Properties

Label 1950.2.bc.a.751.1
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
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: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.a.901.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −2.59808 1.50000i −0.981981 0.566947i −0.0791130 0.996866i \(-0.525209\pi\)
−0.902867 + 0.429919i \(0.858542\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 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 0
\(16\) −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
\(19\) 4.96410 + 2.86603i 1.13884 + 0.657511i 0.946144 0.323747i \(-0.104943\pi\)
0.192699 + 0.981258i \(0.438276\pi\)
\(20\) 0 0
\(21\) 3.00000i 0.654654i
\(22\) −0.133975 + 0.232051i −0.0285635 + 0.0494734i
\(23\) 1.73205 + 3.00000i 0.361158 + 0.625543i 0.988152 0.153481i \(-0.0490483\pi\)
−0.626994 + 0.779024i \(0.715715\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) −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 0
\(31\) 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
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 5.13397 2.96410i 0.844020 0.487295i −0.0146085 0.999893i \(-0.504650\pi\)
0.858629 + 0.512598i \(0.171317\pi\)
\(38\) −5.73205 −0.929861
\(39\) 3.46410 1.00000i 0.554700 0.160128i
\(40\) 0 0
\(41\) −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 −0.541332 0.840809i \(-0.682080\pi\)
0.998828 + 0.0484030i \(0.0154132\pi\)
\(44\) 0.267949i 0.0403949i
\(45\) 0 0
\(46\) −3.00000 1.73205i −0.442326 0.255377i
\(47\) 6.46410i 0.942886i −0.881897 0.471443i \(-0.843733\pi\)
0.881897 0.471443i \(-0.156267\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 2.59808 + 2.50000i 0.360288 + 0.346688i
\(53\) 0.267949 0.0368057 0.0184028 0.999831i \(-0.494142\pi\)
0.0184028 + 0.999831i \(0.494142\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 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 \(0.934814\pi\)
\(60\) 0 0
\(61\) 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
\(65\) 0 0
\(66\) 0.267949 0.0329823
\(67\) −1.26795 + 0.732051i −0.154905 + 0.0894342i −0.575449 0.817838i \(-0.695173\pi\)
0.420544 + 0.907272i \(0.361839\pi\)
\(68\) −2.00000 3.46410i −0.242536 0.420084i
\(69\) 1.73205 3.00000i 0.208514 0.361158i
\(70\) 0 0
\(71\) −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 \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) −2.96410 + 5.13397i −0.344570 + 0.596812i
\(75\) 0 0
\(76\) 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 0
\(81\) −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 \(0.173848\pi\)
−0.854525 + 0.519410i \(0.826152\pi\)
\(84\) 2.59808 + 1.50000i 0.283473 + 0.163663i
\(85\) 0 0
\(86\) 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 \(0.602602\pi\)
\(90\) 0 0
\(91\) 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
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −7.26795 4.19615i −0.737948 0.426055i 0.0833745 0.996518i \(-0.473430\pi\)
−0.821323 + 0.570464i \(0.806764\pi\)
\(98\) −1.73205 1.00000i −0.174964 0.101015i
\(99\) 0.267949i 0.0269299i
\(100\) 0 0
\(101\) −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 \(-0.306586\pi\)
0.570922 + 0.821004i \(0.306586\pi\)
\(104\) −3.50000 0.866025i −0.343203 0.0849208i
\(105\) 0 0
\(106\) −0.232051 + 0.133975i −0.0225388 + 0.0130128i
\(107\) −6.46410 11.1962i −0.624908 1.08237i −0.988559 0.150837i \(-0.951803\pi\)
0.363650 0.931536i \(-0.381530\pi\)
\(108\) 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 0
