Properties

Label 390.2.bb.a.361.2
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 361.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 390.361
Dual form 390.2.bb.a.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.232051 - 0.133975i) q^{11} +1.00000 q^{12} +(0.866025 - 3.50000i) q^{13} +3.00000 q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +1.00000i q^{18} +(4.96410 + 2.86603i) q^{19} +(-0.866025 - 0.500000i) q^{20} +3.00000i q^{21} +(0.133975 - 0.232051i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(2.59808 - 1.50000i) q^{28} +(-0.732051 - 1.26795i) q^{29} +(0.500000 - 0.866025i) q^{30} -4.92820i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.232051 + 0.133975i) q^{33} +4.00000i q^{34} +(1.50000 - 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-5.13397 + 2.96410i) q^{37} +5.73205 q^{38} +(3.46410 - 1.00000i) q^{39} -1.00000 q^{40} +(-3.46410 + 2.00000i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-3.00000 + 5.19615i) q^{43} -0.267949i q^{44} +(0.866025 + 0.500000i) q^{45} +(-3.00000 - 1.73205i) q^{46} +6.46410i q^{47} +(0.500000 - 0.866025i) q^{48} +(1.00000 + 1.73205i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +(-2.59808 - 2.50000i) q^{52} -0.267949 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.133975 - 0.232051i) q^{55} +(1.50000 - 2.59808i) q^{56} +5.73205i q^{57} +(-1.26795 - 0.732051i) q^{58} +(-9.92820 - 5.73205i) q^{59} -1.00000i q^{60} +(0.267949 - 0.464102i) q^{61} +(-2.46410 - 4.26795i) q^{62} +(-2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +(-3.50000 - 0.866025i) q^{65} +0.267949 q^{66} +(1.26795 - 0.732051i) q^{67} +(2.00000 + 3.46410i) q^{68} +(1.73205 - 3.00000i) q^{69} -3.00000i q^{70} +(-11.1962 - 6.46410i) q^{71} +(0.866025 + 0.500000i) q^{72} +6.92820i q^{73} +(-2.96410 + 5.13397i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(4.96410 - 2.86603i) q^{76} +0.803848 q^{77} +(2.50000 - 2.59808i) q^{78} +3.07180 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} -9.46410i q^{83} +(2.59808 + 1.50000i) q^{84} +(3.46410 + 2.00000i) q^{85} +6.00000i q^{86} +(0.732051 - 1.26795i) q^{87} +(-0.133975 - 0.232051i) q^{88} +(-12.2321 + 7.06218i) q^{89} +1.00000 q^{90} +(7.50000 - 7.79423i) q^{91} -3.46410 q^{92} +(4.26795 - 2.46410i) q^{93} +(3.23205 + 5.59808i) q^{94} +(2.86603 - 4.96410i) q^{95} -1.00000i q^{96} +(7.26795 + 4.19615i) q^{97} +(1.73205 + 1.00000i) q^{98} +0.267949i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} - 2q^{10} - 6q^{11} + 4q^{12} + 12q^{14} - 2q^{16} - 8q^{17} + 6q^{19} + 4q^{22} - 4q^{25} - 4q^{26} - 4q^{27} + 4q^{29} + 2q^{30} - 6q^{33} + 6q^{35} + 2q^{36} - 24q^{37} + 16q^{38} - 4q^{40} + 6q^{42} - 12q^{43} - 12q^{46} + 2q^{48} + 4q^{49} - 16q^{51} - 8q^{53} - 4q^{55} + 6q^{56} - 12q^{58} - 12q^{59} + 8q^{61} + 4q^{62} - 4q^{64} - 14q^{65} + 8q^{66} + 12q^{67} + 8q^{68} - 24q^{71} + 2q^{74} - 2q^{75} + 6q^{76} + 24q^{77} + 10q^{78} + 40q^{79} - 2q^{81} - 8q^{82} - 4q^{87} - 4q^{88} - 42q^{89} + 4q^{90} + 30q^{91} + 24q^{93} + 6q^{94} + 8q^{95} + 36q^{97} + O(q^{100}) \)

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
\(7\) 2.59808 + 1.50000i 0.981981 + 0.566947i 0.902867 0.429919i \(-0.141458\pi\)
0.0791130 + 0.996866i \(0.474791\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 0.232051 0.133975i 0.0699660 0.0403949i −0.464609 0.885516i \(-0.653805\pi\)
0.534575 + 0.845121i \(0.320472\pi\)
\(12\) 1.00000 0.288675
\(13\) 0.866025 3.50000i 0.240192 0.970725i
\(14\) 3.00000 0.801784
\(15\) 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 −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.96410 + 2.86603i 1.13884 + 0.657511i 0.946144 0.323747i \(-0.104943\pi\)
0.192699 + 0.981258i \(0.438276\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 3.00000i 0.654654i
\(22\) 0.133975 0.232051i 0.0285635 0.0494734i
\(23\) −1.73205 3.00000i −0.361158 0.625543i 0.626994 0.779024i \(-0.284285\pi\)
−0.988152 + 0.153481i \(0.950952\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) −1.00000 −0.200000
\(26\) −1.00000 3.46410i −0.196116 0.679366i
\(27\) −1.00000 −0.192450
\(28\) 2.59808 1.50000i 0.490990 0.283473i
\(29\) −0.732051 1.26795i −0.135938 0.235452i 0.790017 0.613085i \(-0.210072\pi\)
−0.925956 + 0.377633i \(0.876738\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) 4.92820i 0.885131i −0.896736 0.442566i \(-0.854068\pi\)
0.896736 0.442566i \(-0.145932\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0.232051 + 0.133975i 0.0403949 + 0.0233220i
\(34\) 4.00000i 0.685994i
\(35\) 1.50000 2.59808i 0.253546 0.439155i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −5.13397 + 2.96410i −0.844020 + 0.487295i −0.858629 0.512598i \(-0.828683\pi\)
0.0146085 + 0.999893i \(0.495350\pi\)
\(38\) 5.73205 0.929861
\(39\) 3.46410 1.00000i 0.554700 0.160128i
\(40\) −1.00000 −0.158114
\(41\) −3.46410 + 2.00000i −0.541002 + 0.312348i −0.745485 0.666523i \(-0.767782\pi\)
0.204483 + 0.978870i \(0.434449\pi\)
\(42\) 1.50000 + 2.59808i 0.231455 + 0.400892i
\(43\) −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i \(-0.984587\pi\)
0.541332 + 0.840809i \(0.317920\pi\)
\(44\) 0.267949i 0.0403949i
\(45\) 0.866025 + 0.500000i 0.129099 + 0.0745356i
\(46\) −3.00000 1.73205i −0.442326 0.255377i
\(47\) 6.46410i 0.942886i 0.881897 + 0.471443i \(0.156267\pi\)
−0.881897 + 0.471443i \(0.843733\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) −4.00000 −0.560112
\(52\) −2.59808 2.50000i −0.360288 0.346688i
\(53\) −0.267949 −0.0368057 −0.0184028 0.999831i \(-0.505858\pi\)
