2.76795i 0.694356 0.343322i
\(66\) 1.26795 0.156074
\(67\) 6.29423 + 3.63397i 0.768962 + 0.443961i 0.832504 0.554019i \(-0.186906\pi\)
−0.0635419 + 0.997979i \(0.520240\pi\)
\(68\) −2.59808 + 4.50000i −0.315063 + 0.545705i
\(69\) 4.09808 + 7.09808i 0.493350 + 0.854508i
\(70\) 2.19615i 0.262490i
\(71\) 1.90192 1.09808i 0.225717 0.130318i −0.382878 0.923799i \(-0.625067\pi\)
0.608595 + 0.793481i \(0.291734\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 12.1244i 1.41905i 0.704681 + 0.709524i \(0.251090\pi\)
−0.704681 + 0.709524i \(0.748910\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) 1.00000 1.73205i 0.115470 0.200000i
\(76\) −4.09808 2.36603i −0.470082 0.271402i
\(77\) −1.60770 −0.183214
\(78\) −3.00000 2.00000i −0.339683 0.226455i
\(79\) 8.39230 0.944208 0.472104 0.881543i \(-0.343495\pi\)
0.472104 + 0.881543i \(0.343495\pi\)
\(80\) 1.50000 + 0.866025i 0.167705 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.23205 5.59808i −0.356920 0.618204i
\(83\) 5.66025i 0.621294i −0.950525 0.310647i \(-0.899454\pi\)
0.950525 0.310647i \(-0.100546\pi\)
\(84\) 1.09808 0.633975i 0.119810 0.0691723i
\(85\) 7.79423 4.50000i 0.845403 0.488094i
\(86\) 4.19615i 0.452483i
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) −0.633975 + 1.09808i −0.0675819 + 0.117055i
\(89\) −8.19615 4.73205i −0.868790 0.501596i −0.00184433 0.999998i \(-0.500587\pi\)
−0.866946 + 0.498402i \(0.833920\pi\)
\(90\) 1.73205 0.182574
\(91\) 3.80385 + 2.53590i 0.398752 + 0.265834i
\(92\) −8.19615 −0.854508
\(93\) −8.19615 4.73205i −0.849901 0.490691i
\(94\) −2.36603 + 4.09808i −0.244037 + 0.422684i
\(95\) 4.09808 + 7.09808i 0.420454 + 0.728247i
\(96\) 1.00000i 0.102062i
\(97\) −5.19615 + 3.00000i −0.527589 + 0.304604i −0.740034 0.672569i \(-0.765191\pi\)
0.212445 + 0.977173i \(0.431857\pi\)
\(98\) 4.66987 2.69615i 0.471728 0.272353i
\(99\) 1.26795i 0.127434i
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 9.69615 16.7942i 0.964803 1.67109i 0.254660 0.967031i \(-0.418036\pi\)
0.710143 0.704058i \(-0.248630\pi\)
\(102\) −4.50000 2.59808i −0.445566 0.257248i
\(103\) −6.19615 −0.610525 −0.305263 0.952268i \(-0.598744\pi\)
−0.305263 + 0.952268i \(0.598744\pi\)
\(104\) 3.23205 1.59808i 0.316929 0.156704i
\(105\) −2.19615 −0.214323
\(106\) −2.59808 1.50000i −0.252347 0.145693i
\(107\) 1.09808 1.90192i 0.106155 0.183866i −0.808054 0.589108i \(-0.799479\pi\)
0.914210 + 0.405242i \(0.132813\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 4.39230i 0.420707i 0.977625 + 0.210353i \(0.0674614\pi\)
−0.977625 + 0.210353i \(0.932539\pi\)
\(110\) 1.90192 1.09808i 0.181341 0.104697i
\(111\) −2.59808 + 1.50000i −0.246598 + 0.142374i
\(112\) 1.26795i 0.119810i
\(113\) −0.401924 0.696152i −0.0378098 0.0654885i 0.846501 0.532387i \(-0.178705\pi\)
−0.884311 + 0.466898i \(0.845371\pi\)
\(114\) 2.36603 4.09808i 0.221599 0.383820i
\(115\) 12.2942 + 7.09808i 1.14644 + 0.661899i
\(116\) 3.00000 0.278543
\(117\) 2.00000 3.00000i 0.184900 0.277350i
\(118\) 13.8564 1.27559
\(119\) 5.70577 + 3.29423i 0.523047 + 0.301981i
\(120\) −0.866025 + 1.50000i −0.0790569 + 0.136931i
\(121\) −4.69615 8.13397i −0.426923 0.739452i
\(122\) 15.1962i 1.37579i
\(123\) 5.59808 3.23205i 0.504762 0.291424i
\(124\) 8.19615 4.73205i 0.736036 0.424951i
\(125\) 12.1244i 1.08444i
\(126\) 0.633975 + 1.09808i 0.0564789 + 0.0978244i
\(127\) −2.00000 + 3.46410i −0.177471 + 0.307389i −0.941014 0.338368i \(-0.890125\pi\)
0.763542 + 0.645758i \(0.223458\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −4.19615 −0.369451
\(130\) −6.23205 0.401924i −0.546587 0.0352510i
\(131\) −4.39230 −0.383757 −0.191879 0.981419i \(-0.561458\pi\)
−0.191879 + 0.981419i \(0.561458\pi\)
\(132\) −1.09808 0.633975i −0.0955753 0.0551804i
\(133\) −3.00000 + 5.19615i −0.260133 + 0.450564i
\(134\) −3.63397 6.29423i −0.313928 0.543739i
\(135\) 1.73205i 0.149071i
\(136\) 4.50000 2.59808i 0.385872 0.222783i
\(137\) −7.79423 + 4.50000i −0.665906 + 0.384461i −0.794524 0.607233i \(-0.792279\pi\)
0.128618 + 0.991694i \(0.458946\pi\)
\(138\) 8.19615i 0.697703i
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 1.09808 1.90192i 0.0928044 0.160742i
\(141\) −4.09808 2.36603i −0.345120 0.199255i
\(142\) −2.19615 −0.184297
\(143\) 0.294229 4.56218i 0.0246046 0.381508i
\(144\) 1.00000 0.0833333
\(145\) −4.50000 2.59808i −0.373705 0.215758i
\(146\) 6.06218 10.5000i 0.501709 0.868986i
\(147\) 2.69615 + 4.66987i 0.222375 + 0.385165i
\(148\) 3.00000i 0.246598i
\(149\) −5.30385 + 3.06218i −0.434508 + 0.250863i −0.701265 0.712900i \(-0.747381\pi\)
0.266757 + 0.963764i \(0.414048\pi\)
\(150\) −1.73205 + 1.00000i −0.141421 + 0.0816497i
\(151\) 10.7321i 0.873362i 0.899616 + 0.436681i \(0.143846\pi\)