\(111\) −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 \(0.357572\pi\)
−0.997102 + 0.0760733i \(0.975762\pi\)
\(114\) 2.86603 + 4.96410i 0.268428 + 0.464931i
\(115\) 0 0
\(116\) −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 0
\(121\) −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
\(125\) 0 0
\(126\) −1.50000 + 2.59808i −0.133631 + 0.231455i
\(127\) −6.33013 10.9641i −0.561708 0.972907i −0.997348 0.0727855i \(-0.976811\pi\)
0.435640 0.900121i \(-0.356522\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −6.00000 −0.528271
\(130\) 0 0
\(131\) 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
\(135\) 0 0
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) −11.6603 6.73205i −0.996203 0.575158i −0.0890802 0.996024i \(-0.528393\pi\)
−0.907123 + 0.420867i \(0.861726\pi\)
\(138\) 3.46410i 0.294884i
\(139\) 9.89230 17.1340i 0.839054 1.45328i −0.0516319 0.998666i \(-0.516442\pi\)
0.890686 0.454619i \(-0.150224\pi\)
\(140\) 0 0
\(141\) −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
\(145\) 0 0
\(146\) 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 0
\(151\) 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
\(155\) 0 0
\(156\) 0.866025 3.50000i 0.0693375 0.280224i
\(157\) −21.1962 −1.69164 −0.845819 0.533471i \(-0.820887\pi\)
−0.845819 + 0.533471i \(0.820887\pi\)
\(158\) −2.66025 + 1.53590i −0.211638 + 0.122190i
\(159\) −0.133975 0.232051i −0.0106249 0.0184028i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 2.53590 + 1.46410i 0.198627 + 0.114677i 0.596015 0.802973i \(-0.296750\pi\)
−0.397388 + 0.917651i \(0.630083\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0 0
\(166\) −4.73205 8.19615i −0.367278 0.636145i
\(167\) 0.401924 0.232051i 0.0311018 0.0179566i −0.484368 0.874864i \(-0.660951\pi\)
0.515470 + 0.856907i \(0.327617\pi\)
\(168\) −3.00000 −0.231455
\(169\) −11.5000 6.06218i −0.884615 0.466321i
\(170\) 0 0
\(171\) −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 −0.903575 0.428430i \(-0.859067\pi\)
0.822819 + 0.568304i \(0.192400\pi\)
\(174\) 1.46410i 0.110993i
\(175\) 0 0
\(176\) −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 0
\(181\) 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
\(185\) 0 0
\(186\) 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
\(190\) 0 0
\(191\) 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 −0.160269 0.987073i \(-0.551236\pi\)
0.774696 + 0.632334i \(0.217903\pi\)
\(194\) 8.39230 0.602532
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 9.86603 5.69615i 0.702925 0.405834i −0.105511 0.994418i \(-0.533648\pi\)
0.808436 + 0.588584i \(0.200314\pi\)
\(198\) −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 \(-0.178191\pi\)
\(200\) 0 0
\(201\) 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
\(205\) 0 0
\(206\) −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
\(210\) 0 0
\(211\) 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
\(215\) 0 0
\(216\) 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 0
\(221\) 10.3923 + 10.0000i 0.699062 + 0.672673i
\(222\) 5.92820 0.397875
\(223\) 16.3301 9.42820i 1.09355 0.631359i 0.159028 0.987274i \(-0.449164\pi\)
0.934518 + 0.355915i \(0.115831\pi\)
\(224\) −1.50000 2.59808i −0.100223 0.173591i
\(225\) 0 0
\(226\) 12.0000i 0.798228i
\(227\) −5.66025 3.26795i −0.375684 0.216901i 0.300255 0.953859i \(-0.402928\pi\)
−0.675939 + 0.736958i \(0.736262\pi\)
\(228\) −4.96410 2.86603i −0.328756 0.189807i