−0.0184028 + 0.999831i \(0.505858\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) −0.133975 0.232051i −0.0180651 0.0312897i
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 5.73205i 0.759229i
\(58\) −1.26795 0.732051i −0.166490 0.0961230i
\(59\) −9.92820 5.73205i −1.29254 0.746249i −0.313438 0.949609i \(-0.601481\pi\)
−0.979104 + 0.203359i \(0.934814\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 0.267949 0.464102i 0.0343074 0.0594221i −0.848362 0.529417i \(-0.822411\pi\)
0.882669 + 0.469995i \(0.155744\pi\)
\(62\) −2.46410 4.26795i −0.312941 0.542030i
\(63\) −2.59808 + 1.50000i −0.327327 + 0.188982i
\(64\) −1.00000 −0.125000
\(65\) −3.50000 0.866025i −0.434122 0.107417i
\(66\) 0.267949 0.0329823
\(67\) 1.26795 0.732051i 0.154905 0.0894342i −0.420544 0.907272i \(-0.638161\pi\)
0.575449 + 0.817838i \(0.304827\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 1.73205 3.00000i 0.208514 0.361158i
\(70\) 3.00000i 0.358569i
\(71\) −11.1962 6.46410i −1.32874 0.767148i −0.343634 0.939104i \(-0.611658\pi\)
−0.985105 + 0.171956i \(0.944991\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) −2.96410 + 5.13397i −0.344570 + 0.596812i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 4.96410 2.86603i 0.569422 0.328756i
\(77\) 0.803848 0.0916069
\(78\) 2.50000 2.59808i 0.283069 0.294174i
\(79\) 3.07180 0.345604 0.172802 0.984957i \(-0.444718\pi\)
0.172802 + 0.984957i \(0.444718\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.00000 + 3.46410i −0.220863 + 0.382546i
\(83\) 9.46410i 1.03882i −0.854525 0.519410i \(-0.826152\pi\)
0.854525 0.519410i \(-0.173848\pi\)
\(84\) 2.59808 + 1.50000i 0.283473 + 0.163663i
\(85\) 3.46410 + 2.00000i 0.375735 + 0.216930i
\(86\) 6.00000i 0.646997i
\(87\) 0.732051 1.26795i 0.0784841 0.135938i
\(88\) −0.133975 0.232051i −0.0142817 0.0247367i
\(89\) −12.2321 + 7.06218i −1.29659 + 0.748589i −0.979814 0.199910i \(-0.935935\pi\)
−0.316780 + 0.948499i \(0.602602\pi\)
\(90\) 1.00000 0.105409
\(91\) 7.50000 7.79423i 0.786214 0.817057i
\(92\) −3.46410 −0.361158
\(93\) 4.26795 2.46410i 0.442566 0.255515i
\(94\) 3.23205 + 5.59808i 0.333361 + 0.577397i
\(95\) 2.86603 4.96410i 0.294048 0.509306i
\(96\) 1.00000i 0.102062i
\(97\) 7.26795 + 4.19615i 0.737948 + 0.426055i 0.821323 0.570464i \(-0.193236\pi\)
−0.0833745 + 0.996518i \(0.526570\pi\)
\(98\) 1.73205 + 1.00000i 0.174964 + 0.101015i
\(99\) 0.267949i 0.0269299i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −6.19615 10.7321i −0.616540 1.06788i −0.990112 0.140278i \(-0.955200\pi\)
0.373572 0.927601i \(-0.378133\pi\)
\(102\) −3.46410 + 2.00000i −0.342997 + 0.198030i
\(103\) −11.5885 −1.14184 −0.570922 0.821004i \(-0.693414\pi\)
−0.570922 + 0.821004i \(0.693414\pi\)
\(104\) −3.50000 0.866025i −0.343203 0.0849208i
\(105\) 3.00000 0.292770
\(106\) −0.232051 + 0.133975i −0.0225388 + 0.0130128i
\(107\) 6.46410 + 11.1962i 0.624908 + 1.08237i 0.988559 + 0.150837i \(0.0481970\pi\)
−0.363650 + 0.931536i \(0.618470\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 10.3923i 0.995402i 0.867349 + 0.497701i \(0.165822\pi\)
−0.867349 + 0.497701i \(0.834178\pi\)
\(110\) −0.232051 0.133975i −0.0221252 0.0127740i
\(111\) −5.13397 2.96410i −0.487295 0.281340i
\(112\) 3.00000i 0.283473i
\(113\) 6.00000 10.3923i 0.564433 0.977626i −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) 2.86603 + 4.96410i 0.268428 + 0.464931i
\(115\) −3.00000 + 1.73205i −0.279751 + 0.161515i
\(116\) −1.46410 −0.135938
\(117\) 2.59808 + 2.50000i 0.240192 + 0.231125i
\(118\) −11.4641 −1.05536
\(119\) −10.3923 + 6.00000i −0.952661 + 0.550019i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) −5.46410 + 9.46410i −0.496737 + 0.860373i
\(122\) 0.535898i 0.0485180i
\(123\) −3.46410 2.00000i −0.312348 0.180334i
\(124\) −4.26795 2.46410i −0.383273 0.221283i
\(125\) 1.00000i 0.0894427i
\(126\) −1.50000 + 2.59808i −0.133631 + 0.231455i
\(127\) 6.33013 + 10.9641i 0.561708 + 0.972907i 0.997348 + 0.0727855i \(0.0231889\pi\)
−0.435640 + 0.900121i \(0.643478\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −6.00000 −0.528271
\(130\) −3.46410 + 1.00000i −0.303822 + 0.0877058i
\(131\) 14.3205 1.25119 0.625594 0.780149i \(-0.284857\pi\)
0.625594 + 0.780149i \(0.284857\pi\)
\(132\) 0.232051 0.133975i 0.0201974 0.0116610i
\(133\) 8.59808 + 14.8923i 0.745548 + 1.29133i
\(134\) 0.732051 1.26795i 0.0632396 0.109534i
\(135\) 1.00000i 0.0860663i
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) 11.6603 + 6.73205i 0.996203 + 0.575158i 0.907123 0.420867i \(-0.138274\pi\)
0.0890802 + 0.996024i \(0.471607\pi\)
\(138\) 3.46410i 0.294884i
\(139\) 9.89230 17.1340i 0.839054 1.45328i −0.0516319 0.998666i \(-0.516442\pi\)
0.890686 0.454619i \(-0.150224\pi\)
\(140\) −1.50000 2.59808i −0.126773 0.219578i
\(141\) −5.59808 + 3.23205i −0.471443 + 0.272188i
\(142\) −12.9282 −1.08491
\(143\) −0.267949 0.928203i −0.0224070 0.0776203i
\(144\) 1.00000 0.0833333
\(145\) −1.26795 + 0.732051i −0.105297 + 0.0607935i
\(146\) 3.46410 + 6.00000i 0.286691 + 0.496564i
\(147\) −1.00000 + 1.73205i −0.0824786 + 0.142857i
\(148\) 5.92820i 0.487295i
\(149\) 16.2679 + 9.39230i 1.33272 + 0.769448i 0.985716 0.168415i \(-0.0538649\pi\)
0.347006 + 0.937863i \(0.387198\pi\)
\(150\) −0.866025 0.500000i −0.0707107 0.0408248i
\(151\) 22.7846i 1.85419i −0.374832 0.927093i \(-0.622300\pi\)
0.374832 0.927093i \(-0.377700\pi\)
\(152\) 2.86603 4.96410i 0.232465 0.402642i
\(153\) −2.00000 3.46410i −0.161690 0.280056i
\(154\) 0.696152 0.401924i 0.0560976 0.0323879i
\(155\) −4.92820 −0.395843
