Properties

Label 390.2.bb.b.361.1
Level $390$
Weight $2$
Character 390.361
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.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
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 361.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 390.361
Dual form 390.2.bb.b.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(5.59808 - 3.23205i) q^{11} +1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} +2.00000 q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(6.46410 + 3.73205i) q^{19} +(-0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(-3.23205 + 5.59808i) q^{22} +(-1.86603 - 3.23205i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-2.59808 - 2.50000i) q^{26} -1.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(-0.133975 - 0.232051i) q^{29} +(-0.500000 + 0.866025i) q^{30} +1.73205i q^{31} +(0.866025 + 0.500000i) q^{32} +(5.59808 + 3.23205i) q^{33} +4.00000i q^{34} +(-1.00000 + 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{36} +(7.96410 - 4.59808i) q^{37} -7.46410 q^{38} +(-2.50000 + 2.59808i) q^{39} +1.00000 q^{40} +(1.73205 - 1.00000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.96410 + 10.3301i) q^{43} -6.46410i q^{44} +(0.866025 + 0.500000i) q^{45} +(3.23205 + 1.86603i) q^{46} +3.53590i q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +4.00000 q^{51} +(3.50000 + 0.866025i) q^{52} +0.928203 q^{53} +(0.866025 - 0.500000i) q^{54} +(-3.23205 - 5.59808i) q^{55} +(1.00000 - 1.73205i) q^{56} +7.46410i q^{57} +(0.232051 + 0.133975i) q^{58} +(7.33013 + 4.23205i) q^{59} -1.00000i q^{60} +(5.19615 - 9.00000i) q^{61} +(-0.866025 - 1.50000i) q^{62} +(1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +(3.46410 - 1.00000i) q^{65} -6.46410 q^{66} +(-9.92820 + 5.73205i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(1.86603 - 3.23205i) q^{69} -2.00000i q^{70} +(-10.7321 - 6.19615i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(-4.59808 + 7.96410i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(6.46410 - 3.73205i) q^{76} -12.9282 q^{77} +(0.866025 - 3.50000i) q^{78} -13.9282 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} -8.92820i q^{83} +(-1.73205 - 1.00000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -11.9282i q^{86} +(0.133975 - 0.232051i) q^{87} +(3.23205 + 5.59808i) q^{88} +(-0.464102 + 0.267949i) q^{89} -1.00000 q^{90} +(1.73205 - 7.00000i) q^{91} -3.73205 q^{92} +(-1.50000 + 0.866025i) q^{93} +(-1.76795 - 3.06218i) q^{94} +(3.73205 - 6.46410i) q^{95} +1.00000i q^{96} +(0.464102 + 0.267949i) q^{97} +(2.59808 + 1.50000i) q^{98} +6.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} + 2q^{10} + 12q^{11} + 4q^{12} + 4q^{13} + 8q^{14} - 2q^{16} + 8q^{17} + 12q^{19} - 6q^{22} - 4q^{23} - 4q^{25} - 4q^{27} - 4q^{29} - 2q^{30} + 12q^{33} - 4q^{35} + 2q^{36} + 18q^{37} - 16q^{38} - 10q^{39} + 4q^{40} + 4q^{42} - 10q^{43} + 6q^{46} + 2q^{48} - 6q^{49} + 16q^{51} + 14q^{52} - 24q^{53} - 6q^{55} + 4q^{56} - 6q^{58} + 12q^{59} - 4q^{64} - 12q^{66} - 12q^{67} - 8q^{68} + 4q^{69} - 36q^{71} - 8q^{74} - 2q^{75} + 12q^{76} - 24q^{77} - 28q^{79} - 2q^{81} - 4q^{82} + 4q^{87} + 6q^{88} + 12q^{89} - 4q^{90} - 8q^{92} - 6q^{93} - 14q^{94} + 8q^{95} - 12q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) 1.00000i 0.447214i
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −1.73205 1.00000i −0.654654 0.377964i 0.135583 0.990766i \(-0.456709\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 5.59808 3.23205i 1.68788 0.974500i 0.731748 0.681575i \(-0.238705\pi\)
0.956136 0.292925i \(-0.0946285\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) 2.00000 0.534522
\(15\) 0.866025 0.500000i 0.223607 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i \(-0.672127\pi\)
0.999853 + 0.0171533i \(0.00546033\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.46410 + 3.73205i 1.48297 + 0.856191i 0.999813 0.0193444i \(-0.00615788\pi\)
0.483154 + 0.875536i \(0.339491\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 2.00000i 0.436436i
\(22\) −3.23205 + 5.59808i −0.689076 + 1.19351i
\(23\) −1.86603 3.23205i −0.389093 0.673929i 0.603235 0.797564i \(-0.293878\pi\)
−0.992328 + 0.123635i \(0.960545\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) −1.00000 −0.200000
\(26\) −2.59808 2.50000i −0.509525 0.490290i
\(27\) −1.00000 −0.192450
\(28\) −1.73205 + 1.00000i −0.327327 + 0.188982i
\(29\) −0.133975 0.232051i −0.0248785 0.0430908i 0.853318 0.521391i \(-0.174587\pi\)
−0.878197 + 0.478300i \(0.841253\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 1.73205i 0.311086i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 5.59808 + 3.23205i 0.974500 + 0.562628i
\(34\) 4.00000i 0.685994i
\(35\) −1.00000 + 1.73205i −0.169031 + 0.292770i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 7.96410 4.59808i 1.30929 0.755919i 0.327313 0.944916i \(-0.393857\pi\)
0.981978 + 0.188997i \(0.0605237\pi\)
\(38\) −7.46410 −1.21084
\(39\) −2.50000 + 2.59808i −0.400320 + 0.416025i
\(40\) 1.00000 0.158114
\(41\) 1.73205 1.00000i 0.270501 0.156174i −0.358614 0.933486i \(-0.616751\pi\)
0.629115 + 0.777312i \(0.283417\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) −5.96410 + 10.3301i −0.909517 + 1.57533i −0.0947805 + 0.995498i \(0.530215\pi\)
−0.814736 + 0.579831i \(0.803118\pi\)
\(44\) 6.46410i 0.974500i
\(45\) 0.866025 + 0.500000i 0.129099 + 0.0745356i
\(46\) 3.23205 + 1.86603i 0.476540 + 0.275130i
\(47\) 3.53590i 0.515764i 0.966176 + 0.257882i \(0.0830245\pi\)