−0.899616 + 0.436681i \(0.856154\pi\)
\(152\) 2.36603 + 4.09808i 0.191910 + 0.332398i
\(153\) 2.59808 4.50000i 0.210042 0.363803i
\(154\) 1.39230 + 0.803848i 0.112195 + 0.0647759i
\(155\) −16.3923 −1.31666
\(156\) 1.59808 + 3.23205i 0.127948 + 0.258771i
\(157\) 7.19615 0.574315 0.287158 0.957883i \(-0.407290\pi\)
0.287158 + 0.957883i \(0.407290\pi\)
\(158\) −7.26795 4.19615i −0.578207 0.333828i
\(159\) 1.50000 2.59808i 0.118958 0.206041i
\(160\) −0.866025 1.50000i −0.0684653 0.118585i
\(161\) 10.3923i 0.819028i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 2.19615 1.26795i 0.172016 0.0993134i −0.411520 0.911401i \(-0.635002\pi\)
0.583536 + 0.812087i \(0.301669\pi\)
\(164\) 6.46410i 0.504762i
\(165\) 1.09808 + 1.90192i 0.0854851 + 0.148065i
\(166\) −2.83013 + 4.90192i −0.219660 + 0.380463i
\(167\) 8.19615 + 4.73205i 0.634237 + 0.366177i 0.782391 0.622787i \(-0.214000\pi\)
−0.148154 + 0.988964i \(0.547333\pi\)
\(168\) −1.26795 −0.0978244
\(169\) −7.89230 + 10.3301i −0.607100 + 0.794625i
\(170\) −9.00000 −0.690268
\(171\) 4.09808 + 2.36603i 0.313388 + 0.180934i
\(172\) 2.09808 3.63397i 0.159977 0.277088i
\(173\) −2.19615 3.80385i −0.166970 0.289201i 0.770383 0.637582i \(-0.220065\pi\)
−0.937353 + 0.348380i \(0.886732\pi\)
\(174\) 3.00000i 0.227429i
\(175\) 2.19615 1.26795i 0.166014 0.0958479i
\(176\) 1.09808 0.633975i 0.0827706 0.0477876i
\(177\) 13.8564i 1.04151i
\(178\) 4.73205 + 8.19615i 0.354682 + 0.614328i
\(179\) 1.09808 1.90192i 0.0820741 0.142156i −0.822067 0.569391i \(-0.807179\pi\)
0.904141 + 0.427235i \(0.140512\pi\)
\(180\) −1.50000 0.866025i −0.111803 0.0645497i
\(181\) −19.5885 −1.45600 −0.727999 0.685578i \(-0.759550\pi\)
−0.727999 + 0.685578i \(0.759550\pi\)
\(182\) −2.02628 4.09808i −0.150198 0.303770i
\(183\) −15.1962 −1.12333
\(184\) 7.09808 + 4.09808i 0.523277 + 0.302114i
\(185\) −2.59808 + 4.50000i −0.191014 + 0.330847i
\(186\) 4.73205 + 8.19615i 0.346971 + 0.600971i
\(187\) 6.58846i 0.481796i
\(188\) 4.09808 2.36603i 0.298883 0.172560i
\(189\) −1.09808 + 0.633975i −0.0798733 + 0.0461149i
\(190\) 8.19615i 0.594611i
\(191\) 10.3923 + 18.0000i 0.751961 + 1.30243i 0.946871 + 0.321613i \(0.104225\pi\)
−0.194910 + 0.980821i \(0.562442\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 20.0885 + 11.5981i 1.44600 + 0.834848i 0.998240 0.0593065i \(-0.0188889\pi\)
0.447759 + 0.894154i \(0.352222\pi\)
\(194\) 6.00000 0.430775
\(195\) 0.401924 6.23205i 0.0287824 0.446286i
\(196\) −5.39230 −0.385165
\(197\) −6.00000 3.46410i −0.427482 0.246807i 0.270791 0.962638i \(-0.412715\pi\)
−0.698273 + 0.715831i \(0.746048\pi\)
\(198\) 0.633975 1.09808i 0.0450546 0.0780369i
\(199\) −11.2942 19.5622i −0.800627 1.38673i −0.919204 0.393781i \(-0.871167\pi\)
0.118578 0.992945i \(-0.462167\pi\)
\(200\) 2.00000i 0.141421i
\(201\) 6.29423 3.63397i 0.443961 0.256321i
\(202\) −16.7942 + 9.69615i −1.18164 + 0.682219i
\(203\) 3.80385i 0.266978i
\(204\) 2.59808 + 4.50000i 0.181902 + 0.315063i
\(205\) 5.59808 9.69615i 0.390987 0.677209i
\(206\) 5.36603 + 3.09808i 0.373869 + 0.215853i
\(207\) 8.19615 0.569672
\(208\) −3.59808 0.232051i −0.249482 0.0160898i
\(209\) 6.00000 0.415029
\(210\) 1.90192 + 1.09808i 0.131245 + 0.0757745i
\(211\) 12.1962 21.1244i 0.839618 1.45426i −0.0505968 0.998719i \(-0.516112\pi\)
0.890215 0.455541i \(-0.150554\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 2.19615i 0.150478i
\(214\) −1.90192 + 1.09808i −0.130013 + 0.0750629i
\(215\) −6.29423 + 3.63397i −0.429263 + 0.247835i
\(216\) 1.00000i 0.0680414i
\(217\) −6.00000 10.3923i −0.407307 0.705476i
\(218\) 2.19615 3.80385i 0.148742 0.257629i
\(219\) 10.5000 + 6.06218i 0.709524 + 0.409644i
\(220\) −2.19615 −0.148065
\(221\) −10.3923 + 15.5885i −0.699062 + 1.04859i
\(222\) 3.00000 0.201347
\(223\) −4.39230 2.53590i −0.294130 0.169816i 0.345673 0.938355i \(-0.387651\pi\)
−0.639803 + 0.768539i \(0.720984\pi\)
\(224\) 0.633975 1.09808i 0.0423592 0.0733683i
\(225\) −1.00000 1.73205i −0.0666667 0.115470i
\(226\) 0.803848i 0.0534711i
\(227\) 17.4904 10.0981i 1.16088 0.670233i 0.209363 0.977838i \(-0.432861\pi\)
0.951514 + 0.307605i \(0.0995276\pi\)
\(228\) −4.09808 + 2.36603i −0.271402 + 0.156694i
\(229\) 7.85641i 0.519166i −0.965721 0.259583i \(-0.916415\pi\)
0.965721 0.259583i \(-0.0835851\pi\)
\(230\) −7.09808 12.2942i −0.468033 0.810657i
\(231\) −0.803848 + 1.39230i −0.0528893 + 0.0916069i
\(232\) −2.59808 1.50000i −0.170572 0.0984798i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) −3.23205 + 1.59808i −0.211286 + 0.104470i
\(235\) −8.19615 −0.534658
\(236\) −12.0000 6.92820i −0.781133 0.450988i
\(237\) 4.19615 7.26795i 0.272569 0.472104i
\(238\) −3.29423 5.70577i −0.213533 0.369850i