\(156\) 0.866025 3.50000i 0.0693375 0.280224i
\(157\) 21.1962 1.69164 0.845819 0.533471i \(-0.179113\pi\)
0.845819 + 0.533471i \(0.179113\pi\)
\(158\) 2.66025 1.53590i 0.211638 0.122190i
\(159\) −0.133975 0.232051i −0.0106249 0.0184028i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 10.3923i 0.819028i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −2.53590 1.46410i −0.198627 0.114677i 0.397388 0.917651i \(-0.369917\pi\)
−0.596015 + 0.802973i \(0.703250\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0.133975 0.232051i 0.0104299 0.0180651i
\(166\) −4.73205 8.19615i −0.367278 0.636145i
\(167\) −0.401924 + 0.232051i −0.0311018 + 0.0179566i −0.515470 0.856907i \(-0.672383\pi\)
0.484368 + 0.874864i \(0.339049\pi\)
\(168\) 3.00000 0.231455
\(169\) −11.5000 6.06218i −0.884615 0.466321i
\(170\) 4.00000 0.306786
\(171\) −4.96410 + 2.86603i −0.379614 + 0.219170i
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) 1.06218 1.83975i 0.0807559 0.139873i −0.822819 0.568304i \(-0.807600\pi\)
0.903575 + 0.428430i \(0.140933\pi\)
\(174\) 1.46410i 0.110993i
\(175\) −2.59808 1.50000i −0.196396 0.113389i
\(176\) −0.232051 0.133975i −0.0174915 0.0100987i
\(177\) 11.4641i 0.861695i
\(178\) −7.06218 + 12.2321i −0.529333 + 0.916831i
\(179\) −4.53590 7.85641i −0.339029 0.587215i 0.645221 0.763996i \(-0.276765\pi\)
−0.984250 + 0.176780i \(0.943432\pi\)
\(180\) 0.866025 0.500000i 0.0645497 0.0372678i
\(181\) 16.9282 1.25826 0.629132 0.777299i \(-0.283411\pi\)
0.629132 + 0.777299i \(0.283411\pi\)
\(182\) 2.59808 10.5000i 0.192582 0.778312i
\(183\) 0.535898 0.0396147
\(184\) −3.00000 + 1.73205i −0.221163 + 0.127688i
\(185\) 2.96410 + 5.13397i 0.217925 + 0.377457i
\(186\) 2.46410 4.26795i 0.180677 0.312941i
\(187\) 1.07180i 0.0783775i
\(188\) 5.59808 + 3.23205i 0.408282 + 0.235722i
\(189\) −2.59808 1.50000i −0.188982 0.109109i
\(190\) 5.73205i 0.415847i
\(191\) 8.66025 15.0000i 0.626634 1.08536i −0.361588 0.932338i \(-0.617765\pi\)
0.988222 0.153024i \(-0.0489012\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −8.53590 + 4.92820i −0.614427 + 0.354740i −0.774696 0.632334i \(-0.782097\pi\)
0.160269 + 0.987073i \(0.448764\pi\)
\(194\) 8.39230 0.602532
\(195\) −1.00000 3.46410i −0.0716115 0.248069i
\(196\) 2.00000 0.142857
\(197\) −9.86603 + 5.69615i −0.702925 + 0.405834i −0.808436 0.588584i \(-0.799686\pi\)
0.105511 + 0.994418i \(0.466352\pi\)
\(198\) 0.133975 + 0.232051i 0.00952116 + 0.0164911i
\(199\) 12.4641 21.5885i 0.883557 1.53037i 0.0361978 0.999345i \(-0.488475\pi\)
0.847359 0.531021i \(-0.178191\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 1.26795 + 0.732051i 0.0894342 + 0.0516349i
\(202\) −10.7321 6.19615i −0.755104 0.435960i
\(203\) 4.39230i 0.308279i
\(204\) −2.00000 + 3.46410i −0.140028 + 0.242536i
\(205\) 2.00000 + 3.46410i 0.139686 + 0.241943i
\(206\) −10.0359 + 5.79423i −0.699234 + 0.403703i
\(207\) 3.46410 0.240772
\(208\) −3.46410 + 1.00000i −0.240192 + 0.0693375i
\(209\) 1.53590 0.106240
\(210\) 2.59808 1.50000i 0.179284 0.103510i
\(211\) 4.03590 + 6.99038i 0.277843 + 0.481238i 0.970848 0.239694i \(-0.0770473\pi\)
−0.693006 + 0.720932i \(0.743714\pi\)
\(212\) −0.133975 + 0.232051i −0.00920141 + 0.0159373i
\(213\) 12.9282i 0.885826i
\(214\) 11.1962 + 6.46410i 0.765353 + 0.441877i
\(215\) 5.19615 + 3.00000i 0.354375 + 0.204598i
\(216\) 1.00000i 0.0680414i
\(217\) 7.39230 12.8038i 0.501822 0.869182i
\(218\) 5.19615 + 9.00000i 0.351928 + 0.609557i
\(219\) −6.00000 + 3.46410i −0.405442 + 0.234082i
\(220\) −0.267949 −0.0180651
\(221\) 10.3923 + 10.0000i 0.699062 + 0.672673i
\(222\) −5.92820 −0.397875
\(223\) −16.3301 + 9.42820i −1.09355 + 0.631359i −0.934518 0.355915i \(-0.884169\pi\)
−0.159028 + 0.987274i \(0.550836\pi\)
\(224\) −1.50000 2.59808i −0.100223 0.173591i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 12.0000i 0.798228i
\(227\) 5.66025 + 3.26795i 0.375684 + 0.216901i 0.675939 0.736958i \(-0.263738\pi\)
−0.300255 + 0.953859i \(0.597072\pi\)
\(228\) 4.96410 + 2.86603i 0.328756 + 0.189807i
\(229\) 4.53590i 0.299741i −0.988706 0.149870i \(-0.952114\pi\)
0.988706 0.149870i \(-0.0478856\pi\)
\(230\) −1.73205 + 3.00000i −0.114208 + 0.197814i
\(231\) 0.401924 + 0.696152i 0.0264446 + 0.0458035i
\(232\) −1.26795 + 0.732051i −0.0832449 + 0.0480615i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 3.50000 + 0.866025i 0.228802 + 0.0566139i
\(235\) 6.46410 0.421671
\(236\) −9.92820 + 5.73205i −0.646271 + 0.373125i
\(237\) 1.53590 + 2.66025i 0.0997673 + 0.172802i
\(238\) −6.00000 + 10.3923i −0.388922 + 0.673633i
\(239\) 3.46410i 0.224074i 0.993704 + 0.112037i \(0.0357375\pi\)
−0.993704 + 0.112037i \(0.964262\pi\)
\(240\) −0.866025 0.500000i −0.0559017 0.0322749i
\(241\) −21.8205 12.5981i −1.40558 0.811513i −0.410624 0.911805i \(-0.634689\pi\)
−0.994958 + 0.100291i \(0.968023\pi\)
\(242\) 10.9282i 0.702492i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −0.267949 0.464102i −0.0171537 0.0297111i
\(245\) 1.73205 1.00000i 0.110657 0.0638877i
\(246\) −4.00000 −0.255031
\(247\) 14.3301 14.8923i 0.911804 0.947575i
\(248\) −4.92820 −0.312941
\(249\) 8.19615 4.73205i 0.519410 0.299882i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −9.76795 + 16.9186i −0.616547 + 1.06789i 0.373563 + 0.927605i \(0.378136\pi\)
−0.990111 + 0.140287i \(0.955198\pi\)
\(252\) 3.00000i 0.188982i
\(253\) −0.803848 0.464102i −0.0505375 0.0291778i
\(254\) 10.9641 + 6.33013i 0.687949 + 0.397187i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.26795 12.5885i −0.453362 0.785246i 0.545230 0.838286i \(-0.316442\pi\)
