Properties

Label 390.2.i.g.61.2
Level $390$
Weight $2$
Character 390.61
Analytic conductor $3.114$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 61.2
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 390.61
Dual form 390.2.i.g.211.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.280776 + 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.280776 + 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.06155 + 3.57071i) q^{11} +1.00000 q^{12} +(2.84233 + 2.21837i) q^{13} -0.561553 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.56155 + 2.70469i) q^{17} +1.00000 q^{18} +(-0.280776 - 0.486319i) q^{19} +(-0.500000 - 0.866025i) q^{20} -0.561553 q^{21} +(-2.06155 - 3.57071i) q^{22} +(-2.34233 + 4.05703i) q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(-3.34233 + 1.35234i) q^{26} +1.00000 q^{27} +(0.280776 - 0.486319i) q^{28} +(-1.21922 + 2.11176i) q^{29} +(-0.500000 - 0.866025i) q^{30} -6.68466 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.06155 - 3.57071i) q^{33} -3.12311 q^{34} +(0.280776 + 0.486319i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.06155 - 3.57071i) q^{37} +0.561553 q^{38} +(-3.34233 + 1.35234i) q^{39} +1.00000 q^{40} +(-6.12311 + 10.6055i) q^{41} +(0.280776 - 0.486319i) q^{42} +(-0.219224 - 0.379706i) q^{43} +4.12311 q^{44} +(-0.500000 - 0.866025i) q^{45} +(-2.34233 - 4.05703i) q^{46} +7.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.34233 - 5.78908i) q^{49} +(-0.500000 + 0.866025i) q^{50} -3.12311 q^{51} +(0.500000 - 3.57071i) q^{52} +8.56155 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.06155 + 3.57071i) q^{55} +(0.280776 + 0.486319i) q^{56} +0.561553 q^{57} +(-1.21922 - 2.11176i) q^{58} +(-3.21922 - 5.57586i) q^{59} +1.00000 q^{60} +(-3.00000 - 5.19615i) q^{61} +(3.34233 - 5.78908i) q^{62} +(0.280776 - 0.486319i) q^{63} +1.00000 q^{64} +(2.84233 + 2.21837i) q^{65} +4.12311 q^{66} +(1.12311 - 1.94528i) q^{67} +(1.56155 - 2.70469i) q^{68} +(-2.34233 - 4.05703i) q^{69} -0.561553 q^{70} +(6.56155 + 11.3649i) q^{71} +(-0.500000 - 0.866025i) q^{72} +9.36932 q^{73} +(2.06155 + 3.57071i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-0.280776 + 0.486319i) q^{76} -2.31534 q^{77} +(0.500000 - 3.57071i) q^{78} +11.5616 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.12311 - 10.6055i) q^{82} -7.12311 q^{83} +(0.280776 + 0.486319i) q^{84} +(1.56155 + 2.70469i) q^{85} +0.438447 q^{86} +(-1.21922 - 2.11176i) q^{87} +(-2.06155 + 3.57071i) q^{88} +(9.40388 - 16.2880i) q^{89} +1.00000 q^{90} +(-0.280776 + 2.00514i) q^{91} +4.68466 q^{92} +(3.34233 - 5.78908i) q^{93} +(-3.50000 + 6.06218i) q^{94} +(-0.280776 - 0.486319i) q^{95} +1.00000 q^{96} +(3.56155 + 6.16879i) q^{97} +(3.34233 + 5.78908i) q^{98} +4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} + 4q^{5} - 2q^{6} - 3q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} + 4q^{5} - 2q^{6} - 3q^{7} + 4q^{8} - 2q^{9} - 2q^{10} + 4q^{12} - q^{13} + 6q^{14} - 2q^{15} - 2q^{16} - 2q^{17} + 4q^{18} + 3q^{19} - 2q^{20} + 6q^{21} + 3q^{23} - 2q^{24} + 4q^{25} - q^{26} + 4q^{27} - 3q^{28} - 9q^{29} - 2q^{30} - 2q^{31} - 2q^{32} + 4q^{34} - 3q^{35} - 2q^{36} - 6q^{38} - q^{39} + 4q^{40} - 8q^{41} - 3q^{42} - 5q^{43} - 2q^{45} + 3q^{46} + 28q^{47} - 2q^{48} + q^{49} - 2q^{50} + 4q^{51} + 2q^{52} + 26q^{53} - 2q^{54} - 3q^{56} - 6q^{57} - 9q^{58} - 17q^{59} + 4q^{60} - 12q^{61} + q^{62} - 3q^{63} + 4q^{64} - q^{65} - 12q^{67} - 2q^{68} + 3q^{69} + 6q^{70} + 18q^{71} - 2q^{72} - 12q^{73} - 2q^{75} + 3q^{76} - 34q^{77} + 2q^{78} + 38q^{79} - 2q^{80} - 2q^{81} - 8q^{82} - 12q^{83} - 3q^{84} - 2q^{85} + 10q^{86} - 9q^{87} + 17q^{89} + 4q^{90} + 3q^{91} - 6q^{92} + q^{93} - 14q^{94} + 3q^{95} + 4q^{96} + 6q^{97} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.00000 0.447214
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 0.280776 + 0.486319i 0.106124 + 0.183811i 0.914197 0.405271i \(-0.132823\pi\)
−0.808073 + 0.589082i \(0.799489\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −2.06155 + 3.57071i −0.621582 + 1.07661i 0.367610 + 0.929980i \(0.380176\pi\)
−0.989191 + 0.146631i \(0.953157\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.84233 + 2.21837i 0.788320 + 0.615265i
\(14\) −0.561553 −0.150081
\(15\) −0.500000 + 0.866025i −0.129099 + 0.223607i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.56155 + 2.70469i 0.378732 + 0.655983i 0.990878 0.134761i \(-0.0430268\pi\)
−0.612146 + 0.790745i \(0.709693\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.280776 0.486319i −0.0644145 0.111569i 0.832020 0.554746i \(-0.187185\pi\)
−0.896434 + 0.443177i \(0.853851\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) −0.561553 −0.122541
\(22\) −2.06155 3.57071i −0.439525 0.761279i
\(23\) −2.34233 + 4.05703i −0.488409 + 0.845950i −0.999911 0.0133324i \(-0.995756\pi\)
0.511502 + 0.859282i \(0.329089\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 1.00000 0.200000
\(26\) −3.34233 + 1.35234i −0.655485 + 0.265217i
\(27\) 1.00000 0.192450
\(28\) 0.280776 0.486319i 0.0530618 0.0919057i
\(29\) −1.21922 + 2.11176i −0.226404 + 0.392143i −0.956740 0.290945i \(-0.906030\pi\)
0.730336 + 0.683088i \(0.239364\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) −6.68466 −1.20060 −0.600300 0.799775i \(-0.704952\pi\)
−0.600300 + 0.799775i \(0.704952\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −2.06155 3.57071i −0.358870 0.621582i
\(34\) −3.12311 −0.535608
\(35\) 0.280776 + 0.486319i 0.0474599 + 0.0822029i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 2.06155 3.57071i 0.338917 0.587022i −0.645312 0.763919i \(-0.723273\pi\)