\(229\) 4.53590i 0.299741i −0.988706 0.149870i \(-0.952114\pi\)
0.988706 0.149870i \(-0.0478856\pi\)
\(230\) 0 0
\(231\) 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 \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 3.50000 + 0.866025i 0.228802 + 0.0566139i
\(235\) 0 0
\(236\) −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 0
\(241\) −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
\(245\) 0 0
\(246\) −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 0
\(251\) −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
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.26795 + 12.5885i 0.453362 + 0.785246i 0.998592 0.0530400i \(-0.0168911\pi\)
−0.545230 + 0.838286i \(0.683558\pi\)
\(258\) 5.19615 3.00000i 0.323498 0.186772i
\(259\) −17.7846 −1.10508
\(260\) 0 0
\(261\) 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 \(-0.893875\pi\)
0.189054 0.981967i \(-0.439458\pi\)
\(264\) 0.133975 0.232051i 0.00824557 0.0142817i
\(265\) 0 0
\(266\) 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 0
\(271\) 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 0
\(276\) −1.73205 3.00000i −0.104257 0.180579i
\(277\) 5.79423 10.0359i 0.348141 0.602999i −0.637778 0.770220i \(-0.720146\pi\)
0.985919 + 0.167222i \(0.0534796\pi\)
\(278\) 19.7846i 1.18660i
\(279\) 4.26795 + 2.46410i 0.255515 + 0.147522i
\(280\) 0 0
\(281\) 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 0.755256 0.655430i \(-0.227513\pi\)
−0.945247 + 0.326355i \(0.894179\pi\)
\(284\) −11.1962 + 6.46410i −0.664369 + 0.383574i
\(285\) 0 0
\(286\) −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 0
\(291\) 8.39230i 0.491966i
\(292\) −6.00000 3.46410i −0.351123 0.202721i
\(293\) −25.3301 14.6244i −1.47980 0.854364i −0.480063 0.877234i \(-0.659386\pi\)
−0.999738 + 0.0228698i \(0.992720\pi\)
\(294\) 2.00000i 0.116642i
\(295\) 0 0
\(296\) 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
\(300\) 0 0
\(301\) −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 0
\(306\) −3.46410 2.00000i −0.198030 0.114332i
\(307\) 28.2487i 1.61224i 0.591753 + 0.806120i \(0.298436\pi\)
−0.591753 + 0.806120i \(0.701564\pi\)
\(308\) −0.401924 + 0.696152i −0.0229017 + 0.0396670i
\(309\) −5.79423 10.0359i −0.329622 0.570922i
\(310\) 0 0
\(311\) 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 \(-0.109234\pi\)
0.941693 + 0.336473i \(0.109234\pi\)
\(314\) 18.3564 10.5981i 1.03591 0.598084i
\(315\) 0 0
\(316\) 1.53590 2.66025i 0.0864010 0.149651i
\(317\) 30.4641i 1.71103i −0.517774 0.855517i \(-0.673239\pi\)
0.517774 0.855517i \(-0.326761\pi\)
\(318\) 0.232051 + 0.133975i 0.0130128 + 0.00751292i
\(319\) −0.339746 0.196152i −0.0190221 0.0109824i
\(320\) 0 0
\(321\) −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 0
\(326\) −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 0
\(331\) 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 0
\(336\) 2.59808 1.50000i 0.141737 0.0818317i
\(337\) 26.3923 1.43768 0.718840 0.695175i \(-0.244673\pi\)
0.718840 + 0.695175i \(0.244673\pi\)
\(338\) 12.9904 0.500000i 0.706584 0.0271964i
\(339\) 12.0000 0.651751
\(340\) 0 0
\(341\) −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
\(345\) 0 0
\(346\) 2.12436i 0.114206i
\(347\) 2.19615 3.80385i 0.117896 0.204201i −0.801038 0.598614i \(-0.795719\pi\)
0.918934 + 0.394412i \(0.129052\pi\)
\(348\) 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 \(0.424327\pi\)
\(350\) 0 0
\(351\) −0.866025 + 3.50000i −0.0462250 + 0.186816i