\(239\) 6.58846i 0.426172i −0.977033 0.213086i \(-0.931649\pi\)
0.977033 0.213086i \(-0.0683514\pi\)
\(240\) 1.50000 0.866025i 0.0968246 0.0559017i
\(241\) 9.69615 5.59808i 0.624584 0.360604i −0.154068 0.988060i \(-0.549237\pi\)
0.778652 + 0.627457i \(0.215904\pi\)
\(242\) 9.39230i 0.603760i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 7.59808 13.1603i 0.486417 0.842499i
\(245\) 8.08846 + 4.66987i 0.516753 + 0.298347i
\(246\) −6.46410 −0.412136
\(247\) −14.1962 9.46410i −0.903280 0.602186i
\(248\) −9.46410 −0.600971
\(249\) −4.90192 2.83013i −0.310647 0.179352i
\(250\) −6.06218 + 10.5000i −0.383406 + 0.664078i
\(251\) 8.19615 + 14.1962i 0.517337 + 0.896053i 0.999797 + 0.0201356i \(0.00640979\pi\)
−0.482461 + 0.875918i \(0.660257\pi\)
\(252\) 1.26795i 0.0798733i
\(253\) 9.00000 5.19615i 0.565825 0.326679i
\(254\) 3.46410 2.00000i 0.217357 0.125491i
\(255\) 9.00000i 0.563602i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 11.5981 20.0885i 0.723468 1.25308i −0.236133 0.971721i \(-0.575880\pi\)
0.959601 0.281363i \(-0.0907865\pi\)
\(258\) 3.63397 + 2.09808i 0.226241 + 0.130621i
\(259\) −3.80385 −0.236360
\(260\) 5.19615 + 3.46410i 0.322252 + 0.214834i
\(261\) −3.00000 −0.185695
\(262\) 3.80385 + 2.19615i 0.235002 + 0.135679i
\(263\) −4.09808 + 7.09808i −0.252698 + 0.437686i −0.964268 0.264930i \(-0.914651\pi\)
0.711570 + 0.702616i \(0.247985\pi\)
\(264\) 0.633975 + 1.09808i 0.0390184 + 0.0675819i
\(265\) 5.19615i 0.319197i
\(266\) 5.19615 3.00000i 0.318597 0.183942i
\(267\) −8.19615 + 4.73205i −0.501596 + 0.289597i
\(268\) 7.26795i 0.443961i
\(269\) 3.80385 + 6.58846i 0.231925 + 0.401705i 0.958374 0.285514i \(-0.0921644\pi\)
−0.726450 + 0.687220i \(0.758831\pi\)
\(270\) 0.866025 1.50000i 0.0527046 0.0912871i
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) −5.19615 −0.315063
\(273\) 4.09808 2.02628i 0.248027 0.122636i
\(274\) 9.00000 0.543710
\(275\) −2.19615 1.26795i −0.132433 0.0764602i
\(276\) −4.09808 + 7.09808i −0.246675 + 0.427254i
\(277\) 2.40192 + 4.16025i 0.144318 + 0.249965i 0.929118 0.369783i \(-0.120568\pi\)
−0.784801 + 0.619748i \(0.787235\pi\)
\(278\) 4.00000i 0.239904i
\(279\) −8.19615 + 4.73205i −0.490691 + 0.283300i
\(280\) −1.90192 + 1.09808i −0.113662 + 0.0656226i
\(281\) 17.5359i 1.04610i 0.852301 + 0.523052i \(0.175207\pi\)
−0.852301 + 0.523052i \(0.824793\pi\)
\(282\) 2.36603 + 4.09808i 0.140895 + 0.244037i
\(283\) −9.90192 + 17.1506i −0.588608 + 1.01950i 0.405807 + 0.913959i \(0.366991\pi\)
−0.994415 + 0.105541i \(0.966343\pi\)
\(284\) 1.90192 + 1.09808i 0.112858 + 0.0651588i
\(285\) 8.19615 0.485498
\(286\) −2.53590 + 3.80385i −0.149951 + 0.224926i
\(287\) 8.19615 0.483804
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) −5.00000 + 8.66025i −0.294118 + 0.509427i
\(290\) 2.59808 + 4.50000i 0.152564 + 0.264249i
\(291\) 6.00000i 0.351726i
\(292\) −10.5000 + 6.06218i −0.614466 + 0.354762i
\(293\) 2.30385 1.33013i 0.134592 0.0777069i −0.431192 0.902260i \(-0.641907\pi\)
0.565784 + 0.824553i \(0.308574\pi\)
\(294\) 5.39230i 0.314486i
\(295\) 12.0000 + 20.7846i 0.698667 + 1.21013i
\(296\) −1.50000 + 2.59808i −0.0871857 + 0.151010i
\(297\) 1.09808 + 0.633975i 0.0637168 + 0.0367869i
\(298\) 6.12436 0.354774
\(299\) −29.4904 1.90192i −1.70547 0.109991i
\(300\) 2.00000 0.115470
\(301\) −4.60770 2.66025i −0.265583 0.153334i
\(302\) 5.36603 9.29423i 0.308780 0.534823i
\(303\) −9.69615 16.7942i −0.557029 0.964803i
\(304\) 4.73205i 0.271402i
\(305\) −22.7942 + 13.1603i −1.30519 + 0.753554i
\(306\) −4.50000 + 2.59808i −0.257248 + 0.148522i
\(307\) 7.26795i 0.414804i 0.978256 + 0.207402i \(0.0665008\pi\)
−0.978256 + 0.207402i \(0.933499\pi\)
\(308\) −0.803848 1.39230i −0.0458035 0.0793339i
\(309\) −3.09808 + 5.36603i −0.176243 + 0.305263i
\(310\) 14.1962 + 8.19615i 0.806287 + 0.465510i
\(311\) 8.19615 0.464761 0.232381 0.972625i \(-0.425349\pi\)
0.232381 + 0.972625i \(0.425349\pi\)
\(312\) 0.232051 3.59808i 0.0131373 0.203701i
\(313\) −3.60770 −0.203919 −0.101959 0.994789i \(-0.532511\pi\)
−0.101959 + 0.994789i \(0.532511\pi\)
\(314\) −6.23205 3.59808i −0.351695 0.203051i
\(315\) −1.09808 + 1.90192i −0.0618696 + 0.107161i
\(316\) 4.19615 + 7.26795i 0.236052 + 0.408854i
\(317\) 18.1244i 1.01797i 0.860777 + 0.508983i \(0.169978\pi\)
−0.860777 + 0.508983i \(0.830022\pi\)
\(318\) −2.59808 + 1.50000i −0.145693 + 0.0841158i
\(319\) −3.29423 + 1.90192i −0.184441 + 0.106487i
\(320\) 1.73205i 0.0968246i
\(321\) −1.09808 1.90192i −0.0612886 0.106155i
\(322\) 5.19615 9.00000i 0.289570 0.501550i
\(323\) −21.2942 12.2942i −1.18484 0.684069i
\(324\) −1.00000 −0.0555556
\(325\) 3.19615 + 6.46410i 0.177291 + 0.358564i
\(326\) −2.53590 −0.140450
\(327\) 3.80385 + 2.19615i 0.210353 + 0.121448i