0.984229 + 0.176897i \(0.0566060\pi\)
\(38\) 0.561553 0.0910959
\(39\) −3.34233 + 1.35234i −0.535201 + 0.216548i
\(40\) 1.00000 0.158114
\(41\) −6.12311 + 10.6055i −0.956268 + 1.65631i −0.224830 + 0.974398i \(0.572183\pi\)
−0.731438 + 0.681908i \(0.761151\pi\)
\(42\) 0.280776 0.486319i 0.0433247 0.0750407i
\(43\) −0.219224 0.379706i −0.0334313 0.0579047i 0.848826 0.528673i \(-0.177310\pi\)
−0.882257 + 0.470768i \(0.843977\pi\)
\(44\) 4.12311 0.621582
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) −2.34233 4.05703i −0.345358 0.598177i
\(47\) 7.00000 1.02105 0.510527 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 3.34233 5.78908i 0.477476 0.827012i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) −3.12311 −0.437322
\(52\) 0.500000 3.57071i 0.0693375 0.495169i
\(53\) 8.56155 1.17602 0.588010 0.808854i \(-0.299912\pi\)
0.588010 + 0.808854i \(0.299912\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −2.06155 + 3.57071i −0.277980 + 0.481475i
\(56\) 0.280776 + 0.486319i 0.0375203 + 0.0649871i
\(57\) 0.561553 0.0743795
\(58\) −1.21922 2.11176i −0.160092 0.277287i
\(59\) −3.21922 5.57586i −0.419107 0.725915i 0.576743 0.816926i \(-0.304324\pi\)
−0.995850 + 0.0910109i \(0.970990\pi\)
\(60\) 1.00000 0.129099
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 3.34233 5.78908i 0.424476 0.735214i
\(63\) 0.280776 0.486319i 0.0353745 0.0612704i
\(64\) 1.00000 0.125000
\(65\) 2.84233 + 2.21837i 0.352548 + 0.275155i
\(66\) 4.12311 0.507519
\(67\) 1.12311 1.94528i 0.137209 0.237653i −0.789230 0.614098i \(-0.789520\pi\)
0.926439 + 0.376444i \(0.122853\pi\)
\(68\) 1.56155 2.70469i 0.189366 0.327992i
\(69\) −2.34233 4.05703i −0.281983 0.488409i
\(70\) −0.561553 −0.0671184
\(71\) 6.56155 + 11.3649i 0.778713 + 1.34877i 0.932684 + 0.360695i \(0.117461\pi\)
−0.153971 + 0.988075i \(0.549206\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 9.36932 1.09660 0.548298 0.836283i \(-0.315276\pi\)
0.548298 + 0.836283i \(0.315276\pi\)
\(74\) 2.06155 + 3.57071i 0.239651 + 0.415087i
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) −0.280776 + 0.486319i −0.0322073 + 0.0557846i
\(77\) −2.31534 −0.263858
\(78\) 0.500000 3.57071i 0.0566139 0.404304i
\(79\) 11.5616 1.30078 0.650388 0.759602i \(-0.274606\pi\)
0.650388 + 0.759602i \(0.274606\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −6.12311 10.6055i −0.676184 1.17118i
\(83\) −7.12311 −0.781862 −0.390931 0.920420i \(-0.627847\pi\)
−0.390931 + 0.920420i \(0.627847\pi\)
\(84\) 0.280776 + 0.486319i 0.0306352 + 0.0530618i
\(85\) 1.56155 + 2.70469i 0.169374 + 0.293365i
\(86\) 0.438447 0.0472790
\(87\) −1.21922 2.11176i −0.130714 0.226404i
\(88\) −2.06155 + 3.57071i −0.219762 + 0.380639i
\(89\) 9.40388 16.2880i 0.996810 1.72652i 0.429281 0.903171i \(-0.358767\pi\)
0.567529 0.823354i \(-0.307900\pi\)
\(90\) 1.00000 0.105409
\(91\) −0.280776 + 2.00514i −0.0294334 + 0.210196i
\(92\) 4.68466 0.488409
\(93\) 3.34233 5.78908i 0.346583 0.600300i
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) −0.280776 0.486319i −0.0288071 0.0498953i
\(96\) 1.00000 0.102062
\(97\) 3.56155 + 6.16879i 0.361621 + 0.626346i 0.988228 0.152990i \(-0.0488901\pi\)
−0.626607 + 0.779335i \(0.715557\pi\)
\(98\) 3.34233 + 5.78908i 0.337626 + 0.584786i
\(99\) 4.12311 0.414388
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 4.43845 7.68762i 0.441642 0.764946i −0.556170 0.831069i \(-0.687729\pi\)
0.997812 + 0.0661225i \(0.0210628\pi\)
\(102\) 1.56155 2.70469i 0.154617 0.267804i
\(103\) 4.56155 0.449463 0.224732 0.974421i \(-0.427849\pi\)
0.224732 + 0.974421i \(0.427849\pi\)
\(104\) 2.84233 + 2.21837i 0.278713 + 0.217529i
\(105\) −0.561553 −0.0548019
\(106\) −4.28078 + 7.41452i −0.415786 + 0.720162i
\(107\) −1.00000 + 1.73205i −0.0966736 + 0.167444i −0.910306 0.413936i \(-0.864154\pi\)
0.813632 + 0.581380i \(0.197487\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −3.75379 −0.359548 −0.179774 0.983708i \(-0.557537\pi\)
−0.179774 + 0.983708i \(0.557537\pi\)
\(110\) −2.06155 3.57071i −0.196561 0.340454i
\(111\) 2.06155 + 3.57071i 0.195674 + 0.338917i
\(112\) −0.561553 −0.0530618
\(113\) −4.34233 7.52113i −0.408492 0.707529i 0.586229 0.810145i \(-0.300612\pi\)
−0.994721 + 0.102617i \(0.967279\pi\)
\(114\) −0.280776 + 0.486319i −0.0262971 + 0.0455479i
\(115\) −2.34233 + 4.05703i −0.218423 + 0.378320i
\(116\) 2.43845 0.226404
\(117\) 0.500000 3.57071i 0.0462250 0.330113i
\(118\) 6.43845 0.592707
\(119\) −0.876894 + 1.51883i −0.0803848 + 0.139231i
\(120\) −0.500000 + 0.866025i −0.0456435 + 0.0790569i
\(121\) −3.00000 5.19615i −0.272727 0.472377i
\(122\) 6.00000 0.543214
\(123\) −6.12311 10.6055i −0.552102 0.956268i
\(124\) 3.34233 + 5.78908i 0.300150 + 0.519875i
\(125\) 1.00000 0.0894427
\(126\) 0.280776 + 0.486319i 0.0250136 + 0.0433247i
\(127\) 4.28078 7.41452i 0.379857 0.657932i −0.611184 0.791489i \(-0.709306\pi\)
0.991041 + 0.133556i \(0.0426397\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0.438447 0.0386031
\(130\) −3.34233 + 1.35234i −0.293142 + 0.118608i
\(131\) −2.12311 −0.185497 −0.0927483 0.995690i \(-0.529565\pi\)
−0.0927483 + 0.995690i \(0.529565\pi\)
\(132\) −2.06155 + 3.57071i −0.179435 + 0.310791i
\(133\) 0.157671 0.273094i 0.0136718 0.0236802i
\(134\) 1.12311 + 1.94528i 0.0970215 + 0.168046i
\(135\) 1.00000 0.0860663
\(136\) 1.56155 + 2.70469i 0.133902 + 0.231925i
\(137\) −5.90388 10.2258i −0.504403 0.873651i −0.999987 0.00509126i \(-0.998379\pi\)
0.495584 0.868560i \(-0.334954\pi\)
\(138\) 4.68466 0.398785
\(139\) −6.28078 10.8786i −0.532729 0.922713i −0.999270 0.0382133i \(-0.987833\pi\)
0.466541 0.884500i \(-0.345500\pi\)