−0.966176 + 0.257882i \(0.916975\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −1.50000 2.59808i −0.214286 0.371154i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 4.00000 0.560112
\(52\) 3.50000 + 0.866025i 0.485363 + 0.120096i
\(53\) 0.928203 0.127499 0.0637493 0.997966i \(-0.479694\pi\)
0.0637493 + 0.997966i \(0.479694\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) −3.23205 5.59808i −0.435810 0.754844i
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 7.46410i 0.988644i
\(58\) 0.232051 + 0.133975i 0.0304698 + 0.0175917i
\(59\) 7.33013 + 4.23205i 0.954301 + 0.550966i 0.894414 0.447239i \(-0.147593\pi\)
0.0598868 + 0.998205i \(0.480926\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 5.19615 9.00000i 0.665299 1.15233i −0.313905 0.949454i \(-0.601637\pi\)
0.979204 0.202878i \(-0.0650293\pi\)
\(62\) −0.866025 1.50000i −0.109985 0.190500i
\(63\) 1.73205 1.00000i 0.218218 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 3.46410 1.00000i 0.429669 0.124035i
\(66\) −6.46410 −0.795676
\(67\) −9.92820 + 5.73205i −1.21292 + 0.700281i −0.963395 0.268086i \(-0.913609\pi\)
−0.249528 + 0.968368i \(0.580276\pi\)
\(68\) −2.00000 3.46410i −0.242536 0.420084i
\(69\) 1.86603 3.23205i 0.224643 0.389093i
\(70\) 2.00000i 0.239046i
\(71\) −10.7321 6.19615i −1.27366 0.735348i −0.297985 0.954570i \(-0.596315\pi\)
−0.975675 + 0.219222i \(0.929648\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 2.00000i 0.234082i −0.993127 0.117041i \(-0.962659\pi\)
0.993127 0.117041i \(-0.0373409\pi\)
\(74\) −4.59808 + 7.96410i −0.534516 + 0.925808i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 6.46410 3.73205i 0.741483 0.428096i
\(77\) −12.9282 −1.47331
\(78\) 0.866025 3.50000i 0.0980581 0.396297i
\(79\) −13.9282 −1.56705 −0.783523 0.621363i \(-0.786579\pi\)
−0.783523 + 0.621363i \(0.786579\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) 8.92820i 0.979998i −0.871723 0.489999i \(-0.836997\pi\)
0.871723 0.489999i \(-0.163003\pi\)
\(84\) −1.73205 1.00000i −0.188982 0.109109i
\(85\) −3.46410 2.00000i −0.375735 0.216930i
\(86\) 11.9282i 1.28625i
\(87\) 0.133975 0.232051i 0.0143636 0.0248785i
\(88\) 3.23205 + 5.59808i 0.344538 + 0.596757i
\(89\) −0.464102 + 0.267949i −0.0491947 + 0.0284026i −0.524396 0.851475i \(-0.675709\pi\)
0.475201 + 0.879877i \(0.342375\pi\)
\(90\) −1.00000 −0.105409
\(91\) 1.73205 7.00000i 0.181568 0.733799i
\(92\) −3.73205 −0.389093
\(93\) −1.50000 + 0.866025i −0.155543 + 0.0898027i
\(94\) −1.76795 3.06218i −0.182350 0.315840i
\(95\) 3.73205 6.46410i 0.382900 0.663203i
\(96\) 1.00000i 0.102062i
\(97\) 0.464102 + 0.267949i 0.0471224 + 0.0272061i 0.523376 0.852102i \(-0.324672\pi\)
−0.476254 + 0.879308i \(0.658006\pi\)
\(98\) 2.59808 + 1.50000i 0.262445 + 0.151523i
\(99\) 6.46410i 0.649667i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −1.46410 2.53590i −0.145684 0.252331i 0.783944 0.620831i \(-0.213205\pi\)
−0.929628 + 0.368500i \(0.879871\pi\)
\(102\) −3.46410 + 2.00000i −0.342997 + 0.198030i
\(103\) −11.8564 −1.16825 −0.584123 0.811665i \(-0.698562\pi\)
−0.584123 + 0.811665i \(0.698562\pi\)
\(104\) −3.46410 + 1.00000i −0.339683 + 0.0980581i
\(105\) −2.00000 −0.195180
\(106\) −0.803848 + 0.464102i −0.0780766 + 0.0450775i
\(107\) 3.92820 + 6.80385i 0.379754 + 0.657753i 0.991026 0.133667i \(-0.0426754\pi\)
−0.611273 + 0.791420i \(0.709342\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 15.8564i 1.51877i 0.650643 + 0.759384i \(0.274500\pi\)
−0.650643 + 0.759384i \(0.725500\pi\)
\(110\) 5.59808 + 3.23205i 0.533756 + 0.308164i
\(111\) 7.96410 + 4.59808i 0.755919 + 0.436430i
\(112\) 2.00000i 0.188982i
\(113\) −0.401924 + 0.696152i −0.0378098 + 0.0654885i −0.884311 0.466898i \(-0.845371\pi\)
0.846501 + 0.532387i \(0.178705\pi\)
\(114\) −3.73205 6.46410i −0.349539 0.605419i
\(115\) −3.23205 + 1.86603i −0.301390 + 0.174008i
\(116\) −0.267949 −0.0248785
\(117\) −3.50000 0.866025i −0.323575 0.0800641i
\(118\) −8.46410 −0.779184
\(119\) −6.92820 + 4.00000i −0.635107 + 0.366679i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 15.3923 26.6603i 1.39930 2.42366i
\(122\) 10.3923i 0.940875i
\(123\) 1.73205 + 1.00000i 0.156174 + 0.0901670i
\(124\) 1.50000 + 0.866025i 0.134704 + 0.0777714i
\(125\) 1.00000i 0.0894427i
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) 2.46410 + 4.26795i 0.218654 + 0.378719i 0.954397 0.298542i \(-0.0965002\pi\)
−0.735743 + 0.677261i \(0.763167\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −11.9282 −1.05022
\(130\) −2.50000 + 2.59808i −0.219265 + 0.227866i
\(131\) −18.6603 −1.63035 −0.815177 0.579212i \(-0.803360\pi\)
−0.815177 + 0.579212i \(0.803360\pi\)
\(132\) 5.59808 3.23205i 0.487250 0.281314i
\(133\) −7.46410 12.9282i −0.647220 1.12102i
\(134\) 5.73205 9.92820i 0.495174 0.857666i
\(135\) 1.00000i 0.0860663i
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) −2.13397 1.23205i −0.182318 0.105261i 0.406063 0.913845i \(-0.366901\pi\)
−0.588381 + 0.808584i \(0.700235\pi\)
\(138\) 3.73205i 0.317693i
\(139\) 6.46410 11.1962i 0.548278 0.949645i −0.450115 0.892971i \(-0.648617\pi\)
0.998393 0.0566745i \(-0.0180497\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) −3.06218 + 1.76795i −0.257882 + 0.148888i
\(142\) 12.3923 1.03994
\(143\) 16.7942 + 16.1603i 1.40440 + 1.35139i
\(144\) 1.00000 0.0833333
\(145\) −0.232051 + 0.133975i −0.0192708 + 0.0111260i
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) 1.50000 2.59808i 0.123718 0.214286i
\(148\) 9.19615i 0.755919i
\(149\) −11.7224 6.76795i −0.960339 0.554452i −0.0640617 0.997946i \(-0.520405\pi\)
−0.896277 + 0.443494i \(0.853739\pi\)