\(328\) 3.23205 5.59808i 0.178460 0.309102i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 2.19615i 0.120894i
\(331\) −10.3923 + 6.00000i −0.571213 + 0.329790i −0.757634 0.652680i \(-0.773645\pi\)
0.186421 + 0.982470i \(0.440311\pi\)
\(332\) 4.90192 2.83013i 0.269028 0.155323i
\(333\) 3.00000i 0.164399i
\(334\) −4.73205 8.19615i −0.258926 0.448474i
\(335\) 6.29423 10.9019i 0.343890 0.595636i
\(336\) 1.09808 + 0.633975i 0.0599050 + 0.0345861i
\(337\) 31.0000 1.68868 0.844339 0.535810i \(-0.179994\pi\)
0.844339 + 0.535810i \(0.179994\pi\)
\(338\) 12.0000 5.00000i 0.652714 0.271964i
\(339\) −0.803848 −0.0436590
\(340\) 7.79423 + 4.50000i 0.422701 + 0.244047i
\(341\) −6.00000 + 10.3923i −0.324918 + 0.562775i
\(342\) −2.36603 4.09808i −0.127940 0.221599i
\(343\) 15.7128i 0.848412i
\(344\) −3.63397 + 2.09808i −0.195931 + 0.113121i
\(345\) 12.2942 7.09808i 0.661899 0.382148i
\(346\) 4.39230i 0.236132i
\(347\) −9.29423 16.0981i −0.498940 0.864190i 0.501059 0.865413i \(-0.332944\pi\)
−0.999999 + 0.00122316i \(0.999611\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) −8.19615 4.73205i −0.438730 0.253301i 0.264329 0.964433i \(-0.414850\pi\)
−0.703059 + 0.711132i \(0.748183\pi\)
\(350\) −2.53590 −0.135549
\(351\) −1.59808 3.23205i −0.0852990 0.172514i
\(352\) −1.26795 −0.0675819
\(353\) −30.9904 17.8923i −1.64945 0.952311i −0.977290 0.211907i \(-0.932033\pi\)
−0.672162 0.740404i \(-0.734634\pi\)
\(354\) 6.92820 12.0000i 0.368230 0.637793i
\(355\) −1.90192 3.29423i −0.100944 0.174840i
\(356\) 9.46410i 0.501596i
\(357\) 5.70577 3.29423i 0.301981 0.174349i
\(358\) −1.90192 + 1.09808i −0.100520 + 0.0580351i
\(359\) 16.0526i 0.847222i −0.905844 0.423611i \(-0.860762\pi\)
0.905844 0.423611i \(-0.139238\pi\)
\(360\) 0.866025 + 1.50000i 0.0456435 + 0.0790569i
\(361\) 1.69615 2.93782i 0.0892712 0.154622i
\(362\) 16.9641 + 9.79423i 0.891613 + 0.514773i
\(363\) −9.39230 −0.492968
\(364\) −0.294229 + 4.56218i −0.0154218 + 0.239123i
\(365\) 21.0000 1.09919
\(366\) 13.1603 + 7.59808i 0.687897 + 0.397158i
\(367\) 6.90192 11.9545i 0.360277 0.624019i −0.627729 0.778432i \(-0.716015\pi\)
0.988006 + 0.154413i \(0.0493487\pi\)
\(368\) −4.09808 7.09808i −0.213627 0.370013i
\(369\) 6.46410i 0.336508i
\(370\) 4.50000 2.59808i 0.233944 0.135068i
\(371\) 3.29423 1.90192i 0.171028 0.0987430i
\(372\) 9.46410i 0.490691i
\(373\) 13.9904 + 24.2321i 0.724394 + 1.25469i 0.959223 + 0.282651i \(0.0912139\pi\)
−0.234828 + 0.972037i \(0.575453\pi\)
\(374\) −3.29423 + 5.70577i −0.170341 + 0.295038i
\(375\) −10.5000 6.06218i −0.542218 0.313050i
\(376\) −4.73205 −0.244037
\(377\) 10.7942 + 0.696152i 0.555931 + 0.0358537i
\(378\) 1.26795 0.0652163
\(379\) 26.1962 + 15.1244i 1.34561 + 0.776886i 0.987624 0.156842i \(-0.0501315\pi\)
0.357982 + 0.933728i \(0.383465\pi\)
\(380\) −4.09808 + 7.09808i −0.210227 + 0.364124i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) 20.7846i 1.06343i
\(383\) 20.1962 11.6603i 1.03198 0.595811i 0.114425 0.993432i \(-0.463497\pi\)
0.917550 + 0.397621i \(0.130164\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 2.78461i 0.141917i
\(386\) −11.5981 20.0885i −0.590327 1.02248i
\(387\) −2.09808 + 3.63397i −0.106651 + 0.184725i
\(388\) −5.19615 3.00000i −0.263795 0.152302i
\(389\) −7.39230 −0.374805 −0.187402 0.982283i \(-0.560007\pi\)
−0.187402 + 0.982283i \(0.560007\pi\)
\(390\) −3.46410 + 5.19615i −0.175412 + 0.263117i
\(391\) −42.5885 −2.15379
\(392\) 4.66987 + 2.69615i 0.235864 + 0.136176i
\(393\) −2.19615 + 3.80385i −0.110781 + 0.191879i
\(394\) 3.46410 + 6.00000i 0.174519 + 0.302276i
\(395\) 14.5359i 0.731380i
\(396\) −1.09808 + 0.633975i −0.0551804 + 0.0318584i
\(397\) 3.80385 2.19615i 0.190910 0.110222i −0.401499 0.915860i \(-0.631511\pi\)
0.592408 + 0.805638i \(0.298177\pi\)
\(398\) 22.5885i 1.13226i
\(399\) 3.00000 + 5.19615i 0.150188 + 0.260133i
\(400\) −1.00000 + 1.73205i −0.0500000 + 0.0866025i
\(401\) −18.1865 10.5000i −0.908192 0.524345i −0.0283431 0.999598i \(-0.509023\pi\)
−0.879849 + 0.475253i \(0.842356\pi\)
\(402\) −7.26795 −0.362492
\(403\) 30.5885 15.1244i 1.52372 0.753398i
\(404\) 19.3923 0.964803
\(405\) 1.50000 + 0.866025i 0.0745356 + 0.0430331i
\(406\) −1.90192 + 3.29423i −0.0943909 + 0.163490i
\(407\) 1.90192 + 3.29423i 0.0942749 + 0.163289i
\(408\) 5.19615i 0.257248i
\(409\) 17.8923 10.3301i 0.884718 0.510792i 0.0125066 0.999922i \(-0.496019\pi\)
0.872211 + 0.489130i \(0.162686\pi\)
\(410\) −9.69615 + 5.59808i −0.478859 + 0.276469i
\(411\) 9.00000i 0.443937i
\(412\) −3.09808 5.36603i −0.152631 0.264365i
\(413\) −8.78461 + 15.2154i −0.432262 + 0.748700i
\(414\) −7.09808 4.09808i −0.348851 0.201409i
\(415\) −9.80385 −0.481252