\(140\) 0.280776 0.486319i 0.0237299 0.0411015i
\(141\) −3.50000 + 6.06218i −0.294753 + 0.510527i
\(142\) −13.1231 −1.10127
\(143\) −13.7808 + 5.57586i −1.15241 + 0.466277i
\(144\) 1.00000 0.0833333
\(145\) −1.21922 + 2.11176i −0.101251 + 0.175372i
\(146\) −4.68466 + 8.11407i −0.387705 + 0.671525i
\(147\) 3.34233 + 5.78908i 0.275671 + 0.477476i
\(148\) −4.12311 −0.338917
\(149\) 1.09612 + 1.89853i 0.0897975 + 0.155534i 0.907425 0.420213i \(-0.138045\pi\)
−0.817628 + 0.575747i \(0.804711\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −15.3693 −1.25074 −0.625369 0.780329i \(-0.715051\pi\)
−0.625369 + 0.780329i \(0.715051\pi\)
\(152\) −0.280776 0.486319i −0.0227740 0.0394457i
\(153\) 1.56155 2.70469i 0.126244 0.218661i
\(154\) 1.15767 2.00514i 0.0932878 0.161579i
\(155\) −6.68466 −0.536925
\(156\) 2.84233 + 2.21837i 0.227568 + 0.177612i
\(157\) 13.8769 1.10750 0.553748 0.832684i \(-0.313197\pi\)
0.553748 + 0.832684i \(0.313197\pi\)
\(158\) −5.78078 + 10.0126i −0.459894 + 0.796560i
\(159\) −4.28078 + 7.41452i −0.339488 + 0.588010i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −2.63068 −0.207327
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 7.21922 + 12.5041i 0.565453 + 0.979394i 0.997007 + 0.0773067i \(0.0246321\pi\)
−0.431554 + 0.902087i \(0.642035\pi\)
\(164\) 12.2462 0.956268
\(165\) −2.06155 3.57071i −0.160492 0.277980i
\(166\) 3.56155 6.16879i 0.276430 0.478791i
\(167\) −2.18466 + 3.78394i −0.169054 + 0.292810i −0.938087 0.346398i \(-0.887405\pi\)
0.769034 + 0.639208i \(0.220738\pi\)
\(168\) −0.561553 −0.0433247
\(169\) 3.15767 + 12.6107i 0.242898 + 0.970052i
\(170\) −3.12311 −0.239531
\(171\) −0.280776 + 0.486319i −0.0214715 + 0.0371897i
\(172\) −0.219224 + 0.379706i −0.0167156 + 0.0289523i
\(173\) −10.0885 17.4739i −0.767018 1.32851i −0.939173 0.343444i \(-0.888407\pi\)
0.172156 0.985070i \(-0.444927\pi\)
\(174\) 2.43845 0.184858
\(175\) 0.280776 + 0.486319i 0.0212247 + 0.0367623i
\(176\) −2.06155 3.57071i −0.155395 0.269153i
\(177\) 6.43845 0.483943
\(178\) 9.40388 + 16.2880i 0.704851 + 1.22084i
\(179\) 6.34233 10.9852i 0.474048 0.821075i −0.525511 0.850787i \(-0.676126\pi\)
0.999559 + 0.0297120i \(0.00945900\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 2.87689 0.213838 0.106919 0.994268i \(-0.465901\pi\)
0.106919 + 0.994268i \(0.465901\pi\)
\(182\) −1.59612 1.24573i −0.118312 0.0923398i
\(183\) 6.00000 0.443533
\(184\) −2.34233 + 4.05703i −0.172679 + 0.299088i
\(185\) 2.06155 3.57071i 0.151568 0.262524i
\(186\) 3.34233 + 5.78908i 0.245071 + 0.424476i
\(187\) −12.8769 −0.941652
\(188\) −3.50000 6.06218i −0.255264 0.442130i
\(189\) 0.280776 + 0.486319i 0.0204235 + 0.0353745i
\(190\) 0.561553 0.0407393
\(191\) −5.43845 9.41967i −0.393512 0.681583i 0.599398 0.800451i \(-0.295407\pi\)
−0.992910 + 0.118868i \(0.962073\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(194\) −7.12311 −0.511409
\(195\) −3.34233 + 1.35234i −0.239349 + 0.0968434i
\(196\) −6.68466 −0.477476
\(197\) −6.40388 + 11.0918i −0.456258 + 0.790262i −0.998760 0.0497931i \(-0.984144\pi\)
0.542502 + 0.840055i \(0.317477\pi\)
\(198\) −2.06155 + 3.57071i −0.146508 + 0.253760i
\(199\) −1.43845 2.49146i −0.101969 0.176615i 0.810527 0.585701i \(-0.199181\pi\)
−0.912496 + 0.409086i \(0.865848\pi\)
\(200\) 1.00000 0.0707107
\(201\) 1.12311 + 1.94528i 0.0792178 + 0.137209i
\(202\) 4.43845 + 7.68762i 0.312288 + 0.540899i
\(203\) −1.36932 −0.0961072
\(204\) 1.56155 + 2.70469i 0.109331 + 0.189366i
\(205\) −6.12311 + 10.6055i −0.427656 + 0.740722i
\(206\) −2.28078 + 3.95042i −0.158909 + 0.275239i
\(207\) 4.68466 0.325606
\(208\) −3.34233 + 1.35234i −0.231749 + 0.0937682i
\(209\) 2.31534 0.160156
\(210\) 0.280776 0.486319i 0.0193754 0.0335592i
\(211\) 10.9654 18.9927i 0.754892 1.30751i −0.190536 0.981680i \(-0.561023\pi\)
0.945428 0.325831i \(-0.105644\pi\)
\(212\) −4.28078 7.41452i −0.294005 0.509231i
\(213\) −13.1231 −0.899180
\(214\) −1.00000 1.73205i −0.0683586 0.118401i
\(215\) −0.219224 0.379706i −0.0149509 0.0258958i
\(216\) 1.00000 0.0680414
\(217\) −1.87689 3.25088i −0.127412 0.220684i
\(218\) 1.87689 3.25088i 0.127119 0.220177i
\(219\) −4.68466 + 8.11407i −0.316560 + 0.548298i
\(220\) 4.12311 0.277980
\(221\) −1.56155 + 11.1517i −0.105041 + 0.750146i
\(222\) −4.12311 −0.276725
\(223\) −13.6501 + 23.6427i −0.914078 + 1.58323i −0.105832 + 0.994384i \(0.533751\pi\)
−0.808246 + 0.588845i \(0.799583\pi\)
\(224\) 0.280776 0.486319i 0.0187602 0.0324936i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) 8.68466 0.577695
\(227\) 10.0000 + 17.3205i 0.663723 + 1.14960i 0.979630 + 0.200812i \(0.0643581\pi\)
−0.315906 + 0.948790i \(0.602309\pi\)
\(228\) −0.280776 0.486319i −0.0185949 0.0322073i
\(229\) −24.2462 −1.60223 −0.801117 0.598507i \(-0.795761\pi\)
−0.801117 + 0.598507i \(0.795761\pi\)
\(230\) −2.34233 4.05703i −0.154449 0.267513i
\(231\) 1.15767 2.00514i 0.0761691 0.131929i
\(232\) −1.21922 + 2.11176i −0.0800460 + 0.138644i
\(233\) −5.31534 −0.348220 −0.174110 0.984726i \(-0.555705\pi\)
−0.174110 + 0.984726i \(0.555705\pi\)
\(234\) 2.84233 + 2.21837i 0.185809 + 0.145019i
\(235\) 7.00000 0.456630
\(236\) −3.21922 + 5.57586i −0.209554 + 0.362957i
\(237\) −5.78078 + 10.0126i −0.375502 + 0.650388i
\(238\) −0.876894 1.51883i −0.0568406 0.0984508i
\(239\) −11.3693 −0.735420 −0.367710 0.929941i \(-0.619858\pi\)
−0.367710 + 0.929941i \(0.619858\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) 14.0616 + 24.3553i 0.905784 + 1.56886i 0.819861 + 0.572563i \(0.194051\pi\)
0.0859232 + 0.996302i \(0.472616\pi\)
\(242\) 6.00000 0.385695