−0.998592 + 0.0530400i \(0.983109\pi\)
\(258\) −5.19615 + 3.00000i −0.323498 + 0.186772i
\(259\) −17.7846 −1.10508
\(260\) −2.50000 + 2.59808i −0.155043 + 0.161126i
\(261\) 1.46410 0.0906256
\(262\) 12.4019 7.16025i 0.766193 0.442362i
\(263\) 12.2583 + 21.2321i 0.755881 + 1.30922i 0.944935 + 0.327258i \(0.106125\pi\)
−0.189054 + 0.981967i \(0.560542\pi\)
\(264\) 0.133975 0.232051i 0.00824557 0.0142817i
\(265\) 0.267949i 0.0164600i
\(266\) 14.8923 + 8.59808i 0.913106 + 0.527182i
\(267\) −12.2321 7.06218i −0.748589 0.432198i
\(268\) 1.46410i 0.0894342i
\(269\) 8.53590 14.7846i 0.520443 0.901434i −0.479275 0.877665i \(-0.659100\pi\)
0.999717 0.0237685i \(-0.00756648\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) 21.1244 12.1962i 1.28321 0.740863i 0.305779 0.952103i \(-0.401083\pi\)
0.977434 + 0.211239i \(0.0677499\pi\)
\(272\) 4.00000 0.242536
\(273\) 10.5000 + 2.59808i 0.635489 + 0.157243i
\(274\) 13.4641 0.813396
\(275\) −0.232051 + 0.133975i −0.0139932 + 0.00807897i
\(276\) −1.73205 3.00000i −0.104257 0.180579i
\(277\) −5.79423 + 10.0359i −0.348141 + 0.602999i −0.985919 0.167222i \(-0.946520\pi\)
0.637778 + 0.770220i \(0.279854\pi\)
\(278\) 19.7846i 1.18660i
\(279\) 4.26795 + 2.46410i 0.255515 + 0.147522i
\(280\) −2.59808 1.50000i −0.155265 0.0896421i
\(281\) 6.92820i 0.413302i 0.978415 + 0.206651i \(0.0662565\pi\)
−0.978415 + 0.206651i \(0.933744\pi\)
\(282\) −3.23205 + 5.59808i −0.192466 + 0.333361i
\(283\) 3.19615 + 5.53590i 0.189992 + 0.329075i 0.945247 0.326355i \(-0.105821\pi\)
−0.755256 + 0.655430i \(0.772487\pi\)
\(284\) −11.1962 + 6.46410i −0.664369 + 0.383574i
\(285\) 5.73205 0.339537
\(286\) −0.696152 0.669873i −0.0411644 0.0396104i
\(287\) −12.0000 −0.708338
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −0.732051 + 1.26795i −0.0429875 + 0.0744565i
\(291\) 8.39230i 0.491966i
\(292\) 6.00000 + 3.46410i 0.351123 + 0.202721i
\(293\) 25.3301 + 14.6244i 1.47980 + 0.854364i 0.999738 0.0228698i \(-0.00728033\pi\)
0.480063 + 0.877234i \(0.340614\pi\)
\(294\) 2.00000i 0.116642i
\(295\) −5.73205 + 9.92820i −0.333733 + 0.578042i
\(296\) 2.96410 + 5.13397i 0.172285 + 0.298406i
\(297\) −0.232051 + 0.133975i −0.0134650 + 0.00777399i
\(298\) 18.7846 1.08816
\(299\) −12.0000 + 3.46410i −0.693978 + 0.200334i
\(300\) −1.00000 −0.0577350
\(301\) −15.5885 + 9.00000i −0.898504 + 0.518751i
\(302\) −11.3923 19.7321i −0.655553 1.13545i
\(303\) 6.19615 10.7321i 0.355960 0.616540i
\(304\) 5.73205i 0.328756i
\(305\) −0.464102 0.267949i −0.0265744 0.0153427i
\(306\) −3.46410 2.00000i −0.198030 0.114332i
\(307\) 28.2487i 1.61224i −0.591753 0.806120i \(-0.701564\pi\)
0.591753 0.806120i \(-0.298436\pi\)
\(308\) 0.401924 0.696152i 0.0229017 0.0396670i
\(309\) −5.79423 10.0359i −0.329622 0.570922i
\(310\) −4.26795 + 2.46410i −0.242403 + 0.139952i
\(311\) 18.9282 1.07332 0.536660 0.843799i \(-0.319686\pi\)
0.536660 + 0.843799i \(0.319686\pi\)
\(312\) −1.00000 3.46410i −0.0566139 0.196116i
\(313\) −33.3205 −1.88339 −0.941693 0.336473i \(-0.890766\pi\)
−0.941693 + 0.336473i \(0.890766\pi\)
\(314\) 18.3564 10.5981i 1.03591 0.598084i
\(315\) 1.50000 + 2.59808i 0.0845154 + 0.146385i
\(316\) 1.53590 2.66025i 0.0864010 0.149651i
\(317\) 30.4641i 1.71103i 0.517774 + 0.855517i \(0.326761\pi\)
−0.517774 + 0.855517i \(0.673239\pi\)
\(318\) −0.232051 0.133975i −0.0130128 0.00751292i
\(319\) −0.339746 0.196152i −0.0190221 0.0109824i
\(320\) 1.00000i 0.0559017i
\(321\) −6.46410 + 11.1962i −0.360791 + 0.624908i
\(322\) −5.19615 9.00000i −0.289570 0.501550i
\(323\) −19.8564 + 11.4641i −1.10484 + 0.637880i
\(324\) −1.00000 −0.0555556
\(325\) −0.866025 + 3.50000i −0.0480384 + 0.194145i
\(326\) −2.92820 −0.162178
\(327\) −9.00000 + 5.19615i −0.497701 + 0.287348i
\(328\) 2.00000 + 3.46410i 0.110432 + 0.191273i
\(329\) −9.69615 + 16.7942i −0.534566 + 0.925896i
\(330\) 0.267949i 0.0147501i
\(331\) 12.4641 + 7.19615i 0.685089 + 0.395536i 0.801770 0.597633i \(-0.203892\pi\)
−0.116681 + 0.993169i \(0.537225\pi\)
\(332\) −8.19615 4.73205i −0.449822 0.259705i
\(333\) 5.92820i 0.324864i
\(334\) −0.232051 + 0.401924i −0.0126973 + 0.0219923i
\(335\) −0.732051 1.26795i −0.0399962 0.0692755i
\(336\) 2.59808 1.50000i 0.141737 0.0818317i
\(337\) −26.3923 −1.43768 −0.718840 0.695175i \(-0.755327\pi\)
−0.718840 + 0.695175i \(0.755327\pi\)
\(338\) −12.9904 + 0.500000i −0.706584 + 0.0271964i
\(339\) 12.0000 0.651751
\(340\) 3.46410 2.00000i 0.187867 0.108465i
\(341\) −0.660254 1.14359i −0.0357548 0.0619291i
\(342\) −2.86603 + 4.96410i −0.154977 + 0.268428i
\(343\) 15.0000i 0.809924i
\(344\) 5.19615 + 3.00000i 0.280158 + 0.161749i
\(345\) −3.00000 1.73205i −0.161515 0.0932505i
\(346\) 2.12436i 0.114206i
\(347\) −2.19615 + 3.80385i −0.117896 + 0.204201i −0.918934 0.394412i \(-0.870948\pi\)
0.801038 + 0.598614i \(0.204281\pi\)
\(348\) −0.732051 1.26795i −0.0392420 0.0679692i
\(349\) −9.12436 + 5.26795i −0.488416 + 0.281987i −0.723917 0.689887i \(-0.757660\pi\)
0.235501 + 0.971874i \(0.424327\pi\)
\(350\) −3.00000 −0.160357
\(351\) −0.866025 + 3.50000i −0.0462250 + 0.186816i
\(352\) −0.267949 −0.0142817
\(353\) 6.58846 3.80385i 0.350668 0.202458i −0.314311 0.949320i \(-0.601774\pi\)
0.664980 + 0.746862i \(0.268440\pi\)
\(354\) −5.73205 9.92820i −0.304655 0.527678i
\(355\) −6.46410 + 11.1962i −0.343079 + 0.594230i
\(356\) 14.1244i 0.748589i
\(357\) −10.3923 6.00000i −0.550019 0.317554i
\(358\) −7.85641 4.53590i −0.415224 0.239730i
\(359\) 0.928203i 0.0489887i 0.999700 + 0.0244943i \(0.00779757\pi\)
−0.999700 + 0.0244943i \(0.992202\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 6.92820 + 12.0000i 0.364642 + 0.631579i