\(416\) 3.00000 + 2.00000i 0.147087 + 0.0980581i
\(417\) 4.00000 0.195881
\(418\) −5.19615 3.00000i −0.254152 0.146735i
\(419\) 2.19615 3.80385i 0.107289 0.185830i −0.807382 0.590029i \(-0.799116\pi\)
0.914671 + 0.404199i \(0.132450\pi\)
\(420\) −1.09808 1.90192i −0.0535806 0.0928044i
\(421\) 6.46410i 0.315041i 0.987516 + 0.157521i \(0.0503500\pi\)
−0.987516 + 0.157521i \(0.949650\pi\)
\(422\) −21.1244 + 12.1962i −1.02832 + 0.593699i
\(423\) −4.09808 + 2.36603i −0.199255 + 0.115040i
\(424\) 3.00000i 0.145693i
\(425\) 5.19615 + 9.00000i 0.252050 + 0.436564i
\(426\) −1.09808 + 1.90192i −0.0532020 + 0.0921485i
\(427\) −16.6865 9.63397i −0.807518 0.466221i
\(428\) 2.19615 0.106155
\(429\) −3.80385 2.53590i −0.183651 0.122434i
\(430\) 7.26795 0.350492
\(431\) 33.0788 + 19.0981i 1.59335 + 0.919922i 0.992727 + 0.120391i \(0.0384149\pi\)
0.600625 + 0.799531i \(0.294918\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 3.89230 + 6.74167i 0.187052 + 0.323984i 0.944266 0.329183i \(-0.106773\pi\)
−0.757214 + 0.653167i \(0.773440\pi\)
\(434\) 12.0000i 0.576018i
\(435\) −4.50000 + 2.59808i −0.215758 + 0.124568i
\(436\) −3.80385 + 2.19615i −0.182171 + 0.105177i
\(437\) 38.7846i 1.85532i
\(438\) −6.06218 10.5000i −0.289662 0.501709i
\(439\) −7.29423 + 12.6340i −0.348135 + 0.602987i −0.985918 0.167229i \(-0.946518\pi\)
0.637784 + 0.770216i \(0.279851\pi\)
\(440\) 1.90192 + 1.09808i 0.0906707 + 0.0523487i
\(441\) 5.39230 0.256776
\(442\) 16.7942 8.30385i 0.798820 0.394974i
\(443\) 16.3923 0.778822 0.389411 0.921064i \(-0.372679\pi\)
0.389411 + 0.921064i \(0.372679\pi\)
\(444\) −2.59808 1.50000i −0.123299 0.0711868i
\(445\) −8.19615 + 14.1962i −0.388535 + 0.672962i
\(446\) 2.53590 + 4.39230i 0.120078 + 0.207982i
\(447\) 6.12436i 0.289672i
\(448\) −1.09808 + 0.633975i −0.0518792 + 0.0299525i
\(449\) 22.9808 13.2679i 1.08453 0.626153i 0.152415 0.988317i \(-0.451295\pi\)
0.932115 + 0.362163i \(0.117962\pi\)
\(450\) 2.00000i 0.0942809i
\(451\) −4.09808 7.09808i −0.192971 0.334235i
\(452\) 0.401924 0.696152i 0.0189049 0.0327443i
\(453\) 9.29423 + 5.36603i 0.436681 + 0.252118i
\(454\) −20.1962 −0.947852
\(455\) 4.39230 6.58846i 0.205914 0.308872i
\(456\) 4.73205 0.221599
\(457\) −27.6962 15.9904i −1.29557 0.747998i −0.315935 0.948781i \(-0.602318\pi\)
−0.979636 + 0.200782i \(0.935652\pi\)
\(458\) −3.92820 + 6.80385i −0.183553 + 0.317923i
\(459\) −2.59808 4.50000i −0.121268 0.210042i
\(460\) 14.1962i 0.661899i
\(461\) −27.6962 + 15.9904i −1.28994 + 0.744746i −0.978643 0.205567i \(-0.934096\pi\)
−0.311295 + 0.950313i \(0.600763\pi\)
\(462\) 1.39230 0.803848i 0.0647759 0.0373984i
\(463\) 15.8038i 0.734467i −0.930129 0.367234i \(-0.880305\pi\)
0.930129 0.367234i \(-0.119695\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) −8.19615 + 14.1962i −0.380087 + 0.658331i
\(466\) −15.5885 9.00000i −0.722121 0.416917i
\(467\) −5.41154 −0.250416 −0.125208 0.992130i \(-0.539960\pi\)
−0.125208 + 0.992130i \(0.539960\pi\)
\(468\) 3.59808 + 0.232051i 0.166321 + 0.0107266i
\(469\) 9.21539 0.425527
\(470\) 7.09808 + 4.09808i 0.327410 + 0.189030i
\(471\) 3.59808 6.23205i 0.165791 0.287158i
\(472\) 6.92820 + 12.0000i 0.318896 + 0.552345i
\(473\) 5.32051i 0.244637i
\(474\) −7.26795 + 4.19615i −0.333828 + 0.192736i
\(475\) −8.19615 + 4.73205i −0.376065 + 0.217121i
\(476\) 6.58846i 0.301981i
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) −3.29423 + 5.70577i −0.150675 + 0.260976i
\(479\) 0.588457 + 0.339746i 0.0268873 + 0.0155234i 0.513383 0.858159i \(-0.328392\pi\)
−0.486496 + 0.873683i \(0.661725\pi\)
\(480\) −1.73205 −0.0790569
\(481\) 0.696152 10.7942i 0.0317418 0.492174i
\(482\) −11.1962 −0.509971
\(483\) 9.00000 + 5.19615i 0.409514 + 0.236433i
\(484\) 4.69615 8.13397i 0.213461 0.369726i
\(485\) 5.19615 + 9.00000i 0.235945 + 0.408669i
\(486\) 1.00000i 0.0453609i
\(487\) 13.0981 7.56218i 0.593530 0.342675i −0.172962 0.984929i \(-0.555334\pi\)
0.766492 + 0.642254i \(0.222000\pi\)
\(488\) −13.1603 + 7.59808i −0.595737 + 0.343949i
\(489\) 2.53590i 0.114677i
\(490\) −4.66987 8.08846i −0.210963 0.365399i
\(491\) −15.2942 + 26.4904i −0.690219 + 1.19549i 0.281547 + 0.959547i \(0.409152\pi\)
−0.971766 + 0.235947i \(0.924181\pi\)
\(492\) 5.59808 + 3.23205i 0.252381 + 0.145712i
\(493\) 15.5885 0.702069
\(494\) 7.56218 + 15.2942i 0.340238 + 0.688120i
\(495\) 2.19615 0.0987097
\(496\) 8.19615 + 4.73205i 0.368018 + 0.212475i
\(497\) 1.39230 2.41154i 0.0624534 0.108172i
\(498\) 2.83013 + 4.90192i 0.126821 + 0.219660i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 10.5000 6.06218i 0.469574 0.271109i
\(501\) 8.19615 4.73205i 0.366177 0.211412i
\(502\) 16.3923i 0.731624i
\(503\) −6.29423 10.9019i −0.280646 0.486093i 0.690898 0.722952i \(-0.257215\pi\)