\(150\) 0.866025 + 0.500000i 0.0707107 + 0.0408248i
\(151\) 10.3923i 0.845714i 0.906196 + 0.422857i \(0.138973\pi\)
−0.906196 + 0.422857i \(0.861027\pi\)
\(152\) −3.73205 + 6.46410i −0.302709 + 0.524308i
\(153\) 2.00000 + 3.46410i 0.161690 + 0.280056i
\(154\) 11.1962 6.46410i 0.902212 0.520892i
\(155\) 1.73205 0.139122
\(156\) 1.00000 + 3.46410i 0.0800641 + 0.277350i
\(157\) −5.00000 −0.399043 −0.199522 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(158\) 12.0622 6.96410i 0.959615 0.554034i
\(159\) 0.464102 + 0.803848i 0.0368057 + 0.0637493i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 7.46410i 0.588254i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 13.0359 + 7.52628i 1.02105 + 0.589504i 0.914408 0.404794i \(-0.132657\pi\)
0.106642 + 0.994297i \(0.465990\pi\)
\(164\) 2.00000i 0.156174i
\(165\) 3.23205 5.59808i 0.251615 0.435810i
\(166\) 4.46410 + 7.73205i 0.346481 + 0.600124i
\(167\) 14.1340 8.16025i 1.09372 0.631459i 0.159155 0.987254i \(-0.449123\pi\)
0.934564 + 0.355794i \(0.115790\pi\)
\(168\) 2.00000 0.154303
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 4.00000 0.306786
\(171\) −6.46410 + 3.73205i −0.494322 + 0.285397i
\(172\) 5.96410 + 10.3301i 0.454758 + 0.787665i
\(173\) −5.46410 + 9.46410i −0.415428 + 0.719542i −0.995473 0.0950419i \(-0.969701\pi\)
0.580045 + 0.814584i \(0.303035\pi\)
\(174\) 0.267949i 0.0203132i
\(175\) 1.73205 + 1.00000i 0.130931 + 0.0755929i
\(176\) −5.59808 3.23205i −0.421971 0.243625i
\(177\) 8.46410i 0.636201i
\(178\) 0.267949 0.464102i 0.0200836 0.0347859i
\(179\) 9.86603 + 17.0885i 0.737421 + 1.27725i 0.953653 + 0.300909i \(0.0972901\pi\)
−0.216231 + 0.976342i \(0.569377\pi\)
\(180\) 0.866025 0.500000i 0.0645497 0.0372678i
\(181\) −2.92820 −0.217652 −0.108826 0.994061i \(-0.534709\pi\)
−0.108826 + 0.994061i \(0.534709\pi\)
\(182\) 2.00000 + 6.92820i 0.148250 + 0.513553i
\(183\) 10.3923 0.768221
\(184\) 3.23205 1.86603i 0.238270 0.137565i
\(185\) −4.59808 7.96410i −0.338057 0.585532i
\(186\) 0.866025 1.50000i 0.0635001 0.109985i
\(187\) 25.8564i 1.89081i
\(188\) 3.06218 + 1.76795i 0.223332 + 0.128941i
\(189\) 1.73205 + 1.00000i 0.125988 + 0.0727393i
\(190\) 7.46410i 0.541503i
\(191\) −10.7321 + 18.5885i −0.776544 + 1.34501i 0.157379 + 0.987538i \(0.449696\pi\)
−0.933923 + 0.357475i \(0.883638\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 9.80385 5.66025i 0.705696 0.407434i −0.103769 0.994601i \(-0.533090\pi\)
0.809466 + 0.587167i \(0.199757\pi\)
\(194\) −0.535898 −0.0384753
\(195\) 2.59808 + 2.50000i 0.186052 + 0.179029i
\(196\) −3.00000 −0.214286
\(197\) 3.80385 2.19615i 0.271013 0.156469i −0.358335 0.933593i \(-0.616655\pi\)
0.629348 + 0.777124i \(0.283322\pi\)
\(198\) −3.23205 5.59808i −0.229692 0.397838i
\(199\) 2.53590 4.39230i 0.179765 0.311362i −0.762035 0.647536i \(-0.775800\pi\)
0.941800 + 0.336174i \(0.109133\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) −9.92820 5.73205i −0.700281 0.404308i
\(202\) 2.53590 + 1.46410i 0.178425 + 0.103014i
\(203\) 0.535898i 0.0376127i
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) 10.2679 5.92820i 0.715402 0.413037i
\(207\) 3.73205 0.259395
\(208\) 2.50000 2.59808i 0.173344 0.180144i
\(209\) 48.2487 3.33743
\(210\) 1.73205 1.00000i 0.119523 0.0690066i
\(211\) 5.66025 + 9.80385i 0.389668 + 0.674925i 0.992405 0.123015i \(-0.0392564\pi\)
−0.602737 + 0.797940i \(0.705923\pi\)
\(212\) 0.464102 0.803848i 0.0318746 0.0552085i
\(213\) 12.3923i 0.849107i
\(214\) −6.80385 3.92820i −0.465101 0.268526i
\(215\) 10.3301 + 5.96410i 0.704509 + 0.406748i
\(216\) 1.00000i 0.0680414i
\(217\) 1.73205 3.00000i 0.117579 0.203653i
\(218\) −7.92820 13.7321i −0.536966 0.930052i
\(219\) 1.73205 1.00000i 0.117041 0.0675737i
\(220\) −6.46410 −0.435810
\(221\) 14.0000 + 3.46410i 0.941742 + 0.233021i
\(222\) −9.19615 −0.617205
\(223\) −17.7846 + 10.2679i −1.19095 + 0.687593i −0.958521 0.285022i \(-0.907999\pi\)
−0.232424 + 0.972614i \(0.574666\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 0.803848i 0.0534711i
\(227\) −14.1962 8.19615i −0.942232 0.543998i −0.0515725 0.998669i \(-0.516423\pi\)
−0.890659 + 0.454672i \(0.849757\pi\)
\(228\) 6.46410 + 3.73205i 0.428096 + 0.247161i
\(229\) 7.85641i 0.519166i 0.965721 + 0.259583i \(0.0835851\pi\)
−0.965721 + 0.259583i \(0.916415\pi\)
\(230\) 1.86603 3.23205i 0.123042 0.213115i
\(231\) −6.46410 11.1962i −0.425307 0.736653i
\(232\) 0.232051 0.133975i 0.0152349 0.00879586i
\(233\) 6.12436 0.401220 0.200610 0.979671i \(-0.435708\pi\)
0.200610 + 0.979671i \(0.435708\pi\)
\(234\) 3.46410 1.00000i 0.226455 0.0653720i
\(235\) 3.53590 0.230657
\(236\) 7.33013 4.23205i 0.477151 0.275483i
\(237\) −6.96410 12.0622i −0.452367 0.783523i
\(238\) 4.00000 6.92820i 0.259281 0.449089i
\(239\) 16.3923i 1.06033i 0.847894 + 0.530165i \(0.177870\pi\)
−0.847894 + 0.530165i \(0.822130\pi\)
\(240\) −0.866025 0.500000i −0.0559017 0.0322749i
\(241\) 15.3564 + 8.86603i 0.989193 + 0.571111i 0.905033 0.425341i \(-0.139846\pi\)
0.0841601 + 0.996452i \(0.473179\pi\)
\(242\) 30.7846i 1.97891i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.19615 9.00000i −0.332650 0.576166i
\(245\) −2.59808 + 1.50000i −0.165985 + 0.0958315i
\(246\) −2.00000 −0.127515
\(247\) −6.46410 + 26.1244i −0.411301 + 1.66225i
\(248\) −1.73205 −0.109985
\(249\) 7.73205 4.46410i 0.489999 0.282901i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −7.86603 + 13.6244i −0.496499 + 0.859962i −0.999992 0.00403776i \(-0.998715\pi\)
0.503493 + 0.863999i \(0.332048\pi\)
\(252\) 2.00000i 0.125988i
\(253\) −20.8923 12.0622i −1.31349 0.758343i