\(362\) 14.6603 8.46410i 0.770526 0.444863i
\(363\) −10.9282 −0.573582
\(364\) −3.00000 10.3923i −0.157243 0.544705i
\(365\) 6.92820 0.362639
\(366\) 0.464102 0.267949i 0.0242590 0.0140059i
\(367\) −10.6603 18.4641i −0.556461 0.963818i −0.997788 0.0664722i \(-0.978826\pi\)
0.441328 0.897346i \(-0.354508\pi\)
\(368\) −1.73205 + 3.00000i −0.0902894 + 0.156386i
\(369\) 4.00000i 0.208232i
\(370\) 5.13397 + 2.96410i 0.266903 + 0.154096i
\(371\) −0.696152 0.401924i −0.0361424 0.0208668i
\(372\) 4.92820i 0.255515i
\(373\) −4.53590 + 7.85641i −0.234860 + 0.406789i −0.959232 0.282620i \(-0.908796\pi\)
0.724372 + 0.689409i \(0.242130\pi\)
\(374\) 0.535898 + 0.928203i 0.0277106 + 0.0479962i
\(375\) −0.866025 + 0.500000i −0.0447214 + 0.0258199i
\(376\) 6.46410 0.333361
\(377\) −5.07180 + 1.46410i −0.261211 + 0.0754051i
\(378\) −3.00000 −0.154303
\(379\) −8.42820 + 4.86603i −0.432928 + 0.249951i −0.700593 0.713561i \(-0.747081\pi\)
0.267665 + 0.963512i \(0.413748\pi\)
\(380\) −2.86603 4.96410i −0.147024 0.254653i
\(381\) −6.33013 + 10.9641i −0.324302 + 0.561708i
\(382\) 17.3205i 0.886194i
\(383\) 4.14359 + 2.39230i 0.211728 + 0.122241i 0.602114 0.798410i \(-0.294325\pi\)
−0.390386 + 0.920651i \(0.627659\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0.803848i 0.0409679i
\(386\) −4.92820 + 8.53590i −0.250839 + 0.434466i
\(387\) −3.00000 5.19615i −0.152499 0.264135i
\(388\) 7.26795 4.19615i 0.368974 0.213027i
\(389\) 17.8564 0.905356 0.452678 0.891674i \(-0.350469\pi\)
0.452678 + 0.891674i \(0.350469\pi\)
\(390\) −2.59808 2.50000i −0.131559 0.126592i
\(391\) 13.8564 0.700749
\(392\) 1.73205 1.00000i 0.0874818 0.0505076i
\(393\) 7.16025 + 12.4019i 0.361187 + 0.625594i
\(394\) −5.69615 + 9.86603i −0.286968 + 0.497043i
\(395\) 3.07180i 0.154559i
\(396\) 0.232051 + 0.133975i 0.0116610 + 0.00673248i
\(397\) −5.13397 2.96410i −0.257667 0.148764i 0.365603 0.930771i \(-0.380863\pi\)
−0.623270 + 0.782007i \(0.714196\pi\)
\(398\) 24.9282i 1.24954i
\(399\) −8.59808 + 14.8923i −0.430442 + 0.745548i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −19.1603 + 11.0622i −0.956817 + 0.552419i −0.895192 0.445681i \(-0.852962\pi\)
−0.0616254 + 0.998099i \(0.519628\pi\)
\(402\) 1.46410 0.0730228
\(403\) −17.2487 4.26795i −0.859220 0.212602i
\(404\) −12.3923 −0.616540
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) −2.19615 3.80385i −0.108993 0.188782i
\(407\) −0.794229 + 1.37564i −0.0393685 + 0.0681882i
\(408\) 4.00000i 0.198030i
\(409\) −33.8205 19.5263i −1.67232 0.965512i −0.966337 0.257280i \(-0.917174\pi\)
−0.705980 0.708232i \(-0.749493\pi\)
\(410\) 3.46410 + 2.00000i 0.171080 + 0.0987730i
\(411\) 13.4641i 0.664135i
\(412\) −5.79423 + 10.0359i −0.285461 + 0.494433i
\(413\) −17.1962 29.7846i −0.846167 1.46560i
\(414\) 3.00000 1.73205i 0.147442 0.0851257i
\(415\) −9.46410 −0.464574
\(416\) −2.50000 + 2.59808i −0.122573 + 0.127381i
\(417\) 19.7846 0.968857
\(418\) 1.33013 0.767949i 0.0650586 0.0375616i
\(419\) −4.92820 8.53590i −0.240758 0.417006i 0.720172 0.693795i \(-0.244063\pi\)
−0.960931 + 0.276790i \(0.910730\pi\)
\(420\) 1.50000 2.59808i 0.0731925 0.126773i
\(421\) 21.8564i 1.06522i 0.846362 + 0.532608i \(0.178788\pi\)
−0.846362 + 0.532608i \(0.821212\pi\)
\(422\) 6.99038 + 4.03590i 0.340286 + 0.196464i
\(423\) −5.59808 3.23205i −0.272188 0.157148i
\(424\) 0.267949i 0.0130128i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) −6.46410 11.1962i −0.313187 0.542455i
\(427\) 1.39230 0.803848i 0.0673784 0.0389009i
\(428\) 12.9282 0.624908
\(429\) 0.669873 0.696152i 0.0323418 0.0336106i
\(430\) 6.00000 0.289346
\(431\) −12.0000 + 6.92820i −0.578020 + 0.333720i −0.760346 0.649518i \(-0.774971\pi\)
0.182326 + 0.983238i \(0.441637\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 4.39230 7.60770i 0.211081 0.365602i −0.740972 0.671536i \(-0.765635\pi\)
0.952053 + 0.305933i \(0.0989684\pi\)
\(434\) 14.7846i 0.709684i
\(435\) −1.26795 0.732051i −0.0607935 0.0350991i
\(436\) 9.00000 + 5.19615i 0.431022 + 0.248851i
\(437\) 19.8564i 0.949861i
\(438\) −3.46410 + 6.00000i −0.165521 + 0.286691i
\(439\) 6.66025 + 11.5359i 0.317877 + 0.550578i 0.980045 0.198777i \(-0.0636969\pi\)
−0.662168 + 0.749355i \(0.730364\pi\)
\(440\) −0.232051 + 0.133975i −0.0110626 + 0.00638699i
\(441\) −2.00000 −0.0952381
\(442\) 14.0000 + 3.46410i 0.665912 + 0.164771i
\(443\) −19.8564 −0.943406 −0.471703 0.881757i \(-0.656361\pi\)
−0.471703 + 0.881757i \(0.656361\pi\)
\(444\) −5.13397 + 2.96410i −0.243648 + 0.140670i
\(445\) 7.06218 + 12.2321i 0.334779 + 0.579855i
\(446\) −9.42820 + 16.3301i −0.446438 + 0.773254i
\(447\) 18.7846i 0.888482i
\(448\) −2.59808 1.50000i −0.122748 0.0708683i
\(449\) −5.30385 3.06218i −0.250304 0.144513i 0.369599 0.929191i \(-0.379495\pi\)
−0.619903 + 0.784678i \(0.712828\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −0.535898 + 0.928203i −0.0252345 + 0.0437074i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 19.7321 11.3923i 0.927093 0.535257i
\(454\) 6.53590 0.306745
\(455\) −7.79423 7.50000i −0.365399 0.351605i
\(456\) 5.73205 0.268428
\(457\) −6.46410 + 3.73205i −0.302378 + 0.174578i −0.643511 0.765437i \(-0.722523\pi\)
0.341133 + 0.940015i \(0.389189\pi\)
\(458\) −2.26795 3.92820i −0.105974 0.183553i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 3.46410i 0.161515i
\(461\) −10.0526 5.80385i −0.468194 0.270312i 0.247289 0.968942i \(-0.420460\pi\)
−0.715484 + 0.698630i \(0.753794\pi\)
\(462\) 0.696152 + 0.401924i 0.0323879 + 0.0186992i