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −3.00000 + 5.19615i −0.192055 + 0.332650i
\(245\) 3.34233 5.78908i 0.213534 0.369851i
\(246\) 12.2462 0.780790
\(247\) 0.280776 2.00514i 0.0178654 0.127584i
\(248\) −6.68466 −0.424476
\(249\) 3.56155 6.16879i 0.225704 0.390931i
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 4.06155 + 7.03482i 0.256363 + 0.444034i 0.965265 0.261273i \(-0.0841424\pi\)
−0.708902 + 0.705307i \(0.750809\pi\)
\(252\) −0.561553 −0.0353745
\(253\) −9.65767 16.7276i −0.607173 1.05165i
\(254\) 4.28078 + 7.41452i 0.268600 + 0.465229i
\(255\) −3.12311 −0.195576
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.78078 4.81645i 0.173460 0.300442i −0.766167 0.642641i \(-0.777839\pi\)
0.939627 + 0.342200i \(0.111172\pi\)
\(258\) −0.219224 + 0.379706i −0.0136483 + 0.0236395i
\(259\) 2.31534 0.143868
\(260\) 0.500000 3.57071i 0.0310087 0.221446i
\(261\) 2.43845 0.150936
\(262\) 1.06155 1.83866i 0.0655830 0.113593i
\(263\) 6.50000 11.2583i 0.400807 0.694218i −0.593016 0.805190i \(-0.702063\pi\)
0.993824 + 0.110972i \(0.0353964\pi\)
\(264\) −2.06155 3.57071i −0.126880 0.219762i
\(265\) 8.56155 0.525932
\(266\) 0.157671 + 0.273094i 0.00966742 + 0.0167445i
\(267\) 9.40388 + 16.2880i 0.575508 + 0.996810i
\(268\) −2.24621 −0.137209
\(269\) −10.6847 18.5064i −0.651455 1.12835i −0.982770 0.184833i \(-0.940826\pi\)
0.331315 0.943520i \(-0.392508\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 6.58854 11.4117i 0.400225 0.693211i −0.593528 0.804814i \(-0.702265\pi\)
0.993753 + 0.111603i \(0.0355985\pi\)
\(272\) −3.12311 −0.189366
\(273\) −1.59612 1.24573i −0.0966015 0.0753951i
\(274\) 11.8078 0.713333
\(275\) −2.06155 + 3.57071i −0.124316 + 0.215322i
\(276\) −2.34233 + 4.05703i −0.140992 + 0.244205i
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) 12.5616 0.753392
\(279\) 3.34233 + 5.78908i 0.200100 + 0.346583i
\(280\) 0.280776 + 0.486319i 0.0167796 + 0.0290631i
\(281\) 16.2462 0.969168 0.484584 0.874745i \(-0.338971\pi\)
0.484584 + 0.874745i \(0.338971\pi\)
\(282\) −3.50000 6.06218i −0.208422 0.360997i
\(283\) −7.78078 + 13.4767i −0.462519 + 0.801107i −0.999086 0.0427513i \(-0.986388\pi\)
0.536567 + 0.843858i \(0.319721\pi\)
\(284\) 6.56155 11.3649i 0.389357 0.674385i
\(285\) 0.561553 0.0332635
\(286\) 2.06155 14.7224i 0.121902 0.870556i
\(287\) −6.87689 −0.405930
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 3.62311 6.27540i 0.213124 0.369141i
\(290\) −1.21922 2.11176i −0.0715953 0.124007i
\(291\) −7.12311 −0.417564
\(292\) −4.68466 8.11407i −0.274149 0.474840i
\(293\) −1.96543 3.40423i −0.114822 0.198877i 0.802887 0.596132i \(-0.203296\pi\)
−0.917709 + 0.397254i \(0.869963\pi\)
\(294\) −6.68466 −0.389857
\(295\) −3.21922 5.57586i −0.187430 0.324639i
\(296\) 2.06155 3.57071i 0.119825 0.207544i
\(297\) −2.06155 + 3.57071i −0.119623 + 0.207194i
\(298\) −2.19224 −0.126993
\(299\) −15.6577 + 6.33527i −0.905506 + 0.366378i
\(300\) 1.00000 0.0577350
\(301\) 0.123106 0.213225i 0.00709569 0.0122901i
\(302\) 7.68466 13.3102i 0.442202 0.765917i
\(303\) 4.43845 + 7.68762i 0.254982 + 0.441642i
\(304\) 0.561553 0.0322073
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) 1.56155 + 2.70469i 0.0892680 + 0.154617i
\(307\) 25.6155 1.46196 0.730978 0.682401i \(-0.239064\pi\)
0.730978 + 0.682401i \(0.239064\pi\)
\(308\) 1.15767 + 2.00514i 0.0659644 + 0.114254i
\(309\) −2.28078 + 3.95042i −0.129749 + 0.224732i
\(310\) 3.34233 5.78908i 0.189832 0.328798i
\(311\) 30.7386 1.74303 0.871514 0.490371i \(-0.163139\pi\)
0.871514 + 0.490371i \(0.163139\pi\)
\(312\) −3.34233 + 1.35234i −0.189222 + 0.0765614i
\(313\) 31.3693 1.77310 0.886549 0.462634i \(-0.153096\pi\)
0.886549 + 0.462634i \(0.153096\pi\)
\(314\) −6.93845 + 12.0177i −0.391559 + 0.678200i
\(315\) 0.280776 0.486319i 0.0158200 0.0274010i
\(316\) −5.78078 10.0126i −0.325194 0.563253i
\(317\) −24.8078 −1.39334 −0.696671 0.717390i \(-0.745336\pi\)
−0.696671 + 0.717390i \(0.745336\pi\)
\(318\) −4.28078 7.41452i −0.240054 0.415786i
\(319\) −5.02699 8.70700i −0.281457 0.487498i
\(320\) 1.00000 0.0559017
\(321\) −1.00000 1.73205i −0.0558146 0.0966736i
\(322\) 1.31534 2.27824i 0.0733011 0.126961i
\(323\) 0.876894 1.51883i 0.0487917 0.0845097i
\(324\) 1.00000 0.0555556
\(325\) 2.84233 + 2.21837i 0.157664 + 0.123053i
\(326\) −14.4384 −0.799672
\(327\) 1.87689 3.25088i 0.103792 0.179774i
\(328\) −6.12311 + 10.6055i −0.338092 + 0.585592i
\(329\) 1.96543 + 3.40423i 0.108358 + 0.187681i
\(330\) 4.12311 0.226969
\(331\) −15.3693 26.6204i −0.844774 1.46319i −0.885817 0.464034i \(-0.846401\pi\)
0.0410432 0.999157i \(-0.486932\pi\)
\(332\) 3.56155 + 6.16879i 0.195466 + 0.338556i
\(333\) −4.12311 −0.225945
\(334\) −2.18466 3.78394i −0.119539 0.207048i
\(335\) 1.12311 1.94528i 0.0613618 0.106282i
\(336\) 0.280776 0.486319i 0.0153176 0.0265309i
\(337\) −6.00000 −0.326841 −0.163420 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) −12.5000 3.57071i −0.679910 0.194221i
\(339\) 8.68466 0.471686
\(340\) 1.56155 2.70469i 0.0846871 0.146682i
\(341\) 13.7808 23.8690i 0.746271 1.29258i
\(342\) −0.280776 0.486319i −0.0151826 0.0262971i
\(343\) 7.68466 0.414933
\(344\) −0.219224 0.379706i −0.0118197 0.0204724i
\(345\) −2.34233 4.05703i −0.126107 0.218423i
\(346\) 20.1771 1.08473
\(347\) −0.438447 0.759413i −0.0235371 0.0407674i 0.854017 0.520245i \(-0.174159\pi\)
−0.877554 + 0.479478i \(0.840826\pi\)
\(348\) −1.21922 + 2.11176i −0.0653572 + 0.113202i
\(349\) −4.24621 + 7.35465i −0.227294 + 0.393686i −0.957005 0.290070i \(-0.906321\pi\)
0.729711 + 0.683756i \(0.239655\pi\)
\(350\) −0.561553 −0.0300163
\(351\) 2.84233 + 2.21837i 0.151712 + 0.118408i
\(352\) 4.12311 0.219762