\(254\) −4.26795 2.46410i −0.267795 0.154611i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 2.66987 + 4.62436i 0.166542 + 0.288459i 0.937202 0.348787i \(-0.113407\pi\)
−0.770660 + 0.637247i \(0.780073\pi\)
\(258\) 10.3301 5.96410i 0.643126 0.371309i
\(259\) −18.3923 −1.14284
\(260\) 0.866025 3.50000i 0.0537086 0.217061i
\(261\) 0.267949 0.0165856
\(262\) 16.1603 9.33013i 0.998384 0.576417i
\(263\) −3.06218 5.30385i −0.188822 0.327049i 0.756036 0.654530i \(-0.227134\pi\)
−0.944858 + 0.327481i \(0.893800\pi\)
\(264\) −3.23205 + 5.59808i −0.198919 + 0.344538i
\(265\) 0.928203i 0.0570191i
\(266\) 12.9282 + 7.46410i 0.792679 + 0.457653i
\(267\) −0.464102 0.267949i −0.0284026 0.0163982i
\(268\) 11.4641i 0.700281i
\(269\) −6.00000 + 10.3923i −0.365826 + 0.633630i −0.988908 0.148527i \(-0.952547\pi\)
0.623082 + 0.782157i \(0.285880\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 1.03590 0.598076i 0.0629263 0.0363305i −0.468207 0.883619i \(-0.655100\pi\)
0.531133 + 0.847288i \(0.321766\pi\)
\(272\) −4.00000 −0.242536
\(273\) 6.92820 2.00000i 0.419314 0.121046i
\(274\) 2.46410 0.148862
\(275\) −5.59808 + 3.23205i −0.337577 + 0.194900i
\(276\) −1.86603 3.23205i −0.112322 0.194547i
\(277\) 1.96410 3.40192i 0.118011 0.204402i −0.800968 0.598707i \(-0.795681\pi\)
0.918980 + 0.394305i \(0.129015\pi\)
\(278\) 12.9282i 0.775382i
\(279\) −1.50000 0.866025i −0.0898027 0.0518476i
\(280\) −1.73205 1.00000i −0.103510 0.0597614i
\(281\) 8.92820i 0.532612i 0.963889 + 0.266306i \(0.0858032\pi\)
−0.963889 + 0.266306i \(0.914197\pi\)
\(282\) 1.76795 3.06218i 0.105280 0.182350i
\(283\) 4.96410 + 8.59808i 0.295085 + 0.511103i 0.975005 0.222184i \(-0.0713186\pi\)
−0.679920 + 0.733287i \(0.737985\pi\)
\(284\) −10.7321 + 6.19615i −0.636830 + 0.367674i
\(285\) 7.46410 0.442135
\(286\) −22.6244 5.59808i −1.33781 0.331021i
\(287\) −4.00000 −0.236113
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0.133975 0.232051i 0.00786726 0.0136265i
\(291\) 0.535898i 0.0314149i
\(292\) −1.73205 1.00000i −0.101361 0.0585206i
\(293\) −27.5885 15.9282i −1.61173 0.930536i −0.988968 0.148128i \(-0.952675\pi\)
−0.622767 0.782408i \(-0.713991\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 4.23205 7.33013i 0.246400 0.426776i
\(296\) 4.59808 + 7.96410i 0.267258 + 0.462904i
\(297\) −5.59808 + 3.23205i −0.324833 + 0.187543i
\(298\) 13.5359 0.784114
\(299\) 9.33013 9.69615i 0.539575 0.560743i
\(300\) −1.00000 −0.0577350
\(301\) 20.6603 11.9282i 1.19084 0.687530i
\(302\) −5.19615 9.00000i −0.299005 0.517892i
\(303\) 1.46410 2.53590i 0.0841104 0.145684i
\(304\) 7.46410i 0.428096i
\(305\) −9.00000 5.19615i −0.515339 0.297531i
\(306\) −3.46410 2.00000i −0.198030 0.114332i
\(307\) 19.4641i 1.11087i −0.831558 0.555437i \(-0.812551\pi\)
0.831558 0.555437i \(-0.187449\pi\)
\(308\) −6.46410 + 11.1962i −0.368326 + 0.637960i
\(309\) −5.92820 10.2679i −0.337244 0.584123i
\(310\) −1.50000 + 0.866025i −0.0851943 + 0.0491869i
\(311\) −28.3923 −1.60998 −0.804990 0.593288i \(-0.797829\pi\)
−0.804990 + 0.593288i \(0.797829\pi\)
\(312\) −2.59808 2.50000i −0.147087 0.141535i
\(313\) −28.0000 −1.58265 −0.791327 0.611393i \(-0.790609\pi\)
−0.791327 + 0.611393i \(0.790609\pi\)
\(314\) 4.33013 2.50000i 0.244363 0.141083i
\(315\) −1.00000 1.73205i −0.0563436 0.0975900i
\(316\) −6.96410 + 12.0622i −0.391761 + 0.678551i
\(317\) 14.5359i 0.816417i −0.912889 0.408209i \(-0.866154\pi\)
0.912889 0.408209i \(-0.133846\pi\)
\(318\) −0.803848 0.464102i −0.0450775 0.0260255i
\(319\) −1.50000 0.866025i −0.0839839 0.0484881i
\(320\) 1.00000i 0.0559017i
\(321\) −3.92820 + 6.80385i −0.219251 + 0.379754i
\(322\) −3.73205 6.46410i −0.207979 0.360230i
\(323\) 25.8564 14.9282i 1.43869 0.830627i
\(324\) −1.00000 −0.0555556
\(325\) −1.00000 3.46410i −0.0554700 0.192154i
\(326\) −15.0526 −0.833684
\(327\) −13.7321 + 7.92820i −0.759384 + 0.438431i
\(328\) 1.00000 + 1.73205i 0.0552158 + 0.0956365i
\(329\) 3.53590 6.12436i 0.194940 0.337647i
\(330\) 6.46410i 0.355837i
\(331\) −14.5359 8.39230i −0.798965 0.461283i 0.0441440 0.999025i \(-0.485944\pi\)
−0.843109 + 0.537742i \(0.819277\pi\)
\(332\) −7.73205 4.46410i −0.424351 0.244999i
\(333\) 9.19615i 0.503946i
\(334\) −8.16025 + 14.1340i −0.446509 + 0.773377i
\(335\) 5.73205 + 9.92820i 0.313175 + 0.542436i
\(336\) −1.73205 + 1.00000i −0.0944911 + 0.0545545i
\(337\) 9.32051 0.507720 0.253860 0.967241i \(-0.418300\pi\)
0.253860 + 0.967241i \(0.418300\pi\)
\(338\) 6.06218 11.5000i 0.329739 0.625518i
\(339\) −0.803848 −0.0436590
\(340\) −3.46410 + 2.00000i −0.187867 + 0.108465i
\(341\) 5.59808 + 9.69615i 0.303153 + 0.525076i
\(342\) 3.73205 6.46410i 0.201806 0.349539i
\(343\) 20.0000i 1.07990i
\(344\) −10.3301 5.96410i −0.556963 0.321563i
\(345\) −3.23205 1.86603i −0.174008 0.100463i
\(346\) 10.9282i 0.587504i
\(347\) −0.803848 + 1.39230i −0.0431528 + 0.0747428i −0.886795 0.462163i \(-0.847074\pi\)
0.843642 + 0.536906i \(0.180407\pi\)
\(348\) −0.133975 0.232051i −0.00718179 0.0124392i
\(349\) 18.5885 10.7321i 0.995017 0.574474i 0.0882471 0.996099i \(-0.471873\pi\)
0.906770 + 0.421625i \(0.138540\pi\)
\(350\) −2.00000 −0.106904
\(351\) −1.00000 3.46410i −0.0533761 0.184900i
\(352\) 6.46410 0.344538
\(353\) 1.73205 1.00000i 0.0921878 0.0532246i −0.453197 0.891410i \(-0.649717\pi\)
0.545385 + 0.838186i \(0.316383\pi\)
\(354\) −4.23205 7.33013i −0.224931 0.389592i
\(355\) −6.19615 + 10.7321i −0.328858 + 0.569598i
\(356\) 0.535898i 0.0284026i
\(357\) −6.92820 4.00000i −0.366679 0.211702i
\(358\) −17.0885 9.86603i −0.903153 0.521436i
\(359\) 5.07180i 0.267679i −0.991003 0.133840i \(-0.957269\pi\)