\(352\) 0.267949 0.0142817
\(353\) −6.58846 + 3.80385i −0.350668 + 0.202458i −0.664980 0.746862i \(-0.731560\pi\)
0.314311 + 0.949320i \(0.398226\pi\)
\(354\) −5.73205 9.92820i −0.304655 0.527678i
\(355\) 0 0
\(356\) 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 0
\(361\) 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
\(365\) 0 0
\(366\) 0.464102 0.267949i 0.0242590 0.0140059i
\(367\) 10.6603 + 18.4641i 0.556461 + 0.963818i 0.997788 + 0.0664722i \(0.0211744\pi\)
−0.441328 + 0.897346i \(0.645492\pi\)
\(368\) 1.73205 3.00000i 0.0902894 0.156386i
\(369\) 4.00000i 0.208232i
\(370\) 0 0
\(371\) −0.696152 0.401924i −0.0361424 0.0208668i
\(372\) 4.92820i 0.255515i
\(373\) 4.53590 7.85641i 0.234860 0.406789i −0.724372 0.689409i \(-0.757870\pi\)
0.959232 + 0.282620i \(0.0912035\pi\)
\(374\) 0.535898 + 0.928203i 0.0277106 + 0.0479962i
\(375\) 0 0
\(376\) 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 \(0.413748\pi\)
\(380\) 0 0
\(381\) −6.33013 + 10.9641i −0.324302 + 0.561708i
\(382\) 17.3205i 0.886194i
\(383\) −4.14359 2.39230i −0.211728 0.122241i 0.390386 0.920651i \(-0.372341\pi\)
−0.602114 + 0.798410i \(0.705675\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) −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 \(0.350469\pi\)
\(390\) 0 0
\(391\) 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
\(395\) 0 0
\(396\) 0.232051 + 0.133975i 0.0116610 + 0.00673248i
\(397\) 5.13397 + 2.96410i 0.257667 + 0.148764i 0.623270 0.782007i \(-0.285804\pi\)
−0.365603 + 0.930771i \(0.619137\pi\)
\(398\) 24.9282i 1.24954i
\(399\) −8.59808 + 14.8923i −0.430442 + 0.745548i
\(400\) 0 0
\(401\) −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 0
\(406\) −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 \(-0.749493\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) −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 \(0.910730\pi\)
\(420\) 0 0
\(421\) 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
\(425\) 0 0
\(426\) −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
\(430\) 0 0
\(431\) −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 −0.952053 0.305933i \(-0.901032\pi\)
0.740972 + 0.671536i \(0.234365\pi\)
\(434\) 14.7846i 0.709684i
\(435\) 0 0
\(436\) 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 0
\(441\) −2.00000 −0.0952381
\(442\) −14.0000 3.46410i −0.665912 0.164771i
\(443\) 19.8564 0.943406 0.471703 0.881757i \(-0.343639\pi\)
0.471703 + 0.881757i \(0.343639\pi\)
\(444\) −5.13397 + 2.96410i −0.243648 + 0.140670i
\(445\) 0 0
\(446\) −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 \(0.712828\pi\)
\(450\) 0 0
\(451\) −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
\(455\) 0 0
\(456\) 5.73205 0.268428
\(457\) 6.46410 3.73205i 0.302378 0.174578i −0.341133 0.940015i \(-0.610811\pi\)
0.643511 + 0.765437i \(0.277477\pi\)
\(458\) 2.26795 + 3.92820i 0.105974 + 0.183553i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) −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 \(0.396609\pi\)
−0.319131 + 0.947711i \(0.603391\pi\)
\(464\) −0.732051 + 1.26795i −0.0339846 + 0.0588631i
\(465\) 0 0
\(466\) 15.5885 9.00000i 0.722121 0.416917i
\(467\) −24.3923 −1.12874 −0.564371 0.825522i \(-0.690881\pi\)
−0.564371 + 0.825522i \(0.690881\pi\)
\(468\) −3.46410 + 1.00000i −0.160128 + 0.0462250i
\(469\) 4.39230 0.202818
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) 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 \(0.503054\pi\)
\(480\) 0 0