\(353\) 12.9309 22.3969i 0.688241 1.19207i −0.284166 0.958775i \(-0.591717\pi\)
0.972407 0.233293i \(-0.0749501\pi\)
\(354\) −3.21922 + 5.57586i −0.171100 + 0.296354i
\(355\) 6.56155 + 11.3649i 0.348251 + 0.603189i
\(356\) −18.8078 −0.996810
\(357\) −0.876894 1.51883i −0.0464102 0.0803848i
\(358\) 6.34233 + 10.9852i 0.335203 + 0.580588i
\(359\) 13.1231 0.692611 0.346306 0.938122i \(-0.387436\pi\)
0.346306 + 0.938122i \(0.387436\pi\)
\(360\) −0.500000 0.866025i −0.0263523 0.0456435i
\(361\) 9.34233 16.1814i 0.491702 0.851652i
\(362\) −1.43845 + 2.49146i −0.0756031 + 0.130948i
\(363\) 6.00000 0.314918
\(364\) 1.87689 0.759413i 0.0983760 0.0398040i
\(365\) 9.36932 0.490412
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) −6.24621 + 10.8188i −0.326050 + 0.564734i −0.981724 0.190309i \(-0.939051\pi\)
0.655675 + 0.755044i \(0.272384\pi\)
\(368\) −2.34233 4.05703i −0.122102 0.211487i
\(369\) 12.2462 0.637512
\(370\) 2.06155 + 3.57071i 0.107175 + 0.185633i
\(371\) 2.40388 + 4.16365i 0.124803 + 0.216166i
\(372\) −6.68466 −0.346583
\(373\) 12.9039 + 22.3502i 0.668138 + 1.15725i 0.978424 + 0.206605i \(0.0662416\pi\)
−0.310287 + 0.950643i \(0.600425\pi\)
\(374\) 6.43845 11.1517i 0.332924 0.576642i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 7.00000 0.360997
\(377\) −8.15009 + 3.29762i −0.419751 + 0.169836i
\(378\) −0.561553 −0.0288832
\(379\) 8.84233 15.3154i 0.454200 0.786697i −0.544442 0.838799i \(-0.683259\pi\)
0.998642 + 0.0521012i \(0.0165918\pi\)
\(380\) −0.280776 + 0.486319i −0.0144035 + 0.0249476i
\(381\) 4.28078 + 7.41452i 0.219311 + 0.379857i
\(382\) 10.8769 0.556510
\(383\) −0.0961180 0.166481i −0.00491140 0.00850679i 0.863559 0.504247i \(-0.168230\pi\)
−0.868471 + 0.495741i \(0.834897\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) −2.31534 −0.118001
\(386\) 0 0
\(387\) −0.219224 + 0.379706i −0.0111438 + 0.0193016i
\(388\) 3.56155 6.16879i 0.180810 0.313173i
\(389\) −18.0540 −0.915373 −0.457686 0.889114i \(-0.651322\pi\)
−0.457686 + 0.889114i \(0.651322\pi\)
\(390\) 0.500000 3.57071i 0.0253185 0.180810i
\(391\) −14.6307 −0.739905
\(392\) 3.34233 5.78908i 0.168813 0.292393i
\(393\) 1.06155 1.83866i 0.0535483 0.0927483i
\(394\) −6.40388 11.0918i −0.322623 0.558799i
\(395\) 11.5616 0.581725
\(396\) −2.06155 3.57071i −0.103597 0.179435i
\(397\) 10.0616 + 17.4271i 0.504975 + 0.874642i 0.999983 + 0.00575403i \(0.00183158\pi\)
−0.495009 + 0.868888i \(0.664835\pi\)
\(398\) 2.87689 0.144206
\(399\) 0.157671 + 0.273094i 0.00789341 + 0.0136718i
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −0.157671 + 0.273094i −0.00787370 + 0.0136377i −0.869935 0.493166i \(-0.835840\pi\)
0.862062 + 0.506803i \(0.169173\pi\)
\(402\) −2.24621 −0.112031
\(403\) −19.0000 14.8290i −0.946457 0.738687i
\(404\) −8.87689 −0.441642
\(405\) −0.500000 + 0.866025i −0.0248452 + 0.0430331i
\(406\) 0.684658 1.18586i 0.0339790 0.0588534i
\(407\) 8.50000 + 14.7224i 0.421329 + 0.729764i
\(408\) −3.12311 −0.154617
\(409\) 9.40388 + 16.2880i 0.464992 + 0.805390i 0.999201 0.0399625i \(-0.0127239\pi\)
−0.534209 + 0.845352i \(0.679391\pi\)
\(410\) −6.12311 10.6055i −0.302399 0.523770i
\(411\) 11.8078 0.582434
\(412\) −2.28078 3.95042i −0.112366 0.194623i
\(413\) 1.80776 3.13114i 0.0889543 0.154073i
\(414\) −2.34233 + 4.05703i −0.115119 + 0.199392i
\(415\) −7.12311 −0.349660
\(416\) 0.500000 3.57071i 0.0245145 0.175069i
\(417\) 12.5616 0.615142
\(418\) −1.15767 + 2.00514i −0.0566235 + 0.0980748i
\(419\) −16.2462 + 28.1393i −0.793679 + 1.37469i 0.129995 + 0.991515i \(0.458504\pi\)
−0.923674 + 0.383178i \(0.874829\pi\)
\(420\) 0.280776 + 0.486319i 0.0137005 + 0.0237299i
\(421\) −32.4924 −1.58358 −0.791792 0.610791i \(-0.790852\pi\)
−0.791792 + 0.610791i \(0.790852\pi\)
\(422\) 10.9654 + 18.9927i 0.533789 + 0.924550i
\(423\) −3.50000 6.06218i −0.170176 0.294753i
\(424\) 8.56155 0.415786
\(425\) 1.56155 + 2.70469i 0.0757464 + 0.131197i
\(426\) 6.56155 11.3649i 0.317908 0.550633i
\(427\) 1.68466 2.91791i 0.0815263 0.141208i
\(428\) 2.00000 0.0966736
\(429\) 2.06155 14.7224i 0.0995327 0.710806i
\(430\) 0.438447 0.0211438
\(431\) 11.3693 19.6922i 0.547641 0.948542i −0.450795 0.892628i \(-0.648859\pi\)
0.998436 0.0559140i \(-0.0178073\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 9.36932 + 16.2281i 0.450261 + 0.779874i 0.998402 0.0565114i \(-0.0179977\pi\)
−0.548141 + 0.836386i \(0.684664\pi\)
\(434\) 3.75379 0.180188
\(435\) −1.21922 2.11176i −0.0584573 0.101251i
\(436\) 1.87689 + 3.25088i 0.0898869 + 0.155689i
\(437\) 2.63068 0.125843
\(438\) −4.68466 8.11407i −0.223842 0.387705i
\(439\) −12.5616 + 21.7572i −0.599530 + 1.03842i 0.393360 + 0.919384i \(0.371313\pi\)
−0.992890 + 0.119032i \(0.962021\pi\)
\(440\) −2.06155 + 3.57071i −0.0982807 + 0.170227i
\(441\) −6.68466 −0.318317
\(442\) −8.87689 6.92820i −0.422231 0.329541i
\(443\) −13.1231 −0.623498 −0.311749 0.950165i \(-0.600915\pi\)
−0.311749 + 0.950165i \(0.600915\pi\)
\(444\) 2.06155 3.57071i 0.0978370 0.169459i
\(445\) 9.40388 16.2880i 0.445787 0.772125i
\(446\) −13.6501 23.6427i −0.646351 1.11951i
\(447\) −2.19224 −0.103689
\(448\) 0.280776 + 0.486319i 0.0132654 + 0.0229764i
\(449\) 10.0885 + 17.4739i 0.476108 + 0.824643i 0.999625 0.0273722i \(-0.00871392\pi\)
−0.523518 + 0.852015i \(0.675381\pi\)
\(450\) 1.00000 0.0471405
\(451\) −25.2462 43.7277i −1.18880 2.05906i
\(452\) −4.34233 + 7.52113i −0.204246 + 0.353764i
\(453\) 7.68466 13.3102i 0.361057 0.625369i
\(454\) −20.0000 −0.938647
\(455\) −0.280776 + 2.00514i −0.0131630 + 0.0940026i
\(456\) 0.561553 0.0262971
\(457\) −10.1231 + 17.5337i −0.473539 + 0.820193i −0.999541 0.0302897i \(-0.990357\pi\)