0.991003 0.133840i \(-0.0427307\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 18.3564 + 31.7942i 0.966127 + 1.67338i
\(362\) 2.53590 1.46410i 0.133284 0.0769515i
\(363\) 30.7846 1.61577
\(364\) −5.19615 5.00000i −0.272352 0.262071i
\(365\) −2.00000 −0.104685
\(366\) −9.00000 + 5.19615i −0.470438 + 0.271607i
\(367\) −7.80385 13.5167i −0.407358 0.705564i 0.587235 0.809416i \(-0.300216\pi\)
−0.994593 + 0.103852i \(0.966883\pi\)
\(368\) −1.86603 + 3.23205i −0.0972733 + 0.168482i
\(369\) 2.00000i 0.104116i
\(370\) 7.96410 + 4.59808i 0.414034 + 0.239043i
\(371\) −1.60770 0.928203i −0.0834674 0.0481899i
\(372\) 1.73205i 0.0898027i
\(373\) 7.89230 13.6699i 0.408648 0.707799i −0.586090 0.810246i \(-0.699334\pi\)
0.994739 + 0.102446i \(0.0326670\pi\)
\(374\) 12.9282 + 22.3923i 0.668501 + 1.15788i
\(375\) −0.866025 + 0.500000i −0.0447214 + 0.0258199i
\(376\) −3.53590 −0.182350
\(377\) 0.669873 0.696152i 0.0345002 0.0358537i
\(378\) −2.00000 −0.102869
\(379\) 24.1244 13.9282i 1.23918 0.715444i 0.270257 0.962788i \(-0.412891\pi\)
0.968928 + 0.247344i \(0.0795579\pi\)
\(380\) −3.73205 6.46410i −0.191450 0.331601i
\(381\) −2.46410 + 4.26795i −0.126240 + 0.218654i
\(382\) 21.4641i 1.09820i
\(383\) 21.9904 + 12.6962i 1.12366 + 0.648743i 0.942332 0.334680i \(-0.108628\pi\)
0.181324 + 0.983423i \(0.441962\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 12.9282i 0.658882i
\(386\) −5.66025 + 9.80385i −0.288099 + 0.499003i
\(387\) −5.96410 10.3301i −0.303172 0.525110i
\(388\) 0.464102 0.267949i 0.0235612 0.0136031i
\(389\) −23.7321 −1.20326 −0.601631 0.798774i \(-0.705482\pi\)
−0.601631 + 0.798774i \(0.705482\pi\)
\(390\) −3.50000 0.866025i −0.177229 0.0438529i
\(391\) −14.9282 −0.754952
\(392\) 2.59808 1.50000i 0.131223 0.0757614i
\(393\) −9.33013 16.1603i −0.470643 0.815177i
\(394\) −2.19615 + 3.80385i −0.110641 + 0.191635i
\(395\) 13.9282i 0.700804i
\(396\) 5.59808 + 3.23205i 0.281314 + 0.162417i
\(397\) 10.5000 + 6.06218i 0.526980 + 0.304252i 0.739786 0.672843i \(-0.234927\pi\)
−0.212806 + 0.977095i \(0.568260\pi\)
\(398\) 5.07180i 0.254226i
\(399\) 7.46410 12.9282i 0.373672 0.647220i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −27.7128 + 16.0000i −1.38391 + 0.799002i −0.992620 0.121265i \(-0.961305\pi\)
−0.391292 + 0.920267i \(0.627972\pi\)
\(402\) 11.4641 0.571777
\(403\) −6.00000 + 1.73205i −0.298881 + 0.0862796i
\(404\) −2.92820 −0.145684
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) −0.267949 0.464102i −0.0132981 0.0230330i
\(407\) 29.7224 51.4808i 1.47329 2.55181i
\(408\) 4.00000i 0.198030i
\(409\) 3.46410 + 2.00000i 0.171289 + 0.0988936i 0.583193 0.812333i \(-0.301803\pi\)
−0.411905 + 0.911227i \(0.635136\pi\)
\(410\) 1.73205 + 1.00000i 0.0855399 + 0.0493865i
\(411\) 2.46410i 0.121545i
\(412\) −5.92820 + 10.2679i −0.292062 + 0.505866i
\(413\) −8.46410 14.6603i −0.416491 0.721384i
\(414\) −3.23205 + 1.86603i −0.158847 + 0.0917101i
\(415\) −8.92820 −0.438268
\(416\) −0.866025 + 3.50000i −0.0424604 + 0.171602i
\(417\) 12.9282 0.633097
\(418\) −41.7846 + 24.1244i −2.04375 + 1.17996i
\(419\) −11.1962 19.3923i −0.546968 0.947376i −0.998480 0.0551112i \(-0.982449\pi\)
0.451512 0.892265i \(-0.350885\pi\)
\(420\) −1.00000 + 1.73205i −0.0487950 + 0.0845154i
\(421\) 4.39230i 0.214068i −0.994255 0.107034i \(-0.965865\pi\)
0.994255 0.107034i \(-0.0341353\pi\)
\(422\) −9.80385 5.66025i −0.477244 0.275537i
\(423\) −3.06218 1.76795i −0.148888 0.0859606i
\(424\) 0.928203i 0.0450775i
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 6.19615 + 10.7321i 0.300205 + 0.519970i
\(427\) −18.0000 + 10.3923i −0.871081 + 0.502919i
\(428\) 7.85641 0.379754
\(429\) −5.59808 + 22.6244i −0.270278 + 1.09231i
\(430\) −11.9282 −0.575229
\(431\) 24.5885 14.1962i 1.18438 0.683805i 0.227360 0.973811i \(-0.426991\pi\)
0.957025 + 0.290006i \(0.0936574\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −9.66025 + 16.7321i −0.464242 + 0.804091i −0.999167 0.0408086i \(-0.987007\pi\)
0.534925 + 0.844900i \(0.320340\pi\)
\(434\) 3.46410i 0.166282i
\(435\) −0.232051 0.133975i −0.0111260 0.00642359i
\(436\) 13.7321 + 7.92820i 0.657646 + 0.379692i
\(437\) 27.8564i 1.33255i
\(438\) −1.00000 + 1.73205i −0.0477818 + 0.0827606i
\(439\) 8.92820 + 15.4641i 0.426120 + 0.738061i 0.996524 0.0833027i \(-0.0265468\pi\)
−0.570404 + 0.821364i \(0.693214\pi\)
\(440\) 5.59808 3.23205i 0.266878 0.154082i
\(441\) 3.00000 0.142857
\(442\) −13.8564 + 4.00000i −0.659082 + 0.190261i
\(443\) 16.3923 0.778822 0.389411 0.921064i \(-0.372679\pi\)
0.389411 + 0.921064i \(0.372679\pi\)
\(444\) 7.96410 4.59808i 0.377960 0.218215i
\(445\) 0.267949 + 0.464102i 0.0127020 + 0.0220005i
\(446\) 10.2679 17.7846i 0.486201 0.842126i
\(447\) 13.5359i 0.640226i
\(448\) 1.73205 + 1.00000i 0.0818317 + 0.0472456i
\(449\) −13.6077 7.85641i −0.642187 0.370767i 0.143270 0.989684i \(-0.454238\pi\)
−0.785456 + 0.618917i \(0.787572\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 6.46410 11.1962i 0.304383 0.527206i
\(452\) 0.401924 + 0.696152i 0.0189049 + 0.0327443i
\(453\) −9.00000 + 5.19615i −0.422857 + 0.244137i
\(454\) 16.3923 0.769329
\(455\) −7.00000 1.73205i −0.328165 0.0811998i
\(456\) −7.46410 −0.349539
\(457\) 21.2487 12.2679i 0.993973 0.573870i 0.0875134 0.996163i \(-0.472108\pi\)
0.906459 + 0.422293i \(0.138775\pi\)
\(458\) −3.92820 6.80385i −0.183553 0.317923i
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 3.73205i 0.174008i
\(461\) 0.401924 + 0.232051i 0.0187195 + 0.0108077i 0.509331 0.860571i \(-0.329893\pi\)
−0.490611 + 0.871379i \(0.663226\pi\)