−0.971544 + 0.236859i \(0.923882\pi\)
\(504\) −0.633975 + 1.09808i −0.0282395 + 0.0489122i
\(505\) −29.0885 16.7942i −1.29442 0.747333i
\(506\) −10.3923 −0.461994
\(507\) 5.00000 + 12.0000i 0.222058 + 0.532939i
\(508\) −4.00000 −0.177471
\(509\) 23.0885 + 13.3301i 1.02338 + 0.590847i 0.915081 0.403271i \(-0.132127\pi\)
0.108297 + 0.994119i \(0.465460\pi\)
\(510\) −4.50000 + 7.79423i −0.199263 + 0.345134i
\(511\) 7.68653 + 13.3135i 0.340032 + 0.588953i
\(512\) 1.00000i 0.0441942i
\(513\) 4.09808 2.36603i 0.180934 0.104463i
\(514\) −20.0885 + 11.5981i −0.886064 + 0.511569i
\(515\) 10.7321i 0.472911i
\(516\) −2.09808 3.63397i −0.0923627 0.159977i
\(517\) −3.00000 + 5.19615i −0.131940 + 0.228527i
\(518\) 3.29423 + 1.90192i 0.144740 + 0.0835657i
\(519\) −4.39230 −0.192801
\(520\) −2.76795 5.59808i −0.121383 0.245492i
\(521\) −29.1962 −1.27911 −0.639553 0.768747i \(-0.720881\pi\)
−0.639553 + 0.768747i \(0.720881\pi\)
\(522\) 2.59808 + 1.50000i 0.113715 + 0.0656532i
\(523\) −16.2942 + 28.2224i −0.712497 + 1.23408i 0.251420 + 0.967878i \(0.419102\pi\)
−0.963917 + 0.266203i \(0.914231\pi\)
\(524\) −2.19615 3.80385i −0.0959394 0.166172i
\(525\) 2.53590i 0.110676i
\(526\) 7.09808 4.09808i 0.309491 0.178685i
\(527\) 42.5885 24.5885i 1.85518 1.07109i
\(528\) 1.26795i 0.0551804i
\(529\) −22.0885 38.2583i −0.960368 1.66341i
\(530\) −2.59808 + 4.50000i −0.112853 + 0.195468i
\(531\) 12.0000 + 6.92820i 0.520756 + 0.300658i
\(532\) −6.00000 −0.260133
\(533\) −1.50000 + 23.2583i −0.0649722 + 1.00743i
\(534\) 9.46410 0.409552
\(535\) −3.29423 1.90192i −0.142422 0.0822273i
\(536\) 3.63397 6.29423i 0.156964 0.271869i
\(537\) −1.09808 1.90192i −0.0473855 0.0820741i
\(538\) 7.60770i 0.327991i
\(539\) 5.92116 3.41858i 0.255042 0.147249i
\(540\) −1.50000 + 0.866025i −0.0645497 + 0.0372678i
\(541\) 10.8564i 0.466753i −0.972386 0.233377i \(-0.925022\pi\)
0.972386 0.233377i \(-0.0749775\pi\)
\(542\) 0 0
\(543\) −9.79423 + 16.9641i −0.420311 + 0.727999i
\(544\) 4.50000 + 2.59808i 0.192936 + 0.111392i
\(545\) 7.60770 0.325878
\(546\) −4.56218 0.294229i −0.195243 0.0125918i
\(547\) 4.19615 0.179415 0.0897073 0.995968i \(-0.471407\pi\)
0.0897073 + 0.995968i \(0.471407\pi\)
\(548\) −7.79423 4.50000i −0.332953 0.192230i
\(549\) −7.59808 + 13.1603i −0.324278 + 0.561666i
\(550\) 1.26795 + 2.19615i 0.0540655 + 0.0936443i
\(551\) 14.1962i 0.604776i
\(552\) 7.09808 4.09808i 0.302114 0.174426i
\(553\) 9.21539 5.32051i 0.391878 0.226251i
\(554\) 4.80385i 0.204096i
\(555\) 2.59808 + 4.50000i 0.110282 + 0.191014i
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) −22.2846 12.8660i −0.944229 0.545151i −0.0529457 0.998597i \(-0.516861\pi\)
−0.891284 + 0.453446i \(0.850194\pi\)
\(558\) 9.46410 0.400647
\(559\) 8.39230 12.5885i 0.354957 0.532435i
\(560\) 2.19615 0.0928044
\(561\) −5.70577 3.29423i −0.240898 0.139082i
\(562\) 8.76795 15.1865i 0.369854 0.640605i
\(563\) −16.3923 28.3923i −0.690853 1.19659i −0.971559 0.236799i \(-0.923902\pi\)
0.280705 0.959794i \(-0.409432\pi\)
\(564\) 4.73205i 0.199255i
\(565\) −1.20577 + 0.696152i −0.0507272 + 0.0292874i
\(566\) 17.1506 9.90192i 0.720895 0.416209i
\(567\) 1.26795i 0.0532489i
\(568\) −1.09808 1.90192i −0.0460743 0.0798029i
\(569\) 4.39230 7.60770i 0.184135 0.318931i −0.759150 0.650916i \(-0.774385\pi\)
0.943285 + 0.331985i \(0.107718\pi\)
\(570\) −7.09808 4.09808i −0.297306 0.171650i
\(571\) 24.1962 1.01258 0.506289 0.862364i \(-0.331017\pi\)
0.506289 + 0.862364i \(0.331017\pi\)
\(572\) 4.09808 2.02628i 0.171349 0.0847230i
\(573\) 20.7846 0.868290
\(574\) −7.09808 4.09808i −0.296268 0.171050i
\(575\) −8.19615 + 14.1962i −0.341803 + 0.592020i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 19.7321i 0.821456i 0.911758 + 0.410728i \(0.134725\pi\)
−0.911758 + 0.410728i \(0.865275\pi\)
\(578\) 8.66025 5.00000i 0.360219 0.207973i
\(579\) 20.0885 11.5981i 0.834848 0.482000i
\(580\) 5.19615i 0.215758i
\(581\) −3.58846 6.21539i −0.148874 0.257858i
\(582\) 3.00000 5.19615i 0.124354 0.215387i
\(583\) −3.29423 1.90192i −0.136433 0.0787696i
\(584\) 12.1244 0.501709
\(585\) −5.19615 3.46410i −0.214834 0.143223i
\(586\) −2.66025 −0.109894
\(587\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) −2.69615 + 4.66987i −0.111187 + 0.192582i
\(589\) 22.3923 + 38.7846i 0.922659 + 1.59809i
\(590\) 24.0000i 0.988064i
\(591\) −6.00000 + 3.46410i −0.246807 + 0.142494i
\(592\) 2.59808 1.50000i 0.106780 0.0616496i
\(593\) 19.1436i 0.786133i −0.919510 0.393067i \(-0.871414\pi\)
0.919510 0.393067i \(-0.128586\pi\)
\(594\) −0.633975 1.09808i −0.0260123 0.0450546i
\(595\) 5.70577 9.88269i 0.233914 0.405151i
\(596\) −5.30385 3.06218i −0.217254 0.125432i
\(597\) −22.5885 −0.924484