\(463\) 40.7846i 1.89542i −0.319131 0.947711i \(-0.603391\pi\)
0.319131 0.947711i \(-0.396609\pi\)
\(464\) −0.732051 + 1.26795i −0.0339846 + 0.0588631i
\(465\) −2.46410 4.26795i −0.114270 0.197921i
\(466\) 15.5885 9.00000i 0.722121 0.416917i
\(467\) 24.3923 1.12874 0.564371 0.825522i \(-0.309119\pi\)
0.564371 + 0.825522i \(0.309119\pi\)
\(468\) 3.46410 1.00000i 0.160128 0.0462250i
\(469\) 4.39230 0.202818
\(470\) 5.59808 3.23205i 0.258220 0.149083i
\(471\) 10.5981 + 18.3564i 0.488334 + 0.845819i
\(472\) −5.73205 + 9.92820i −0.263839 + 0.456983i
\(473\) 1.60770i 0.0739219i
\(474\) 2.66025 + 1.53590i 0.122190 + 0.0705461i
\(475\) −4.96410 2.86603i −0.227769 0.131502i
\(476\) 12.0000i 0.550019i
\(477\) 0.133975 0.232051i 0.00613428 0.0106249i
\(478\) 1.73205 + 3.00000i 0.0792222 + 0.137217i
\(479\) −19.2679 + 11.1244i −0.880375 + 0.508285i −0.870782 0.491669i \(-0.836387\pi\)
−0.00959301 + 0.999954i \(0.503054\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 5.92820 + 20.5359i 0.270303 + 0.936356i
\(482\) −25.1962 −1.14765
\(483\) 9.00000 5.19615i 0.409514 0.236433i
\(484\) 5.46410 + 9.46410i 0.248368 + 0.430186i
\(485\) 4.19615 7.26795i 0.190537 0.330021i
\(486\) 1.00000i 0.0453609i
\(487\) 18.1865 + 10.5000i 0.824110 + 0.475800i 0.851832 0.523815i \(-0.175492\pi\)
−0.0277214 + 0.999616i \(0.508825\pi\)
\(488\) −0.464102 0.267949i −0.0210089 0.0121295i
\(489\) 2.92820i 0.132418i
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) −2.69615 4.66987i −0.121676 0.210748i 0.798753 0.601659i \(-0.205493\pi\)
−0.920429 + 0.390911i \(0.872160\pi\)
\(492\) −3.46410 + 2.00000i −0.156174 + 0.0901670i
\(493\) 5.85641 0.263759
\(494\) 4.96410 20.0622i 0.223345 0.902640i
\(495\) 0.267949 0.0120434
\(496\) −4.26795 + 2.46410i −0.191637 + 0.110641i
\(497\) −19.3923 33.5885i −0.869864 1.50665i
\(498\) 4.73205 8.19615i 0.212048 0.367278i
\(499\) 33.3205i 1.49163i 0.666153 + 0.745815i \(0.267940\pi\)
−0.666153 + 0.745815i \(0.732060\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) −0.401924 0.232051i −0.0179566 0.0103673i
\(502\) 19.5359i 0.871930i
\(503\) −1.86603 + 3.23205i −0.0832020 + 0.144110i −0.904624 0.426211i \(-0.859848\pi\)
0.821422 + 0.570321i \(0.193181\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) −10.7321 + 6.19615i −0.477570 + 0.275725i
\(506\) −0.928203 −0.0412637
\(507\) −0.500000 12.9904i −0.0222058 0.576923i
\(508\) 12.6603 0.561708
\(509\) 25.3923 14.6603i 1.12549 0.649804i 0.182696 0.983169i \(-0.441517\pi\)
0.942798 + 0.333365i \(0.108184\pi\)
\(510\) 2.00000 + 3.46410i 0.0885615 + 0.153393i
\(511\) −10.3923 + 18.0000i −0.459728 + 0.796273i
\(512\) 1.00000i 0.0441942i
\(513\) −4.96410 2.86603i −0.219170 0.126538i
\(514\) −12.5885 7.26795i −0.555253 0.320575i
\(515\) 11.5885i 0.510648i
\(516\) −3.00000 + 5.19615i −0.132068 + 0.228748i
\(517\) 0.866025 + 1.50000i 0.0380878 + 0.0659699i
\(518\) −15.4019 + 8.89230i −0.676722 + 0.390705i
\(519\) 2.12436 0.0932489
\(520\) −0.866025 + 3.50000i −0.0379777 + 0.153485i
\(521\) −6.60770 −0.289488 −0.144744 0.989469i \(-0.546236\pi\)
−0.144744 + 0.989469i \(0.546236\pi\)
\(522\) 1.26795 0.732051i 0.0554966 0.0320410i
\(523\) 20.8564 + 36.1244i 0.911987 + 1.57961i 0.811254 + 0.584694i \(0.198786\pi\)
0.100733 + 0.994913i \(0.467881\pi\)
\(524\) 7.16025 12.4019i 0.312797 0.541781i
\(525\) 3.00000i 0.130931i
\(526\) 21.2321 + 12.2583i 0.925761 + 0.534489i
\(527\) 17.0718 + 9.85641i 0.743659 + 0.429352i
\(528\) 0.267949i 0.0116610i
\(529\) 5.50000 9.52628i 0.239130 0.414186i
\(530\) 0.133975 + 0.232051i 0.00581948 + 0.0100796i
\(531\) 9.92820 5.73205i 0.430847 0.248750i
\(532\) 17.1962 0.745548
\(533\) 4.00000 + 13.8564i 0.173259 + 0.600188i
\(534\) −14.1244 −0.611221
\(535\) 11.1962 6.46410i 0.484052 0.279467i
\(536\) −0.732051 1.26795i −0.0316198 0.0547671i
\(537\) 4.53590 7.85641i 0.195738 0.339029i
\(538\) 17.0718i 0.736017i
\(539\) 0.464102 + 0.267949i 0.0199903 + 0.0115414i
\(540\) 0.866025 + 0.500000i 0.0372678 + 0.0215166i
\(541\) 14.7846i 0.635640i 0.948151 + 0.317820i \(0.102951\pi\)
−0.948151 + 0.317820i \(0.897049\pi\)
\(542\) 12.1962 21.1244i 0.523870 0.907369i
\(543\) 8.46410 + 14.6603i 0.363229 + 0.629132i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) 10.3923 0.445157
\(546\) 10.3923 3.00000i 0.444750 0.128388i
\(547\) −5.32051 −0.227488 −0.113744 0.993510i \(-0.536284\pi\)
−0.113744 + 0.993510i \(0.536284\pi\)
\(548\) 11.6603 6.73205i 0.498101 0.287579i
\(549\) 0.267949 + 0.464102i 0.0114358 + 0.0198074i
\(550\) −0.133975 + 0.232051i −0.00571270 + 0.00989468i
\(551\) 8.39230i 0.357524i
\(552\) −3.00000 1.73205i −0.127688 0.0737210i
\(553\) 7.98076 + 4.60770i 0.339377 + 0.195939i
\(554\) 11.5885i 0.492346i
\(555\) −2.96410 + 5.13397i −0.125819 + 0.217925i
\(556\) −9.89230 17.1340i −0.419527 0.726642i
\(557\) −19.5788 + 11.3038i −0.829582 + 0.478959i −0.853710 0.520749i \(-0.825653\pi\)
0.0241275 + 0.999709i \(0.492319\pi\)
\(558\) 4.92820 0.208627
\(559\) 15.5885 + 15.0000i 0.659321 + 0.634432i
\(560\) −3.00000 −0.126773
\(561\) −0.928203 + 0.535898i −0.0391888 + 0.0226256i
\(562\) 3.46410 + 6.00000i 0.146124 + 0.253095i
\(563\) 7.66025 13.2679i 0.322841 0.559177i −0.658232 0.752815i \(-0.728695\pi\)
0.981073 + 0.193638i \(0.0620287\pi\)
\(564\) 6.46410i 0.272188i
\(565\) −10.3923 6.00000i −0.437208 0.252422i
\(566\) 5.53590 + 3.19615i 0.232691 + 0.134344i
\(567\) 3.00000i 0.125988i
\(568\) −6.46410 + 11.1962i −0.271228 + 0.469780i
\(569\) 8.16025 + 14.1340i 0.342096 + 0.592527i 0.984822 0.173569i \(-0.0555300\pi\)