\(462\) 11.1962 + 6.46410i 0.520892 + 0.300737i
\(463\) 7.07180i 0.328654i −0.986406 0.164327i \(-0.947455\pi\)
0.986406 0.164327i \(-0.0525453\pi\)
\(464\) −0.133975 + 0.232051i −0.00621961 + 0.0107727i
\(465\) 0.866025 + 1.50000i 0.0401610 + 0.0695608i
\(466\) −5.30385 + 3.06218i −0.245696 + 0.141853i
\(467\) −15.8564 −0.733747 −0.366873 0.930271i \(-0.619572\pi\)
−0.366873 + 0.930271i \(0.619572\pi\)
\(468\) −2.50000 + 2.59808i −0.115563 + 0.120096i
\(469\) 22.9282 1.05873
\(470\) −3.06218 + 1.76795i −0.141248 + 0.0815494i
\(471\) −2.50000 4.33013i −0.115194 0.199522i
\(472\) −4.23205 + 7.33013i −0.194796 + 0.337396i
\(473\) 77.1051i 3.54530i
\(474\) 12.0622 + 6.96410i 0.554034 + 0.319872i
\(475\) −6.46410 3.73205i −0.296593 0.171238i
\(476\) 8.00000i 0.366679i
\(477\) −0.464102 + 0.803848i −0.0212498 + 0.0368057i
\(478\) −8.19615 14.1962i −0.374883 0.649317i
\(479\) 4.73205 2.73205i 0.216213 0.124831i −0.387983 0.921667i \(-0.626828\pi\)
0.604195 + 0.796836i \(0.293495\pi\)
\(480\) 1.00000 0.0456435
\(481\) 23.8923 + 22.9904i 1.08940 + 1.04827i
\(482\) −17.7321 −0.807673
\(483\) −6.46410 + 3.73205i −0.294127 + 0.169814i
\(484\) −15.3923 26.6603i −0.699650 1.21183i
\(485\) 0.267949 0.464102i 0.0121669 0.0210738i
\(486\) 1.00000i 0.0453609i
\(487\) 20.0718 + 11.5885i 0.909540 + 0.525123i 0.880283 0.474449i \(-0.157353\pi\)
0.0292568 + 0.999572i \(0.490686\pi\)
\(488\) 9.00000 + 5.19615i 0.407411 + 0.235219i
\(489\) 15.0526i 0.680700i
\(490\) 1.50000 2.59808i 0.0677631 0.117369i
\(491\) 8.66025 + 15.0000i 0.390832 + 0.676941i 0.992559 0.121761i \(-0.0388541\pi\)
−0.601728 + 0.798701i \(0.705521\pi\)
\(492\) 1.73205 1.00000i 0.0780869 0.0450835i
\(493\) −1.07180 −0.0482713
\(494\) −7.46410 25.8564i −0.335826 1.16333i
\(495\) 6.46410 0.290540
\(496\) 1.50000 0.866025i 0.0673520 0.0388857i
\(497\) 12.3923 + 21.4641i 0.555871 + 0.962797i
\(498\) −4.46410 + 7.73205i −0.200041 + 0.346481i
\(499\) 6.53590i 0.292587i −0.989241 0.146293i \(-0.953266\pi\)
0.989241 0.146293i \(-0.0467344\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 14.1340 + 8.16025i 0.631459 + 0.364573i
\(502\) 15.7321i 0.702156i
\(503\) 15.5885 27.0000i 0.695055 1.20387i −0.275107 0.961414i \(-0.588713\pi\)
0.970162 0.242457i \(-0.0779533\pi\)
\(504\) 1.00000 + 1.73205i 0.0445435 + 0.0771517i
\(505\) −2.53590 + 1.46410i −0.112846 + 0.0651517i
\(506\) 24.1244 1.07246
\(507\) −11.5000 6.06218i −0.510733 0.269231i
\(508\) 4.92820 0.218654
\(509\) 1.20577 0.696152i 0.0534449 0.0308564i −0.473039 0.881041i \(-0.656843\pi\)
0.526484 + 0.850185i \(0.323510\pi\)
\(510\) 2.00000 + 3.46410i 0.0885615 + 0.153393i
\(511\) −2.00000 + 3.46410i −0.0884748 + 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) −6.46410 3.73205i −0.285397 0.164774i
\(514\) −4.62436 2.66987i −0.203972 0.117763i
\(515\) 11.8564i 0.522456i
\(516\) −5.96410 + 10.3301i −0.262555 + 0.454758i
\(517\) 11.4282 + 19.7942i 0.502612 + 0.870549i
\(518\) 15.9282 9.19615i 0.699845 0.404056i
\(519\) −10.9282 −0.479695
\(520\) 1.00000 + 3.46410i 0.0438529 + 0.151911i
\(521\) −17.3205 −0.758825 −0.379413 0.925228i \(-0.623874\pi\)
−0.379413 + 0.925228i \(0.623874\pi\)
\(522\) −0.232051 + 0.133975i −0.0101566 + 0.00586391i
\(523\) −5.89230 10.2058i −0.257653 0.446267i 0.707960 0.706252i \(-0.249616\pi\)
−0.965613 + 0.259985i \(0.916282\pi\)
\(524\) −9.33013 + 16.1603i −0.407588 + 0.705964i
\(525\) 2.00000i 0.0872872i
\(526\) 5.30385 + 3.06218i 0.231259 + 0.133517i
\(527\) 6.00000 + 3.46410i 0.261364 + 0.150899i
\(528\) 6.46410i 0.281314i
\(529\) 4.53590 7.85641i 0.197213 0.341583i
\(530\) 0.464102 + 0.803848i 0.0201593 + 0.0349169i
\(531\) −7.33013 + 4.23205i −0.318100 + 0.183655i
\(532\) −14.9282 −0.647220
\(533\) 5.19615 + 5.00000i 0.225070 + 0.216574i
\(534\) 0.535898 0.0231906
\(535\) 6.80385 3.92820i 0.294156 0.169831i
\(536\) −5.73205 9.92820i −0.247587 0.428833i
\(537\) −9.86603 + 17.0885i −0.425750 + 0.737421i
\(538\) 12.0000i 0.517357i
\(539\) −16.7942 9.69615i −0.723379 0.417643i
\(540\) 0.866025 + 0.500000i 0.0372678 + 0.0215166i
\(541\) 26.9282i 1.15773i −0.815422 0.578867i \(-0.803495\pi\)
0.815422 0.578867i \(-0.196505\pi\)
\(542\) −0.598076 + 1.03590i −0.0256896 + 0.0444956i
\(543\) −1.46410 2.53590i −0.0628306 0.108826i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) 15.8564 0.679214
\(546\) −5.00000 + 5.19615i −0.213980 + 0.222375i
\(547\) 22.9282 0.980339 0.490170 0.871627i \(-0.336935\pi\)
0.490170 + 0.871627i \(0.336935\pi\)
\(548\) −2.13397 + 1.23205i −0.0911589 + 0.0526306i
\(549\) 5.19615 + 9.00000i 0.221766 + 0.384111i
\(550\) 3.23205 5.59808i 0.137815 0.238703i
\(551\) 2.00000i 0.0852029i
\(552\) 3.23205 + 1.86603i 0.137565 + 0.0794233i
\(553\) 24.1244 + 13.9282i 1.02587 + 0.592287i
\(554\) 3.92820i 0.166893i
\(555\) 4.59808 7.96410i 0.195177 0.338057i
\(556\) −6.46410 11.1962i −0.274139 0.474823i
\(557\) 15.3397 8.85641i 0.649966 0.375258i −0.138477 0.990366i \(-0.544221\pi\)
0.788443 + 0.615108i \(0.210887\pi\)
\(558\) 1.73205 0.0733236
\(559\) −41.7487 10.3301i −1.76578 0.436918i
\(560\) 2.00000 0.0845154
\(561\) 22.3923 12.9282i 0.945404 0.545829i
\(562\) −4.46410 7.73205i −0.188307 0.326157i
\(563\) 2.33975 4.05256i 0.0986085 0.170795i −0.812500 0.582961i \(-0.801894\pi\)
0.911109 + 0.412166i \(0.135228\pi\)
\(564\) 3.53590i 0.148888i
\(565\) 0.696152 + 0.401924i 0.0292874 + 0.0169091i
\(566\) −8.59808 4.96410i −0.361404 0.208657i
\(567\) 2.00000i 0.0839921i
\(568\) 6.19615 10.7321i 0.259985 0.450307i
\(569\) −14.6603 25.3923i −0.614590 1.06450i −0.990456 0.137827i \(-0.955988\pi\)