0.526002 + 0.850483i \(0.323690\pi\)
\(458\) 12.1231 20.9978i 0.566476 0.981164i
\(459\) 1.56155 + 2.70469i 0.0728870 + 0.126244i
\(460\) 4.68466 0.218423
\(461\) 15.0270 + 26.0275i 0.699877 + 1.21222i 0.968509 + 0.248979i \(0.0800950\pi\)
−0.268632 + 0.963243i \(0.586572\pi\)
\(462\) 1.15767 + 2.00514i 0.0538597 + 0.0932878i
\(463\) −7.61553 −0.353924 −0.176962 0.984218i \(-0.556627\pi\)
−0.176962 + 0.984218i \(0.556627\pi\)
\(464\) −1.21922 2.11176i −0.0566010 0.0980359i
\(465\) 3.34233 5.78908i 0.154997 0.268462i
\(466\) 2.65767 4.60322i 0.123114 0.213240i
\(467\) −17.8617 −0.826543 −0.413271 0.910608i \(-0.635614\pi\)
−0.413271 + 0.910608i \(0.635614\pi\)
\(468\) −3.34233 + 1.35234i −0.154499 + 0.0625121i
\(469\) 1.26137 0.0582445
\(470\) −3.50000 + 6.06218i −0.161443 + 0.279627i
\(471\) −6.93845 + 12.0177i −0.319707 + 0.553748i
\(472\) −3.21922 5.57586i −0.148177 0.256650i
\(473\) 1.80776 0.0831211
\(474\) −5.78078 10.0126i −0.265520 0.459894i
\(475\) −0.280776 0.486319i −0.0128829 0.0223138i
\(476\) 1.75379 0.0803848
\(477\) −4.28078 7.41452i −0.196003 0.339488i
\(478\) 5.68466 9.84612i 0.260010 0.450351i
\(479\) 19.1231 33.1222i 0.873757 1.51339i 0.0156760 0.999877i \(-0.495010\pi\)
0.858081 0.513514i \(-0.171657\pi\)
\(480\) 1.00000 0.0456435
\(481\) 13.7808 5.57586i 0.628349 0.254237i
\(482\) −28.1231 −1.28097
\(483\) 1.31534 2.27824i 0.0598501 0.103663i
\(484\) −3.00000 + 5.19615i −0.136364 + 0.236189i
\(485\) 3.56155 + 6.16879i 0.161722 + 0.280110i
\(486\) 1.00000 0.0453609
\(487\) −6.52699 11.3051i −0.295766 0.512282i 0.679397 0.733771i \(-0.262242\pi\)
−0.975163 + 0.221489i \(0.928908\pi\)
\(488\) −3.00000 5.19615i −0.135804 0.235219i
\(489\) −14.4384 −0.652929
\(490\) 3.34233 + 5.78908i 0.150991 + 0.261524i
\(491\) 8.71922 15.1021i 0.393493 0.681550i −0.599415 0.800439i \(-0.704600\pi\)
0.992908 + 0.118889i \(0.0379332\pi\)
\(492\) −6.12311 + 10.6055i −0.276051 + 0.478134i
\(493\) −7.61553 −0.342986
\(494\) 1.59612 + 1.24573i 0.0718127 + 0.0560481i
\(495\) 4.12311 0.185320
\(496\) 3.34233 5.78908i 0.150075 0.259938i
\(497\) −3.68466 + 6.38202i −0.165280 + 0.286273i
\(498\) 3.56155 + 6.16879i 0.159597 + 0.276430i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) −2.18466 3.78394i −0.0976033 0.169054i
\(502\) −8.12311 −0.362552
\(503\) 21.5270 + 37.2858i 0.959841 + 1.66249i 0.722879 + 0.690974i \(0.242818\pi\)
0.236962 + 0.971519i \(0.423848\pi\)
\(504\) 0.280776 0.486319i 0.0125068 0.0216624i
\(505\) 4.43845 7.68762i 0.197508 0.342094i
\(506\) 19.3153 0.858672
\(507\) −12.5000 3.57071i −0.555144 0.158581i
\(508\) −8.56155 −0.379857
\(509\) −20.2732 + 35.1142i −0.898594 + 1.55641i −0.0693009 + 0.997596i \(0.522077\pi\)
−0.829293 + 0.558814i \(0.811256\pi\)
\(510\) 1.56155 2.70469i 0.0691467 0.119766i
\(511\) 2.63068 + 4.55648i 0.116375 + 0.201567i
\(512\) 1.00000 0.0441942
\(513\) −0.280776 0.486319i −0.0123966 0.0214715i
\(514\) 2.78078 + 4.81645i 0.122655 + 0.212444i
\(515\) 4.56155 0.201006
\(516\) −0.219224 0.379706i −0.00965078 0.0167156i
\(517\) −14.4309 + 24.9950i −0.634669 + 1.09928i
\(518\) −1.15767 + 2.00514i −0.0508651 + 0.0881010i
\(519\) 20.1771 0.885676
\(520\) 2.84233 + 2.21837i 0.124644 + 0.0972820i
\(521\) −6.31534 −0.276680 −0.138340 0.990385i \(-0.544177\pi\)
−0.138340 + 0.990385i \(0.544177\pi\)
\(522\) −1.21922 + 2.11176i −0.0533640 + 0.0924291i
\(523\) 14.9039 25.8143i 0.651701 1.12878i −0.331009 0.943628i \(-0.607389\pi\)
0.982710 0.185152i \(-0.0592777\pi\)
\(524\) 1.06155 + 1.83866i 0.0463741 + 0.0803224i
\(525\) −0.561553 −0.0245082
\(526\) 6.50000 + 11.2583i 0.283413 + 0.490887i
\(527\) −10.4384 18.0799i −0.454706 0.787574i
\(528\) 4.12311 0.179435
\(529\) 0.526988 + 0.912769i 0.0229125 + 0.0396856i
\(530\) −4.28078 + 7.41452i −0.185945 + 0.322066i
\(531\) −3.21922 + 5.57586i −0.139702 + 0.241972i
\(532\) −0.315342 −0.0136718
\(533\) −40.9309 + 16.5611i −1.77291 + 0.717341i
\(534\) −18.8078 −0.813892
\(535\) −1.00000 + 1.73205i −0.0432338 + 0.0748831i
\(536\) 1.12311 1.94528i 0.0485108 0.0840231i
\(537\) 6.34233 + 10.9852i 0.273692 + 0.474048i
\(538\) 21.3693 0.921297
\(539\) 13.7808 + 23.8690i 0.593580 + 1.02811i
\(540\) −0.500000 0.866025i −0.0215166 0.0372678i
\(541\) −27.3693 −1.17670 −0.588349 0.808607i \(-0.700222\pi\)
−0.588349 + 0.808607i \(0.700222\pi\)
\(542\) 6.58854 + 11.4117i 0.283002 + 0.490174i
\(543\) −1.43845 + 2.49146i −0.0617297 + 0.106919i
\(544\) 1.56155 2.70469i 0.0669510 0.115963i
\(545\) −3.75379 −0.160795
\(546\) 1.87689 0.759413i 0.0803237 0.0324999i
\(547\) −5.61553 −0.240103 −0.120051 0.992768i \(-0.538306\pi\)
−0.120051 + 0.992768i \(0.538306\pi\)
\(548\) −5.90388 + 10.2258i −0.252201 + 0.436826i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) −2.06155 3.57071i −0.0879049 0.152256i
\(551\) 1.36932 0.0583349
\(552\) −2.34233 4.05703i −0.0996962 0.172679i
\(553\) 3.24621 + 5.62260i 0.138043 + 0.239097i
\(554\) −1.00000 −0.0424859
\(555\) 2.06155 + 3.57071i 0.0875080 + 0.151568i
\(556\) −6.28078 + 10.8786i −0.266364 + 0.461356i
\(557\) 4.28078 7.41452i 0.181382 0.314163i −0.760969 0.648788i \(-0.775276\pi\)
0.942352 + 0.334625i \(0.108610\pi\)
\(558\) −6.68466 −0.282984
\(559\) 0.219224 1.56557i 0.00927217 0.0662165i
\(560\) −0.561553 −0.0237299
\(561\) 6.43845 11.1517i 0.271831 0.470826i
\(562\) −8.12311 + 14.0696i −0.342653 + 0.593492i
\(563\) 16.4924 + 28.5657i 0.695073 + 1.20390i 0.970156 + 0.242481i \(0.0779612\pi\)
−0.275083 + 0.961420i \(0.588705\pi\)
\(564\) 7.00000 0.294753
\(565\) −4.34233 7.52113i −0.182683 0.316417i
\(566\) −7.78078 13.4767i −0.327050 0.566468i