\(481\) 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
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −18.1865 10.5000i −0.824110 0.475800i 0.0277214 0.999616i \(-0.491175\pi\)
−0.851832 + 0.523815i \(0.824508\pi\)
\(488\) 0.464102 + 0.267949i 0.0210089 + 0.0121295i
\(489\) 2.92820i 0.132418i
\(490\) 0 0
\(491\) −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 0
\(496\) −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 0
\(501\) −0.401924 0.232051i −0.0179566 0.0103673i
\(502\) 19.5359i 0.871930i
\(503\) 1.86603 3.23205i 0.0832020 0.144110i −0.821422 0.570321i \(-0.806819\pi\)
0.904624 + 0.426211i \(0.140152\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) 0 0
\(506\) −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 \(0.108184\pi\)
\(510\) 0 0
\(511\) −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
\(515\) 0 0
\(516\) −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 0
\(521\) −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 \(-0.801214\pi\)
−0.100733 0.994913i \(-0.532119\pi\)
\(524\) 7.16025 12.4019i 0.312797 0.541781i
\(525\) 0 0
\(526\) 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 0
\(531\) 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
\(535\) 0 0
\(536\) −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 0
\(541\) 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
\(545\) 0 0
\(546\) 10.3923 3.00000i 0.444750 0.128388i
\(547\) 5.32051 0.227488 0.113744 0.993510i \(-0.463716\pi\)
0.113744 + 0.993510i \(0.463716\pi\)
\(548\) −11.6603 + 6.73205i −0.498101 + 0.287579i
\(549\) 0.267949 + 0.464102i 0.0114358 + 0.0198074i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) −9.89230 17.1340i −0.419527 0.726642i
\(557\) 19.5788 11.3038i 0.829582 0.478959i −0.0241275 0.999709i \(-0.507681\pi\)
0.853710 + 0.520749i \(0.174347\pi\)
\(558\) −4.92820 −0.208627
\(559\) 15.5885 + 15.0000i 0.659321 + 0.634432i
\(560\) 0 0
\(561\) −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 −0.981073 0.193638i \(-0.937971\pi\)
0.658232 + 0.752815i \(0.271305\pi\)
\(564\) 6.46410i 0.272188i
\(565\) 0 0
\(566\) 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 \(0.722197\pi\)
\(570\) 0 0
\(571\) 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
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 9.32051i 0.388018i 0.981000 + 0.194009i \(0.0621491\pi\)
−0.981000 + 0.194009i \(0.937851\pi\)
\(578\) −0.866025 0.500000i −0.0360219 0.0207973i
\(579\) −8.53590 4.92820i −0.354740 0.204809i
\(580\) 0 0
\(581\) 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
\(585\) 0 0
\(586\) 29.2487 1.20825
\(587\) 7.73205 4.46410i 0.319136 0.184253i −0.331871 0.943325i \(-0.607680\pi\)
0.651007 + 0.759071i \(0.274347\pi\)
\(588\) −1.00000 1.73205i −0.0412393 0.0714286i
\(589\) 14.1244 24.4641i 0.581984 1.00803i
\(590\) 0 0
\(591\) −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 \(0.371440\pi\)
−0.392992 + 0.919542i \(0.628560\pi\)
\(594\) −0.133975 + 0.232051i −0.00549704 + 0.00952116i
\(595\) 0 0
\(596\) 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 0
\(601\) −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
\(605\) 0 0
\(606\) 12.3923i 0.503403i
\(607\) −10.7224 + 18.5718i −0.435210 + 0.753806i −0.997313 0.0732615i \(-0.976659\pi\)
0.562103 + 0.827067i \(0.309993\pi\)
\(608\) 2.86603 + 4.96410i 0.116233 + 0.201321i
\(609\) 3.80385 2.19615i 0.154140 0.0889926i
\(610\) 0 0
\(611\) 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 \(0.696308\pi\)