\(598\) 24.5885 + 16.3923i 1.00550 + 0.670331i
\(599\) 16.3923 0.669771 0.334886 0.942259i \(-0.391302\pi\)
0.334886 + 0.942259i \(0.391302\pi\)
\(600\) −1.73205 1.00000i −0.0707107 0.0408248i
\(601\) 9.89230 17.1340i 0.403516 0.698909i −0.590632 0.806941i \(-0.701121\pi\)
0.994147 + 0.108032i \(0.0344548\pi\)
\(602\) 2.66025 + 4.60770i 0.108424 + 0.187796i
\(603\) 7.26795i 0.295974i
\(604\) −9.29423 + 5.36603i −0.378177 + 0.218340i
\(605\) −14.0885 + 8.13397i −0.572777 + 0.330693i
\(606\) 19.3923i 0.787759i
\(607\) 3.60770 + 6.24871i 0.146432 + 0.253627i 0.929906 0.367797i \(-0.119888\pi\)
−0.783474 + 0.621424i \(0.786554\pi\)
\(608\) −2.36603 + 4.09808i −0.0959550 + 0.166199i
\(609\) −3.29423 1.90192i −0.133489 0.0770698i
\(610\) 26.3205 1.06569
\(611\) 15.2942 7.56218i 0.618738 0.305933i
\(612\) 5.19615 0.210042
\(613\) −11.3827 6.57180i −0.459742 0.265432i 0.252194 0.967677i \(-0.418848\pi\)
−0.711936 + 0.702244i \(0.752181\pi\)
\(614\) 3.63397 6.29423i 0.146655 0.254014i
\(615\) −5.59808 9.69615i −0.225736 0.390987i
\(616\) 1.60770i 0.0647759i
\(617\) −27.1865 + 15.6962i −1.09449 + 0.631903i −0.934768 0.355259i \(-0.884393\pi\)
−0.159721 + 0.987162i \(0.551059\pi\)
\(618\) 5.36603 3.09808i 0.215853 0.124623i
\(619\) 28.3923i 1.14118i −0.821234 0.570592i \(-0.806714\pi\)
0.821234 0.570592i \(-0.193286\pi\)
\(620\) −8.19615 14.1962i −0.329165 0.570131i
\(621\) 4.09808 7.09808i 0.164450 0.284836i
\(622\) −7.09808 4.09808i −0.284607 0.164318i
\(623\) −12.0000 −0.480770
\(624\) −2.00000 + 3.00000i −0.0800641 + 0.120096i
\(625\) −11.0000 −0.440000
\(626\) 3.12436 + 1.80385i 0.124874 + 0.0720962i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) 3.59808 + 6.23205i 0.143579 + 0.248686i
\(629\) 15.5885i 0.621552i
\(630\) 1.90192 1.09808i 0.0757745 0.0437484i
\(631\) −1.60770 + 0.928203i −0.0640013 + 0.0369512i −0.531659 0.846958i \(-0.678431\pi\)
0.467658 + 0.883910i \(0.345098\pi\)
\(632\) 8.39230i 0.333828i
\(633\) −12.1962 21.1244i −0.484754 0.839618i
\(634\) 9.06218 15.6962i 0.359905 0.623374i
\(635\) 6.00000 + 3.46410i 0.238103 + 0.137469i
\(636\) 3.00000 0.118958
\(637\) −19.4019 1.25129i −0.768732 0.0495779i
\(638\) 3.80385 0.150596
\(639\) −1.90192 1.09808i −0.0752389 0.0434392i
\(640\) 0.866025 1.50000i 0.0342327 0.0592927i
\(641\) −20.5981 35.6769i −0.813575 1.40915i −0.910347 0.413847i \(-0.864185\pi\)
0.0967715 0.995307i \(-0.469148\pi\)
\(642\) 2.19615i 0.0866752i
\(643\) −24.0000 + 13.8564i −0.946468 + 0.546443i −0.891982 0.452071i \(-0.850685\pi\)
−0.0544858 + 0.998515i \(0.517352\pi\)
\(644\) −9.00000 + 5.19615i −0.354650 + 0.204757i
\(645\) 7.26795i 0.286175i
\(646\) 12.2942 + 21.2942i 0.483710 + 0.837810i
\(647\) −24.5885 + 42.5885i −0.966672 + 1.67433i −0.261618 + 0.965172i \(0.584256\pi\)
−0.705054 + 0.709153i \(0.749077\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 17.5692 0.689652
\(650\) 0.464102 7.19615i 0.0182036 0.282256i
\(651\) −12.0000 −0.470317
\(652\) 2.19615 + 1.26795i 0.0860080 + 0.0496567i
\(653\) −6.58846 + 11.4115i −0.257826 + 0.446568i −0.965659 0.259812i \(-0.916340\pi\)
0.707833 + 0.706380i \(0.249673\pi\)
\(654\) −2.19615 3.80385i −0.0858764 0.148742i
\(655\) 7.60770i 0.297257i
\(656\) −5.59808 + 3.23205i −0.218568 + 0.126190i
\(657\) 10.5000 6.06218i 0.409644 0.236508i
\(658\) 6.00000i 0.233904i
\(659\) 18.5885 + 32.1962i 0.724103 + 1.25418i 0.959342 + 0.282246i \(0.0910796\pi\)
−0.235238 + 0.971938i \(0.575587\pi\)
\(660\) −1.09808 + 1.90192i −0.0427426 + 0.0740323i
\(661\) −7.79423 4.50000i −0.303160 0.175030i 0.340701 0.940172i \(-0.389335\pi\)
−0.643862 + 0.765142i \(0.722669\pi\)
\(662\) 12.0000 0.466393
\(663\) 8.30385 + 16.7942i 0.322495 + 0.652234i
\(664\) −5.66025 −0.219660
\(665\) 9.00000 + 5.19615i 0.349005 + 0.201498i
\(666\) 1.50000 2.59808i 0.0581238 0.100673i
\(667\) 12.2942 + 21.2942i 0.476034 + 0.824516i
\(668\) 9.46410i 0.366177i
\(669\) −4.39230 + 2.53590i −0.169816 + 0.0980435i
\(670\) −10.9019 + 6.29423i −0.421178 + 0.243167i
\(671\) 19.2679i 0.743831i
\(672\) −0.633975 1.09808i −0.0244561 0.0423592i
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) −26.8468 15.5000i −1.03410 0.597038i
\(675\) −2.00000 −0.0769800
\(676\) −12.8923 1.66987i −0.495858 0.0642259i
\(677\) −16.3923 −0.630007 −0.315004 0.949090i \(-0.602006\pi\)
−0.315004 + 0.949090i \(0.602006\pi\)
\(678\) 0.696152 + 0.401924i 0.0267356 + 0.0154358i
\(679\) −3.80385 + 6.58846i −0.145978 + 0.252842i
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) 20.1962i 0.773918i
\(682\) 10.3923 6.00000i 0.397942 0.229752i
\(683\) −24.0000 + 13.8564i −0.918334 + 0.530201i −0.883103 0.469179i \(-0.844550\pi\)
−0.0352311 + 0.999379i \(0.511217\pi\)