−0.642726 + 0.766096i \(0.722197\pi\)
\(570\) 4.96410 2.86603i 0.207923 0.120045i
\(571\) 10.8564 0.454326 0.227163 0.973857i \(-0.427055\pi\)
0.227163 + 0.973857i \(0.427055\pi\)
\(572\) −0.937822 0.232051i −0.0392123 0.00970253i
\(573\) 17.3205 0.723575
\(574\) −10.3923 + 6.00000i −0.433766 + 0.250435i
\(575\) 1.73205 + 3.00000i 0.0722315 + 0.125109i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 9.32051i 0.388018i −0.981000 0.194009i \(-0.937851\pi\)
0.981000 0.194009i \(-0.0621491\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) −8.53590 4.92820i −0.354740 0.204809i
\(580\) 1.46410i 0.0607935i
\(581\) 14.1962 24.5885i 0.588956 1.02010i
\(582\) 4.19615 + 7.26795i 0.173936 + 0.301266i
\(583\) −0.0621778 + 0.0358984i −0.00257514 + 0.00148676i
\(584\) 6.92820 0.286691
\(585\) 2.50000 2.59808i 0.103362 0.107417i
\(586\) 29.2487 1.20825
\(587\) −7.73205 + 4.46410i −0.319136 + 0.184253i −0.651007 0.759071i \(-0.725653\pi\)
0.331871 + 0.943325i \(0.392320\pi\)
\(588\) 1.00000 + 1.73205i 0.0412393 + 0.0714286i
\(589\) 14.1244 24.4641i 0.581984 1.00803i
\(590\) 11.4641i 0.471970i
\(591\) −9.86603 5.69615i −0.405834 0.234308i
\(592\) 5.13397 + 2.96410i 0.211005 + 0.121824i
\(593\) 44.7846i 1.83908i −0.392992 0.919542i \(-0.628560\pi\)
0.392992 0.919542i \(-0.371440\pi\)
\(594\) −0.133975 + 0.232051i −0.00549704 + 0.00952116i
\(595\) 6.00000 + 10.3923i 0.245976 + 0.426043i
\(596\) 16.2679 9.39230i 0.666361 0.384724i
\(597\) 24.9282 1.02024
\(598\) −8.66025 + 9.00000i −0.354144 + 0.368037i
\(599\) 28.9282 1.18197 0.590987 0.806681i \(-0.298738\pi\)
0.590987 + 0.806681i \(0.298738\pi\)
\(600\) −0.866025 + 0.500000i −0.0353553 + 0.0204124i
\(601\) −15.3564 26.5981i −0.626401 1.08496i −0.988268 0.152729i \(-0.951194\pi\)
0.361867 0.932230i \(-0.382139\pi\)
\(602\) −9.00000 + 15.5885i −0.366813 + 0.635338i
\(603\) 1.46410i 0.0596228i
\(604\) −19.7321 11.3923i −0.802886 0.463546i
\(605\) 9.46410 + 5.46410i 0.384770 + 0.222147i
\(606\) 12.3923i 0.503403i
\(607\) 10.7224 18.5718i 0.435210 0.753806i −0.562103 0.827067i \(-0.690007\pi\)
0.997313 + 0.0732615i \(0.0233408\pi\)
\(608\) −2.86603 4.96410i −0.116233 0.201321i
\(609\) 3.80385 2.19615i 0.154140 0.0889926i
\(610\) −0.535898 −0.0216979
\(611\) 22.6244 + 5.59808i 0.915283 + 0.226474i
\(612\) −4.00000 −0.161690
\(613\) 38.9711 22.5000i 1.57403 0.908766i 0.578362 0.815780i \(-0.303692\pi\)
0.995667 0.0929864i \(-0.0296413\pi\)
\(614\) −14.1244 24.4641i −0.570013 0.987291i
\(615\) −2.00000 + 3.46410i −0.0806478 + 0.139686i
\(616\) 0.803848i 0.0323879i
\(617\) −30.7128 17.7321i −1.23645 0.713865i −0.268084 0.963395i \(-0.586391\pi\)
−0.968367 + 0.249530i \(0.919724\pi\)
\(618\) −10.0359 5.79423i −0.403703 0.233078i
\(619\) 2.51666i 0.101153i 0.998720 + 0.0505766i \(0.0161059\pi\)
−0.998720 + 0.0505766i \(0.983894\pi\)
\(620\) −2.46410 + 4.26795i −0.0989607 + 0.171405i
\(621\) 1.73205 + 3.00000i 0.0695048 + 0.120386i
\(622\) 16.3923 9.46410i 0.657272 0.379476i
\(623\) −42.3731 −1.69764
\(624\) −2.59808 2.50000i −0.104006 0.100080i
\(625\) 1.00000 0.0400000
\(626\) −28.8564 + 16.6603i −1.15333 + 0.665878i
\(627\) 0.767949 + 1.33013i 0.0306689 + 0.0531202i
\(628\) 10.5981 18.3564i 0.422909 0.732500i
\(629\) 23.7128i 0.945492i
\(630\) 2.59808 + 1.50000i 0.103510 + 0.0597614i
\(631\) −6.92820 4.00000i −0.275807 0.159237i 0.355716 0.934594i \(-0.384237\pi\)
−0.631524 + 0.775356i \(0.717570\pi\)
\(632\) 3.07180i 0.122190i
\(633\) −4.03590 + 6.99038i −0.160413 + 0.277843i
\(634\) 15.2321 + 26.3827i 0.604942 + 1.04779i
\(635\) 10.9641 6.33013i 0.435097 0.251203i
\(636\) −0.267949 −0.0106249
\(637\) 6.92820 2.00000i 0.274505 0.0792429i
\(638\) −0.392305 −0.0155315
\(639\) 11.1962 6.46410i 0.442913 0.255716i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −7.23205 + 12.5263i −0.285649 + 0.494758i −0.972766 0.231788i \(-0.925542\pi\)
0.687117 + 0.726546i \(0.258876\pi\)
\(642\) 12.9282i 0.510235i
\(643\) 11.0718 + 6.39230i 0.436629 + 0.252088i 0.702167 0.712013i \(-0.252216\pi\)
−0.265538 + 0.964100i \(0.585549\pi\)
\(644\) −9.00000 5.19615i −0.354650 0.204757i
\(645\) 6.00000i 0.236250i
\(646\) −11.4641 + 19.8564i −0.451049 + 0.781240i
\(647\) 17.8660 + 30.9449i 0.702386 + 1.21657i 0.967627 + 0.252386i \(0.0812152\pi\)
−0.265241 + 0.964182i \(0.585451\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −3.07180 −0.120579
\(650\) 1.00000 + 3.46410i 0.0392232 + 0.135873i
\(651\) 14.7846 0.579455
\(652\) −2.53590 + 1.46410i −0.0993134 + 0.0573386i
\(653\) 0.794229 + 1.37564i 0.0310806 + 0.0538331i 0.881147 0.472842i \(-0.156772\pi\)
−0.850067 + 0.526675i \(0.823438\pi\)
\(654\) −5.19615 + 9.00000i −0.203186 + 0.351928i
\(655\) 14.3205i 0.559549i
\(656\) 3.46410 + 2.00000i 0.135250 + 0.0780869i
\(657\) −6.00000 3.46410i −0.234082 0.135147i
\(658\) 19.3923i 0.755991i
\(659\) 19.8564 34.3923i 0.773496 1.33973i −0.162140 0.986768i \(-0.551840\pi\)
0.935636 0.352966i \(-0.114827\pi\)
\(660\) −0.133975 0.232051i −0.00521495 0.00903257i
\(661\) −18.7128 + 10.8038i −0.727844 + 0.420221i −0.817633 0.575740i \(-0.804714\pi\)
0.0897889 + 0.995961i \(0.471381\pi\)
\(662\) 14.3923 0.559373
\(663\) −3.46410 + 14.0000i −0.134535 + 0.543715i
\(664\) −9.46410 −0.367278
\(665\) 14.8923 8.59808i 0.577499 0.333419i
\(666\) −2.96410 5.13397i −0.114857 0.198937i
\(667\) −2.53590 + 4.39230i −0.0981904 + 0.170071i
\(668\) 0.464102i 0.0179566i
\(669\) −16.3301 9.42820i −0.631359 0.364515i
\(670\) −1.26795 0.732051i −0.0489852 0.0282816i
\(671\) 0.143594i 0.00554337i
\(672\) 1.50000 2.59808i 0.0578638 0.100223i