\(567\) −0.561553 −0.0235830
\(568\) 6.56155 + 11.3649i 0.275317 + 0.476862i
\(569\) −13.0885 + 22.6700i −0.548700 + 0.950377i 0.449664 + 0.893198i \(0.351544\pi\)
−0.998364 + 0.0571787i \(0.981790\pi\)
\(570\) −0.280776 + 0.486319i −0.0117604 + 0.0203697i
\(571\) 23.6847 0.991172 0.495586 0.868559i \(-0.334953\pi\)
0.495586 + 0.868559i \(0.334953\pi\)
\(572\) 11.7192 + 9.14657i 0.490005 + 0.382437i
\(573\) 10.8769 0.454389
\(574\) 3.43845 5.95557i 0.143518 0.248580i
\(575\) −2.34233 + 4.05703i −0.0976819 + 0.169190i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −40.7386 −1.69597 −0.847986 0.530019i \(-0.822185\pi\)
−0.847986 + 0.530019i \(0.822185\pi\)
\(578\) 3.62311 + 6.27540i 0.150701 + 0.261022i
\(579\) 0 0
\(580\) 2.43845 0.101251
\(581\) −2.00000 3.46410i −0.0829740 0.143715i
\(582\) 3.56155 6.16879i 0.147631 0.255705i
\(583\) −17.6501 + 30.5709i −0.730992 + 1.26612i
\(584\) 9.36932 0.387705
\(585\) 0.500000 3.57071i 0.0206725 0.147631i
\(586\) 3.93087 0.162383
\(587\) 20.1231 34.8542i 0.830569 1.43859i −0.0670179 0.997752i \(-0.521348\pi\)
0.897587 0.440837i \(-0.145318\pi\)
\(588\) 3.34233 5.78908i 0.137835 0.238738i
\(589\) 1.87689 + 3.25088i 0.0773361 + 0.133950i
\(590\) 6.43845 0.265067
\(591\) −6.40388 11.0918i −0.263421 0.456258i
\(592\) 2.06155 + 3.57071i 0.0847293 + 0.146755i
\(593\) 33.1771 1.36242 0.681210 0.732088i \(-0.261454\pi\)
0.681210 + 0.732088i \(0.261454\pi\)
\(594\) −2.06155 3.57071i −0.0845865 0.146508i
\(595\) −0.876894 + 1.51883i −0.0359492 + 0.0622658i
\(596\) 1.09612 1.89853i 0.0448987 0.0777669i
\(597\) 2.87689 0.117743
\(598\) 2.34233 16.7276i 0.0957850 0.684041i
\(599\) −14.0000 −0.572024 −0.286012 0.958226i \(-0.592330\pi\)
−0.286012 + 0.958226i \(0.592330\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) −14.9924 + 25.9676i −0.611554 + 1.05924i 0.379425 + 0.925222i \(0.376122\pi\)
−0.990979 + 0.134020i \(0.957212\pi\)
\(602\) 0.123106 + 0.213225i 0.00501741 + 0.00869041i
\(603\) −2.24621 −0.0914728
\(604\) 7.68466 + 13.3102i 0.312684 + 0.541585i
\(605\) −3.00000 5.19615i −0.121967 0.211254i
\(606\) −8.87689 −0.360599
\(607\) −16.2116 28.0794i −0.658010 1.13971i −0.981130 0.193349i \(-0.938065\pi\)
0.323120 0.946358i \(-0.395268\pi\)
\(608\) −0.280776 + 0.486319i −0.0113870 + 0.0197228i
\(609\) 0.684658 1.18586i 0.0277438 0.0480536i
\(610\) 6.00000 0.242933
\(611\) 19.8963 + 15.5286i 0.804918 + 0.628219i
\(612\) −3.12311 −0.126244
\(613\) −9.93845 + 17.2139i −0.401410 + 0.695263i −0.993896 0.110318i \(-0.964813\pi\)
0.592486 + 0.805581i \(0.298146\pi\)
\(614\) −12.8078 + 22.1837i −0.516879 + 0.895261i
\(615\) −6.12311 10.6055i −0.246907 0.427656i
\(616\) −2.31534 −0.0932878
\(617\) 14.6577 + 25.3878i 0.590096 + 1.02208i 0.994219 + 0.107371i \(0.0342433\pi\)
−0.404123 + 0.914704i \(0.632423\pi\)
\(618\) −2.28078 3.95042i −0.0917463 0.158909i
\(619\) −20.5616 −0.826439 −0.413219 0.910632i \(-0.635596\pi\)
−0.413219 + 0.910632i \(0.635596\pi\)
\(620\) 3.34233 + 5.78908i 0.134231 + 0.232495i
\(621\) −2.34233 + 4.05703i −0.0939944 + 0.162803i
\(622\) −15.3693 + 26.6204i −0.616253 + 1.06738i
\(623\) 10.5616 0.423140
\(624\) 0.500000 3.57071i 0.0200160 0.142943i
\(625\) 1.00000 0.0400000
\(626\) −15.6847 + 27.1666i −0.626885 + 1.08580i
\(627\) −1.15767 + 2.00514i −0.0462329 + 0.0800778i
\(628\) −6.93845 12.0177i −0.276874 0.479560i
\(629\) 12.8769 0.513435
\(630\) 0.280776 + 0.486319i 0.0111864 + 0.0193754i
\(631\) 6.87689 + 11.9111i 0.273765 + 0.474175i 0.969823 0.243811i \(-0.0783977\pi\)
−0.696058 + 0.717986i \(0.745064\pi\)
\(632\) 11.5616 0.459894
\(633\) 10.9654 + 18.9927i 0.435837 + 0.754892i
\(634\) 12.4039 21.4842i 0.492621 0.853245i
\(635\) 4.28078 7.41452i 0.169877 0.294236i
\(636\) 8.56155 0.339488
\(637\) 22.3423 9.03996i 0.885235 0.358176i
\(638\) 10.0540 0.398041
\(639\) 6.56155 11.3649i 0.259571 0.449590i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 5.71922 + 9.90599i 0.225896 + 0.391263i 0.956588 0.291444i \(-0.0941358\pi\)
−0.730692 + 0.682707i \(0.760802\pi\)
\(642\) 2.00000 0.0789337
\(643\) −10.8769 18.8393i −0.428943 0.742951i 0.567837 0.823141i \(-0.307780\pi\)
−0.996780 + 0.0801904i \(0.974447\pi\)
\(644\) 1.31534 + 2.27824i 0.0518317 + 0.0897752i
\(645\) 0.438447 0.0172638
\(646\) 0.876894 + 1.51883i 0.0345009 + 0.0597574i
\(647\) −17.5270 + 30.3576i −0.689057 + 1.19348i 0.283086 + 0.959094i \(0.408642\pi\)
−0.972143 + 0.234387i \(0.924692\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 26.5464 1.04204
\(650\) −3.34233 + 1.35234i −0.131097 + 0.0530433i
\(651\) 3.75379 0.147123
\(652\) 7.21922 12.5041i 0.282727 0.489697i
\(653\) 22.2808 38.5914i 0.871914 1.51020i 0.0119002 0.999929i \(-0.496212\pi\)
0.860014 0.510270i \(-0.170455\pi\)
\(654\) 1.87689 + 3.25088i 0.0733924 + 0.127119i
\(655\) −2.12311 −0.0829566
\(656\) −6.12311 10.6055i −0.239067 0.414076i
\(657\) −4.68466 8.11407i −0.182766 0.316560i
\(658\) −3.93087 −0.153241
\(659\) 3.02699 + 5.24290i 0.117915 + 0.204234i 0.918941 0.394395i \(-0.129046\pi\)
−0.801026 + 0.598629i \(0.795712\pi\)
\(660\) −2.06155 + 3.57071i −0.0802458 + 0.138990i
\(661\) −14.8078 + 25.6478i −0.575955 + 0.997584i 0.419982 + 0.907532i \(0.362036\pi\)
−0.995937 + 0.0900513i \(0.971297\pi\)
\(662\) 30.7386 1.19469
\(663\) −8.87689 6.92820i −0.344750 0.269069i
\(664\) −7.12311 −0.276430
\(665\) 0.157671 0.273094i 0.00611421 0.0105901i
\(666\) 2.06155 3.57071i 0.0798835 0.138362i
\(667\) −5.71165 9.89286i −0.221156 0.383053i
\(668\) 4.36932 0.169054
\(669\) −13.6501 23.6427i −0.527743 0.914078i
\(670\) 1.12311 + 1.94528i 0.0433894 + 0.0751526i