\(684\) 4.73205i 0.180934i
\(685\) 7.79423 + 13.5000i 0.297802 + 0.515808i
\(686\) 7.85641 13.6077i 0.299959 0.519544i
\(687\) −6.80385 3.92820i −0.259583 0.149870i
\(688\) 4.19615 0.159977
\(689\) 4.79423 + 9.69615i 0.182646 + 0.369394i
\(690\) −14.1962 −0.540438
\(691\) 22.0981 + 12.7583i 0.840650 + 0.485350i 0.857485 0.514509i \(-0.172026\pi\)
−0.0168348 + 0.999858i \(0.505359\pi\)
\(692\) 2.19615 3.80385i 0.0834852 0.144601i
\(693\) 0.803848 + 1.39230i 0.0305356 + 0.0528893i
\(694\) 18.5885i 0.705608i
\(695\) 6.00000 3.46410i 0.227593 0.131401i
\(696\) −2.59808 + 1.50000i −0.0984798 + 0.0568574i
\(697\) 33.5885i 1.27225i
\(698\) 4.73205 + 8.19615i 0.179111 + 0.310229i
\(699\) 9.00000 15.5885i 0.340411 0.589610i
\(700\) 2.19615 + 1.26795i 0.0830068 + 0.0479240i
\(701\) 16.3923 0.619129 0.309564 0.950878i \(-0.399817\pi\)
0.309564 + 0.950878i \(0.399817\pi\)
\(702\) −0.232051 + 3.59808i −0.00875819 + 0.135801i
\(703\) 14.1962 0.535418
\(704\) 1.09808 + 0.633975i 0.0413853 + 0.0238938i
\(705\) −4.09808 + 7.09808i −0.154342 + 0.267329i
\(706\) 17.8923 + 30.9904i 0.673386 + 1.16634i
\(707\) 24.5885i 0.924744i
\(708\) −12.0000 + 6.92820i −0.450988 + 0.260378i
\(709\) −39.1865 + 22.6244i −1.47168 + 0.849676i −0.999494 0.0318226i \(-0.989869\pi\)
−0.472188 + 0.881498i \(0.656536\pi\)
\(710\) 3.80385i 0.142756i
\(711\) −4.19615 7.26795i −0.157368 0.272569i
\(712\) −4.73205 + 8.19615i −0.177341 + 0.307164i
\(713\) 67.1769 + 38.7846i 2.51580 + 1.45250i
\(714\) −6.58846 −0.246567
\(715\) −7.90192 0.509619i −0.295515 0.0190587i
\(716\) 2.19615 0.0820741
\(717\) −5.70577 3.29423i −0.213086 0.123025i
\(718\) −8.02628 + 13.9019i −0.299538 + 0.518815i
\(719\) 15.8038 + 27.3731i 0.589384 + 1.02084i 0.994313 + 0.106495i \(0.0339628\pi\)
−0.404929 + 0.914348i \(0.632704\pi\)
\(720\) 1.73205i 0.0645497i
\(721\) −6.80385 + 3.92820i −0.253389 + 0.146294i
\(722\) −2.93782 + 1.69615i −0.109334 + 0.0631243i
\(723\) 11.1962i 0.416389i
\(724\) −9.79423 16.9641i −0.364000 0.630466i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 8.13397 + 4.69615i 0.301880 + 0.174291i
\(727\) 13.8038 0.511956 0.255978 0.966683i \(-0.417602\pi\)
0.255978 + 0.966683i \(0.417602\pi\)
\(728\) 2.53590 3.80385i 0.0939866 0.140980i
\(729\) 1.00000 0.0370370
\(730\) −18.1865 10.5000i −0.673114 0.388622i
\(731\) 10.9019 18.8827i 0.403222 0.698401i
\(732\) −7.59808 13.1603i −0.280833 0.486417i
\(733\) 20.3205i 0.750555i −0.926912 0.375278i \(-0.877547\pi\)
0.926912 0.375278i \(-0.122453\pi\)
\(734\) −11.9545 + 6.90192i −0.441248 + 0.254755i
\(735\) 8.08846 4.66987i 0.298347 0.172251i
\(736\) 8.19615i 0.302114i
\(737\) −4.60770 7.98076i −0.169727 0.293975i
\(738\) −3.23205 + 5.59808i −0.118973 + 0.206068i
\(739\) 4.39230 + 2.53590i 0.161574 + 0.0932845i 0.578607 0.815607i \(-0.303597\pi\)
−0.417033 + 0.908891i \(0.636930\pi\)
\(740\) −5.19615 −0.191014
\(741\) −15.2942 + 7.56218i −0.561848 + 0.277804i
\(742\) −3.80385 −0.139644
\(743\) −14.1962 8.19615i −0.520806 0.300688i 0.216458 0.976292i \(-0.430550\pi\)
−0.737264 + 0.675604i \(0.763883\pi\)
\(744\) −4.73205 + 8.19615i −0.173485 + 0.300486i
\(745\) 5.30385 + 9.18653i 0.194318 + 0.336569i
\(746\) 27.9808i 1.02445i
\(747\) −4.90192 + 2.83013i −0.179352 + 0.103549i
\(748\) 5.70577 3.29423i 0.208624 0.120449i
\(749\) 2.78461i 0.101747i
\(750\) 6.06218 + 10.5000i 0.221359 + 0.383406i
\(751\) 13.4904 23.3660i 0.492271 0.852638i −0.507689 0.861540i \(-0.669500\pi\)
0.999960 + 0.00890181i \(0.00283357\pi\)
\(752\) 4.09808 + 2.36603i 0.149441 + 0.0862801i
\(753\) 16.3923 0.597369
\(754\) −9.00000 6.00000i −0.327761 0.218507i
\(755\) 18.5885 0.676503
\(756\) −1.09808 0.633975i −0.0399366 0.0230574i
\(757\) 11.3923 19.7321i 0.414060 0.717174i −0.581269 0.813712i \(-0.697444\pi\)
0.995329 + 0.0965379i \(0.0307769\pi\)
\(758\) −15.1244 26.1962i −0.549341 0.951487i
\(759\) 10.3923i 0.377217i
\(760\) 7.09808 4.09808i 0.257474 0.148653i
\(761\) 14.1962 8.19615i 0.514610 0.297110i −0.220117 0.975474i \(-0.570644\pi\)
0.734727 + 0.678363i \(0.237310\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 2.78461 + 4.82309i 0.100810 + 0.174607i
\(764\) −10.3923 + 18.0000i −0.375980 + 0.651217i
\(765\) −7.79423 4.50000i −0.281801 0.162698i
\(766\) −23.3205 −0.842604
\(767\) −41.5692 27.7128i −1.50098 1.00065i
\(768\) −1.00000 −0.0360844
\(769\) −18.8038 10.8564i −0.678084 0.391492i 0.121049 0.992647i \(-0.461374\pi\)
−0.799133 + 0.601155i \(0.794708\pi\)
\(770\) 1.39230 2.41154i 0.0501752 0.0869060i
\(771\) −11.5981 20.0885i −0.417695 0.723468i
\(772\) 23.1962i 0.834848i
\(773\) 7.98076 4.60770i 0.287048 0.165727i −0.349562 0.936913i \(-0.613670\pi\)
0.636610 + 0.771186i \(0.280336\pi\)
\(774\) 3.63397