\(673\) 8.39230 + 14.5359i 0.323500 + 0.560318i 0.981208 0.192955i \(-0.0618072\pi\)
−0.657708 + 0.753273i \(0.728474\pi\)
\(674\) −22.8564 + 13.1962i −0.880396 + 0.508297i
\(675\) 1.00000 0.0384900
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 10.9282 0.420005 0.210002 0.977701i \(-0.432653\pi\)
0.210002 + 0.977701i \(0.432653\pi\)
\(678\) 10.3923 6.00000i 0.399114 0.230429i
\(679\) 12.5885 + 21.8038i 0.483101 + 0.836755i
\(680\) 2.00000 3.46410i 0.0766965 0.132842i
\(681\) 6.53590i 0.250456i
\(682\) −1.14359 0.660254i −0.0437905 0.0252824i
\(683\) 35.7846 + 20.6603i 1.36926 + 0.790543i 0.990834 0.135089i \(-0.0431319\pi\)
0.378427 + 0.925631i \(0.376465\pi\)
\(684\) 5.73205i 0.219170i
\(685\) 6.73205 11.6603i 0.257218 0.445515i
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) 3.92820 2.26795i 0.149870 0.0865277i
\(688\) 6.00000 0.228748
\(689\) −0.232051 + 0.937822i −0.00884043 + 0.0357282i
\(690\) −3.46410 −0.131876
\(691\) 13.0359 7.52628i 0.495909 0.286313i −0.231114 0.972927i \(-0.574237\pi\)
0.727023 + 0.686614i \(0.240904\pi\)
\(692\) −1.06218 1.83975i −0.0403779 0.0699366i
\(693\) −0.401924 + 0.696152i −0.0152678 + 0.0264446i
\(694\) 4.39230i 0.166730i
\(695\) −17.1340 9.89230i −0.649929 0.375237i
\(696\) −1.26795 0.732051i −0.0480615 0.0277483i
\(697\) 16.0000i 0.606043i
\(698\) −5.26795 + 9.12436i −0.199395 + 0.345362i
\(699\) 9.00000 + 15.5885i 0.340411 + 0.589610i
\(700\) −2.59808 + 1.50000i −0.0981981 + 0.0566947i
\(701\) −4.39230 −0.165895 −0.0829475 0.996554i \(-0.526433\pi\)
−0.0829475 + 0.996554i \(0.526433\pi\)
\(702\) 1.00000 + 3.46410i 0.0377426 + 0.130744i
\(703\) −33.9808 −1.28161
\(704\) −0.232051 + 0.133975i −0.00874574 + 0.00504936i
\(705\) 3.23205 + 5.59808i 0.121726 + 0.210836i
\(706\) 3.80385 6.58846i 0.143160 0.247960i
\(707\) 37.1769i 1.39818i
\(708\) −9.92820 5.73205i −0.373125 0.215424i
\(709\) −23.6603 13.6603i −0.888579 0.513022i −0.0151019 0.999886i \(-0.504807\pi\)
−0.873478 + 0.486864i \(0.838141\pi\)
\(710\) 12.9282i 0.485187i
\(711\) −1.53590 + 2.66025i −0.0576007 + 0.0997673i
\(712\) 7.06218 + 12.2321i 0.264666 + 0.458415i
\(713\) −14.7846 + 8.53590i −0.553688 + 0.319672i
\(714\) −12.0000 −0.449089
\(715\) −0.928203 + 0.267949i −0.0347128 + 0.0100207i
\(716\) −9.07180 −0.339029
\(717\) −3.00000 + 1.73205i −0.112037 + 0.0646846i
\(718\) 0.464102 + 0.803848i 0.0173201 + 0.0299993i
\(719\) −8.00000 + 13.8564i −0.298350 + 0.516757i −0.975759 0.218850i \(-0.929769\pi\)
0.677409 + 0.735607i \(0.263103\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) −30.1077 17.3827i −1.12127 0.647365i
\(722\) 12.0000 + 6.92820i 0.446594 + 0.257841i
\(723\) 25.1962i 0.937055i
\(724\) 8.46410 14.6603i 0.314566 0.544844i
\(725\) 0.732051 + 1.26795i 0.0271877 + 0.0470905i
\(726\) −9.46410 + 5.46410i −0.351246 + 0.202792i
\(727\) −4.66025 −0.172839 −0.0864196 0.996259i \(-0.527543\pi\)
−0.0864196 + 0.996259i \(0.527543\pi\)
\(728\) −7.79423 7.50000i −0.288873 0.277968i
\(729\) 1.00000 0.0370370
\(730\) 6.00000 3.46410i 0.222070 0.128212i
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0.267949 0.464102i 0.00990369 0.0171537i
\(733\) 20.8564i 0.770349i 0.922844 + 0.385174i \(0.125859\pi\)
−0.922844 + 0.385174i \(0.874141\pi\)
\(734\) −18.4641 10.6603i −0.681522 0.393477i
\(735\) 1.73205 + 1.00000i 0.0638877 + 0.0368856i
\(736\) 3.46410i 0.127688i
\(737\) 0.196152 0.339746i 0.00722537 0.0125147i
\(738\) −2.00000 3.46410i −0.0736210 0.127515i
\(739\) 31.0359 17.9186i 1.14167 0.659146i 0.194829 0.980837i \(-0.437585\pi\)
0.946845 + 0.321691i \(0.104251\pi\)
\(740\) 5.92820 0.217925
\(741\) 20.0622 + 4.96410i 0.737003 + 0.182361i
\(742\) −0.803848 −0.0295102
\(743\) −9.46410 + 5.46410i −0.347204 + 0.200458i −0.663453 0.748218i \(-0.730910\pi\)
0.316249 + 0.948676i \(0.397576\pi\)
\(744\) −2.46410 4.26795i −0.0903383 0.156471i
\(745\) 9.39230 16.2679i 0.344107 0.596012i
\(746\) 9.07180i 0.332142i
\(747\) 8.19615 + 4.73205i 0.299882 + 0.173137i
\(748\) 0.928203 + 0.535898i 0.0339385 + 0.0195944i
\(749\) 38.7846i 1.41716i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 10.5885 + 18.3397i 0.386378 + 0.669227i 0.991959 0.126557i \(-0.0403926\pi\)
−0.605581 + 0.795784i \(0.707059\pi\)
\(752\) 5.59808 3.23205i 0.204141 0.117861i
\(753\) −19.5359 −0.711928
\(754\) −3.66025 + 3.80385i −0.133299 + 0.138528i
\(755\) −22.7846 −0.829217
\(756\) −2.59808 + 1.50000i −0.0944911 + 0.0545545i
\(757\) −10.8660 18.8205i −0.394932 0.684043i 0.598160 0.801377i \(-0.295899\pi\)
−0.993093 + 0.117334i \(0.962565\pi\)
\(758\) −4.86603 + 8.42820i −0.176742 + 0.306126i
\(759\) 0.928203i 0.0336916i
\(760\) −4.96410 2.86603i −0.180067 0.103962i
\(761\) 6.91154 + 3.99038i 0.250543 + 0.144651i 0.620013 0.784592i \(-0.287127\pi\)
−0.369470 + 0.929243i \(0.620461\pi\)
\(762\) 12.6603i 0.458633i
\(763\) −15.5885 + 27.0000i −0.564340 + 0.977466i
\(764\) −8.66025 15.0000i −0.313317 0.542681i
\(765\) −3.46410 + 2.00000i −0.125245 + 0.0723102i
\(766\) 4.78461 0.172875
\(767\) −28.6603 + 29.7846i −1.03486 + 1.07546i
\(768\) −1.00000 −0.0360844
\(769\) 13.6077 7.85641i 0.490706 0.283309i −0.234161 0.972198i \(-0.575234\pi\)
0.724867 + 0.688889i \(0.241901\pi\)
\(770\) −0.401924 0.696152i −0.0144843 0.0250876i
\(771\) 7.26795 12.5885i 0.261749 0.453362i
\(772\) 9.85641i 0.354740i
\(773\) −28.2391 16.3038i −1.01569 0.586409i −0.102837 0.994698i \(-0.532792\pi\)
−0.912852 + 0.408290i \(0.866125\pi\)
\(774\) −5.19615 3.00000i −0.186772 0.107833i
\(775\) 4.92820i 0.177026i
\(776\) 4.19615 7.26795i