0.375867 0.926674i \(-0.377345\pi\)
\(570\) −6.46410 + 3.73205i −0.270751 + 0.156318i
\(571\) −17.1769 −0.718832 −0.359416 0.933178i \(-0.617024\pi\)
−0.359416 + 0.933178i \(0.617024\pi\)
\(572\) 22.3923 6.46410i 0.936269 0.270278i
\(573\) −21.4641 −0.896676
\(574\) 3.46410 2.00000i 0.144589 0.0834784i
\(575\) 1.86603 + 3.23205i 0.0778186 + 0.134786i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 10.0000i 0.416305i 0.978096 + 0.208153i \(0.0667451\pi\)
−0.978096 + 0.208153i \(0.933255\pi\)
\(578\) −0.866025 0.500000i −0.0360219 0.0207973i
\(579\) 9.80385 + 5.66025i 0.407434 + 0.235232i
\(580\) 0.267949i 0.0111260i
\(581\) −8.92820 + 15.4641i −0.370404 + 0.641559i
\(582\) −0.267949 0.464102i −0.0111069 0.0192376i
\(583\) 5.19615 3.00000i 0.215203 0.124247i
\(584\) 2.00000 0.0827606
\(585\) −0.866025 + 3.50000i −0.0358057 + 0.144707i
\(586\) 31.8564 1.31598
\(587\) −2.07180 + 1.19615i −0.0855122 + 0.0493705i −0.542146 0.840284i \(-0.682388\pi\)
0.456634 + 0.889655i \(0.349055\pi\)
\(588\) −1.50000 2.59808i −0.0618590 0.107143i
\(589\) −6.46410 + 11.1962i −0.266349 + 0.461329i
\(590\) 8.46410i 0.348462i
\(591\) 3.80385 + 2.19615i 0.156469 + 0.0903376i
\(592\) −7.96410 4.59808i −0.327323 0.188980i
\(593\) 45.1051i 1.85225i −0.377223 0.926123i \(-0.623121\pi\)
0.377223 0.926123i \(-0.376879\pi\)
\(594\) 3.23205 5.59808i 0.132613 0.229692i
\(595\) 4.00000 + 6.92820i 0.163984 + 0.284029i
\(596\) −11.7224 + 6.76795i −0.480170 + 0.277226i
\(597\) 5.07180 0.207575
\(598\) −3.23205 + 13.0622i −0.132168 + 0.534152i
\(599\) −10.3923 −0.424618 −0.212309 0.977203i \(-0.568098\pi\)
−0.212309 + 0.977203i \(0.568098\pi\)
\(600\) 0.866025 0.500000i 0.0353553 0.0204124i
\(601\) 9.89230 + 17.1340i 0.403516 + 0.698909i 0.994147 0.108032i \(-0.0344548\pi\)
−0.590632 + 0.806941i \(0.701121\pi\)
\(602\) −11.9282 + 20.6603i −0.486157 + 0.842049i
\(603\) 11.4641i 0.466854i
\(604\) 9.00000 + 5.19615i 0.366205 + 0.211428i
\(605\) −26.6603 15.3923i −1.08389 0.625786i
\(606\) 2.92820i 0.118950i
\(607\) 9.58846 16.6077i 0.389183 0.674086i −0.603156 0.797623i \(-0.706091\pi\)
0.992340 + 0.123537i \(0.0394239\pi\)
\(608\) 3.73205 + 6.46410i 0.151355 + 0.262154i
\(609\) −0.464102 + 0.267949i −0.0188063 + 0.0108578i
\(610\) 10.3923 0.420772
\(611\) −12.2487 + 3.53590i −0.495530 + 0.143047i
\(612\) 4.00000 0.161690
\(613\) −33.8205 + 19.5263i −1.36600 + 0.788659i −0.990414 0.138130i \(-0.955891\pi\)
−0.375583 + 0.926789i \(0.622558\pi\)
\(614\) 9.73205 + 16.8564i 0.392754 + 0.680269i
\(615\) 1.00000 1.73205i 0.0403239 0.0698430i
\(616\) 12.9282i 0.520892i
\(617\) −19.4545 11.2321i −0.783208 0.452185i 0.0543580 0.998522i \(-0.482689\pi\)
−0.837566 + 0.546336i \(0.816022\pi\)
\(618\) 10.2679 + 5.92820i 0.413037 + 0.238467i
\(619\) 24.2487i 0.974638i 0.873224 + 0.487319i \(0.162025\pi\)
−0.873224 + 0.487319i \(0.837975\pi\)
\(620\) 0.866025 1.50000i 0.0347804 0.0602414i
\(621\) 1.86603 + 3.23205i 0.0748810 + 0.129698i
\(622\) 24.5885 14.1962i 0.985907 0.569214i
\(623\) 1.07180 0.0429406
\(624\) 3.50000 + 0.866025i 0.140112 + 0.0346688i
\(625\) 1.00000 0.0400000
\(626\) 24.2487 14.0000i 0.969173 0.559553i
\(627\) 24.1244 + 41.7846i 0.963434 + 1.66872i
\(628\) −2.50000 + 4.33013i −0.0997609 + 0.172791i
\(629\) 36.7846i 1.46670i
\(630\) 1.73205 + 1.00000i 0.0690066 + 0.0398410i
\(631\) 27.2487 + 15.7321i 1.08475 + 0.626283i 0.932175 0.362008i \(-0.117909\pi\)
0.152579 + 0.988291i \(0.451242\pi\)
\(632\) 13.9282i 0.554034i
\(633\) −5.66025 + 9.80385i −0.224975 + 0.389668i
\(634\) 7.26795 + 12.5885i 0.288647 + 0.499952i
\(635\) 4.26795 2.46410i 0.169368 0.0977849i
\(636\) 0.928203 0.0368057
\(637\) 7.50000 7.79423i 0.297161 0.308819i
\(638\) 1.73205 0.0685725
\(639\) 10.7321 6.19615i 0.424553 0.245116i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −0.0717968 + 0.124356i −0.00283580 + 0.00491175i −0.867440 0.497542i \(-0.834236\pi\)
0.864604 + 0.502454i \(0.167569\pi\)
\(642\) 7.85641i 0.310068i
\(643\) −17.7846 10.2679i −0.701357 0.404928i 0.106496 0.994313i \(-0.466037\pi\)
−0.807852 + 0.589385i \(0.799370\pi\)
\(644\) 6.46410 + 3.73205i 0.254721 + 0.147063i
\(645\) 11.9282i 0.469673i
\(646\) −14.9282 + 25.8564i −0.587342 + 1.01731i
\(647\) 6.66025 + 11.5359i 0.261842 + 0.453523i 0.966731 0.255794i \(-0.0823369\pi\)
−0.704890 + 0.709317i \(0.749004\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 54.7128 2.14767
\(650\) 2.59808 + 2.50000i 0.101905 + 0.0980581i
\(651\) 3.46410 0.135769
\(652\) 13.0359 7.52628i 0.510525 0.294752i
\(653\) −2.12436 3.67949i −0.0831325 0.143990i 0.821461 0.570264i \(-0.193159\pi\)
−0.904594 + 0.426274i \(0.859826\pi\)
\(654\) 7.92820 13.7321i 0.310017 0.536966i
\(655\) 18.6603i 0.729116i
\(656\) −1.73205 1.00000i −0.0676252 0.0390434i
\(657\) 1.73205 + 1.00000i 0.0675737 + 0.0390137i
\(658\) 7.07180i 0.275687i
\(659\) 0.133975 0.232051i 0.00521891 0.00903942i −0.863404 0.504513i \(-0.831672\pi\)
0.868623 + 0.495473i \(0.165005\pi\)
\(660\) −3.23205 5.59808i −0.125807 0.217905i
\(661\) −7.51666 + 4.33975i −0.292364 + 0.168797i −0.639008 0.769200i \(-0.720655\pi\)
0.346643 + 0.937997i \(0.387321\pi\)
\(662\) 16.7846 0.652352
\(663\) 4.00000 + 13.8564i 0.155347 + 0.538138i
\(664\) 8.92820 0.346481
\(665\) −12.9282 + 7.46410i −0.501334 + 0.289445i
\(666\) −4.59808 7.96410i −0.178172 0.308603i
\(667\) −0.500000 + 0.866025i −0.0193601 + 0.0335326i
\(668\) 16.3205i 0.631459i
\(669\) −17.7846 10.2679i −0.687593 0.396982i
\(670\) −9.92820 5.73205i −0.383560 0.221448i
\(671\) 67.1769i 2.59334i