\(671\) 24.7386 0.955024
\(672\) 0.280776 + 0.486319i 0.0108312 + 0.0187602i
\(673\) −12.8769 + 22.3034i −0.496368 + 0.859734i −0.999991 0.00418904i \(-0.998667\pi\)
0.503623 + 0.863923i \(0.332000\pi\)
\(674\) 3.00000 5.19615i 0.115556 0.200148i
\(675\) 1.00000 0.0384900
\(676\) 9.34233 9.03996i 0.359320 0.347691i
\(677\) −37.1231 −1.42676 −0.713378 0.700779i \(-0.752836\pi\)
−0.713378 + 0.700779i \(0.752836\pi\)
\(678\) −4.34233 + 7.52113i −0.166766 + 0.288847i
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) 1.56155 + 2.70469i 0.0598828 + 0.103720i
\(681\) −20.0000 −0.766402
\(682\) 13.7808 + 23.8690i 0.527693 + 0.913991i
\(683\) −8.56155 14.8290i −0.327599 0.567418i 0.654436 0.756117i \(-0.272906\pi\)
−0.982035 + 0.188700i \(0.939573\pi\)
\(684\) 0.561553 0.0214715
\(685\) −5.90388 10.2258i −0.225576 0.390709i
\(686\) −3.84233 + 6.65511i −0.146701 + 0.254093i
\(687\) 12.1231 20.9978i 0.462525 0.801117i
\(688\) 0.438447 0.0167156
\(689\) 24.3348 + 18.9927i 0.927080 + 0.723564i
\(690\) 4.68466 0.178342
\(691\) 10.2808 17.8068i 0.391099 0.677404i −0.601496 0.798876i \(-0.705428\pi\)
0.992595 + 0.121472i \(0.0387616\pi\)
\(692\) −10.0885 + 17.4739i −0.383509 + 0.664257i
\(693\) 1.15767 + 2.00514i 0.0439763 + 0.0761691i
\(694\) 0.876894 0.0332865
\(695\) −6.28078 10.8786i −0.238243 0.412650i
\(696\) −1.21922 2.11176i −0.0462146 0.0800460i
\(697\) −38.2462 −1.44868
\(698\) −4.24621 7.35465i −0.160721 0.278378i
\(699\) 2.65767 4.60322i 0.100522 0.174110i
\(700\) 0.280776 0.486319i 0.0106124 0.0183811i
\(701\) −36.3002 −1.37104 −0.685520 0.728054i \(-0.740425\pi\)
−0.685520 + 0.728054i \(0.740425\pi\)
\(702\) −3.34233 + 1.35234i −0.126148 + 0.0510410i
\(703\) −2.31534 −0.0873248
\(704\) −2.06155 + 3.57071i −0.0776977 + 0.134576i
\(705\) −3.50000 + 6.06218i −0.131818 + 0.228315i
\(706\) 12.9309 + 22.3969i 0.486660 + 0.842919i
\(707\) 4.98485 0.187474
\(708\) −3.21922 5.57586i −0.120986 0.209554i
\(709\) −17.1231 29.6581i −0.643072 1.11383i −0.984743 0.174013i \(-0.944326\pi\)
0.341672 0.939819i \(-0.389007\pi\)
\(710\) −13.1231 −0.492501
\(711\) −5.78078 10.0126i −0.216796 0.375502i
\(712\) 9.40388 16.2880i 0.352425 0.610419i
\(713\) 15.6577 27.1199i 0.586384 1.01565i
\(714\) 1.75379 0.0656339
\(715\) −13.7808 + 5.57586i −0.515372 + 0.208525i
\(716\) −12.6847 −0.474048
\(717\) 5.68466 9.84612i 0.212297 0.367710i
\(718\) −6.56155 + 11.3649i −0.244875 + 0.424136i
\(719\) −22.4924 38.9580i −0.838826 1.45289i −0.890877 0.454245i \(-0.849909\pi\)
0.0520512 0.998644i \(-0.483424\pi\)
\(720\) 1.00000 0.0372678
\(721\) 1.28078 + 2.21837i 0.0476986 + 0.0826164i
\(722\) 9.34233 + 16.1814i 0.347685 + 0.602209i
\(723\) −28.1231 −1.04591
\(724\) −1.43845 2.49146i −0.0534595 0.0925945i
\(725\) −1.21922 + 2.11176i −0.0452808 + 0.0784287i
\(726\) −3.00000 + 5.19615i −0.111340 + 0.192847i
\(727\) 38.4233 1.42504 0.712521 0.701651i \(-0.247554\pi\)
0.712521 + 0.701651i \(0.247554\pi\)
\(728\) −0.280776 + 2.00514i −0.0104063 + 0.0743156i
\(729\) 1.00000 0.0370370
\(730\) −4.68466 + 8.11407i −0.173387 + 0.300315i
\(731\) 0.684658 1.18586i 0.0253230 0.0438607i
\(732\) −3.00000 5.19615i −0.110883 0.192055i
\(733\) 20.0691 0.741270 0.370635 0.928779i \(-0.379140\pi\)
0.370635 + 0.928779i \(0.379140\pi\)
\(734\) −6.24621 10.8188i −0.230552 0.399328i
\(735\) 3.34233 + 5.78908i 0.123284 + 0.213534i
\(736\) 4.68466 0.172679
\(737\) 4.63068 + 8.02058i 0.170573 + 0.295442i
\(738\) −6.12311 + 10.6055i −0.225395 + 0.390395i
\(739\) 13.7732 23.8559i 0.506655 0.877553i −0.493315 0.869851i \(-0.664215\pi\)
0.999970 0.00770202i \(-0.00245165\pi\)
\(740\) −4.12311 −0.151568
\(741\) 1.59612 + 1.24573i 0.0586349 + 0.0457631i
\(742\) −4.80776 −0.176499
\(743\) −6.58854 + 11.4117i −0.241710 + 0.418654i −0.961202 0.275847i \(-0.911042\pi\)
0.719491 + 0.694501i \(0.244375\pi\)
\(744\) 3.34233 5.78908i 0.122536 0.212238i
\(745\) 1.09612 + 1.89853i 0.0401587 + 0.0695568i
\(746\) −25.8078 −0.944889
\(747\) 3.56155 + 6.16879i 0.130310 + 0.225704i
\(748\) 6.43845 + 11.1517i 0.235413 + 0.407747i
\(749\) −1.12311 −0.0410374
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 11.9039 20.6181i 0.434379 0.752366i −0.562866 0.826548i \(-0.690301\pi\)
0.997245 + 0.0741820i \(0.0236346\pi\)
\(752\) −3.50000 + 6.06218i −0.127632 + 0.221065i
\(753\) −8.12311 −0.296022
\(754\) 1.21922 8.70700i 0.0444015 0.317090i
\(755\) −15.3693 −0.559347
\(756\) 0.280776 0.486319i 0.0102117 0.0176873i
\(757\) 14.2116 24.6153i 0.516531 0.894658i −0.483285 0.875463i \(-0.660556\pi\)
0.999816 0.0191948i \(-0.00611027\pi\)
\(758\) 8.84233 + 15.3154i 0.321168 + 0.556279i
\(759\) 19.3153 0.701102
\(760\) −0.280776 0.486319i −0.0101848 0.0176406i
\(761\) 8.96543 + 15.5286i 0.324997 + 0.562911i 0.981512 0.191402i \(-0.0613035\pi\)
−0.656515 + 0.754313i \(0.727970\pi\)
\(762\) −8.56155 −0.310152
\(763\) −1.05398 1.82554i −0.0381565 0.0660889i
\(764\) −5.43845 + 9.41967i −0.196756 + 0.340792i
\(765\) 1.56155 2.70469i 0.0564581 0.0977882i
\(766\) 0.192236 0.00694577
\(767\) 3.21922 22.9899i 0.116239 0.830116i
\(768\) 1.00000 0.0360844
\(769\) 16.6577 28.8519i 0.600691 1.04043i −0.392026 0.919954i \(-0.628226\pi\)
0.992717 0.120473i \(-0.0384411\pi\)
\(770\) 1.15767 2.00514i 0.0417196 0.0722604i
\(771\) 2.78078 + 4.81645i 0.100147 + 0.173460i
\(772\) 0 0
\(773\) −12.0885 20.9380i −0.434795 0.753086i 0.562484 0.826808i \(-0.309846\pi\)
−0.997279 + 0.0737217i \(0.976512\pi\)
\(774\) −0.219224 0.379706i −0.00787983 0.0136483i
\(775\) −6.68466 −0.240120
\(776\) 3.56155 + 6.16879i 0.127852 + 0.221447i
\(777\) −1.15767 + 2.00514i −0.0415312 + 0.0719342i