\(672\) 1.00000 1.73205i 0.0385758 0.0668153i
\(673\) −16.0000 27.7128i −0.616755 1.06825i −0.990074 0.140548i \(-0.955114\pi\)
0.373319 0.927703i \(-0.378220\pi\)
\(674\) −8.07180 + 4.66025i −0.310914 + 0.179506i
\(675\) 1.00000 0.0384900
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) 32.3923 1.24494 0.622469 0.782645i \(-0.286130\pi\)
0.622469 + 0.782645i \(0.286130\pi\)
\(678\) 0.696152 0.401924i 0.0267356 0.0154358i
\(679\) −0.535898 0.928203i −0.0205659 0.0356212i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 16.3923i 0.628154i
\(682\) −9.69615 5.59808i −0.371285 0.214361i
\(683\) −35.3205 20.3923i −1.35150 0.780290i −0.363042 0.931773i \(-0.618262\pi\)
−0.988460 + 0.151483i \(0.951595\pi\)
\(684\) 7.46410i 0.285397i
\(685\) −1.23205 + 2.13397i −0.0470742 + 0.0815350i
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) −6.80385 + 3.92820i −0.259583 + 0.149870i
\(688\) 11.9282 0.454758
\(689\) 0.928203 + 3.21539i 0.0353617 + 0.122497i
\(690\) 3.73205 0.142077
\(691\) −23.5359 + 13.5885i −0.895348 + 0.516929i −0.875688 0.482877i \(-0.839592\pi\)
−0.0196598 + 0.999807i \(0.506258\pi\)
\(692\) 5.46410 + 9.46410i 0.207714 + 0.359771i
\(693\) 6.46410 11.1962i 0.245551 0.425307i
\(694\) 1.60770i 0.0610273i
\(695\) −11.1962 6.46410i −0.424694 0.245197i
\(696\) 0.232051 + 0.133975i 0.00879586 + 0.00507829i
\(697\) 8.00000i 0.303022i
\(698\) −10.7321 + 18.5885i −0.406214 + 0.703583i
\(699\) 3.06218 + 5.30385i 0.115822 + 0.200610i
\(700\) 1.73205 1.00000i 0.0654654 0.0377964i
\(701\) −0.267949 −0.0101203 −0.00506015 0.999987i \(-0.501611\pi\)
−0.00506015 + 0.999987i \(0.501611\pi\)
\(702\) 2.59808 + 2.50000i 0.0980581 + 0.0943564i
\(703\) 68.6410 2.58884
\(704\) −5.59808 + 3.23205i −0.210985 + 0.121812i
\(705\) 1.76795 + 3.06218i 0.0665848 + 0.115328i
\(706\) −1.00000 + 1.73205i −0.0376355 + 0.0651866i
\(707\) 5.85641i 0.220253i
\(708\) 7.33013 + 4.23205i 0.275483 + 0.159050i
\(709\) −19.8564 11.4641i −0.745723 0.430543i 0.0784234 0.996920i \(-0.475011\pi\)
−0.824146 + 0.566377i \(0.808345\pi\)
\(710\) 12.3923i 0.465075i
\(711\) 6.96410 12.0622i 0.261174 0.452367i
\(712\) −0.267949 0.464102i −0.0100418 0.0173929i
\(713\) 5.59808 3.23205i 0.209650 0.121041i
\(714\) 8.00000 0.299392
\(715\) 16.1603 16.7942i 0.604359 0.628069i
\(716\) 19.7321 0.737421
\(717\) −14.1962 + 8.19615i −0.530165 + 0.306091i
\(718\) 2.53590 + 4.39230i 0.0946389 + 0.163919i
\(719\) 17.3205 30.0000i 0.645946 1.11881i −0.338136 0.941097i \(-0.609796\pi\)
0.984082 0.177714i \(-0.0568702\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 20.5359 + 11.8564i 0.764797 + 0.441556i
\(722\) −31.7942 18.3564i −1.18326 0.683155i
\(723\) 17.7321i 0.659462i
\(724\) −1.46410 + 2.53590i −0.0544129 + 0.0942459i
\(725\) 0.133975 + 0.232051i 0.00497569 + 0.00861815i
\(726\) −26.6603 + 15.3923i −0.989455 + 0.571262i
\(727\) −31.7128 −1.17616 −0.588082 0.808802i \(-0.700117\pi\)
−0.588082 + 0.808802i \(0.700117\pi\)
\(728\) 7.00000 + 1.73205i 0.259437 + 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 1.73205 1.00000i 0.0641061 0.0370117i
\(731\) 23.8564 + 41.3205i 0.882361 + 1.52829i
\(732\) 5.19615 9.00000i 0.192055 0.332650i
\(733\) 50.9282i 1.88108i 0.339688 + 0.940538i \(0.389678\pi\)
−0.339688 + 0.940538i \(0.610322\pi\)
\(734\) 13.5167 + 7.80385i 0.498909 + 0.288045i
\(735\) −2.59808 1.50000i −0.0958315 0.0553283i
\(736\) 3.73205i 0.137565i
\(737\) −37.0526 + 64.1769i −1.36485 + 2.36399i
\(738\) −1.00000 1.73205i −0.0368105 0.0637577i
\(739\) −16.7321 + 9.66025i −0.615498 + 0.355358i −0.775114 0.631821i \(-0.782308\pi\)
0.159616 + 0.987179i \(0.448974\pi\)
\(740\) −9.19615 −0.338057
\(741\) −25.8564 + 7.46410i −0.949859 + 0.274201i
\(742\) 1.85641 0.0681508
\(743\) −35.0429 + 20.2321i −1.28560 + 0.742242i −0.977866 0.209230i \(-0.932904\pi\)
−0.307734 + 0.951472i \(0.599571\pi\)
\(744\) −0.866025 1.50000i −0.0317500 0.0549927i
\(745\) −6.76795 + 11.7224i −0.247958 + 0.429477i
\(746\) 15.7846i 0.577916i
\(747\) 7.73205 + 4.46410i 0.282901 + 0.163333i
\(748\) −22.3923 12.9282i −0.818744 0.472702i
\(749\) 15.7128i 0.574134i
\(750\) 0.500000 0.866025i 0.0182574 0.0316228i
\(751\) −7.03590 12.1865i −0.256744 0.444693i 0.708624 0.705586i \(-0.249316\pi\)
−0.965368 + 0.260893i \(0.915983\pi\)
\(752\) 3.06218 1.76795i 0.111666 0.0644705i
\(753\) −15.7321 −0.573308
\(754\) −0.232051 + 0.937822i −0.00845079 + 0.0341535i
\(755\) 10.3923 0.378215
\(756\) 1.73205 1.00000i 0.0629941 0.0363696i
\(757\) 9.00000 + 15.5885i 0.327111 + 0.566572i 0.981937 0.189207i \(-0.0605917\pi\)
−0.654827 + 0.755779i \(0.727258\pi\)
\(758\) −13.9282 + 24.1244i −0.505895 + 0.876236i
\(759\) 24.1244i 0.875659i
\(760\) 6.46410 + 3.73205i 0.234478 + 0.135376i
\(761\) 4.39230 + 2.53590i 0.159221 + 0.0919262i 0.577493 0.816395i \(-0.304031\pi\)
−0.418272 + 0.908322i \(0.637364\pi\)
\(762\) 4.92820i 0.178530i
\(763\) 15.8564 27.4641i 0.574040 0.994267i
\(764\) 10.7321 + 18.5885i 0.388272 + 0.672507i
\(765\) 3.46410 2.00000i 0.125245 0.0723102i
\(766\) −25.3923 −0.917461
\(767\) −7.33013 + 29.6244i −0.264676 + 1.06967i
\(768\) −1.00000 −0.0360844
\(769\) −10.0359 + 5.79423i −0.361904 + 0.208945i −0.669916 0.742437i \(-0.733670\pi\)
0.308012 + 0.951383i \(0.400336\pi\)
\(770\) −6.46410 11.1962i −0.232950 0.403481i
\(771\) −2.66987 + 4.62436i −0.0961531 + 0.166542i
\(772\) 11.3205i 0.407434i
\(773\) 24.0000 + 13.8564i 0.863220 + 0.498380i 0.865089 0.501618i \(-0.167262\pi\)
−0.00186926 + 0.999998i \(0.500595\pi\)
\(774\) 10.3301 + 5.96410i 0.371309 + 0.214375i
\(775\) 1.73205i 0.0622171i