−0.995667 + 0.0929864i \(0.970359\pi\)
\(614\) −14.1244 24.4641i −0.570013 0.987291i
\(615\) 0 0
\(616\) 0.803848i 0.0323879i
\(617\) 30.7128 + 17.7321i 1.23645 + 0.713865i 0.968367 0.249530i \(-0.0802761\pi\)
0.268084 + 0.963395i \(0.413609\pi\)
\(618\) 10.0359 + 5.79423i 0.403703 + 0.233078i
\(619\) 2.51666i 0.101153i 0.998720 + 0.0505766i \(0.0161059\pi\)
−0.998720 + 0.0505766i \(0.983894\pi\)
\(620\) 0 0
\(621\) 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
\(625\) 0 0
\(626\) −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
\(630\) 0 0
\(631\) −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
\(635\) 0 0
\(636\) −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 0
\(641\) −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 0.265538 0.964100i \(-0.414451\pi\)
−0.702167 + 0.712013i \(0.747784\pi\)
\(644\) −9.00000 5.19615i −0.354650 0.204757i
\(645\) 0 0
\(646\) −11.4641 + 19.8564i −0.451049 + 0.781240i
\(647\) −17.8660 30.9449i −0.702386 1.21657i −0.967627 0.252386i \(-0.918785\pi\)
0.265241 0.964182i \(-0.414549\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −3.07180 −0.120579
\(650\) 0 0
\(651\) 14.7846 0.579455
\(652\) 2.53590 1.46410i 0.0993134 0.0573386i
\(653\) −0.794229 1.37564i −0.0310806 0.0538331i 0.850067 0.526675i \(-0.176562\pi\)
−0.881147 + 0.472842i \(0.843228\pi\)
\(654\) −5.19615 + 9.00000i −0.203186 + 0.351928i
\(655\) 0 0
\(656\) 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 0
\(661\) −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
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) 0.143594i 0.00554337i
\(672\) −1.50000 + 2.59808i −0.0578638 + 0.100223i
\(673\) −8.39230 14.5359i −0.323500 0.560318i 0.657708 0.753273i \(-0.271526\pi\)
−0.981208 + 0.192955i \(0.938193\pi\)
\(674\) −22.8564 + 13.1962i −0.880396 + 0.508297i
\(675\) 0 0
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) −10.9282 −0.420005 −0.210002 0.977701i \(-0.567347\pi\)
−0.210002 + 0.977701i \(0.567347\pi\)
\(678\) −10.3923 + 6.00000i −0.399114 + 0.230429i
\(679\) 12.5885 + 21.8038i 0.483101 + 0.836755i
\(680\) 0 0
\(681\) 6.53590i 0.250456i
\(682\) 1.14359 + 0.660254i 0.0437905 + 0.0252824i
\(683\) −35.7846 20.6603i −1.36926 0.790543i −0.378427 0.925631i \(-0.623535\pi\)
−0.990834 + 0.135089i \(0.956868\pi\)
\(684\) 5.73205i 0.219170i
\(685\) 0 0
\(686\) −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
\(690\) 0 0
\(691\) 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
\(695\) 0 0
\(696\) −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
\(700\) 0 0
\(701\) −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
\(705\) 0 0
\(706\) 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 \(0.838141\pi\)
\(710\) 0 0
\(711\) −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 0
\(716\) −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 \(0.263103\pi\)
\(720\) 0 0
\(721\) −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 0
\(726\) −9.46410 + 5.46410i −0.351246 + 0.202792i
\(727\) 4.66025 0.172839 0.0864196 0.996259i \(-0.472457\pi\)
0.0864196 + 0.996259i \(0.472457\pi\)
\(728\) 7.79423 + 7.50000i 0.288873 + 0.277968i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −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 \(-0.874141\pi\)
0.922844 0.385174i \(-0.125859\pi\)
\(734\) −18.4641 10.6603i −0.681522 0.393477i
\(735\) 0 0
\(736\) 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 \(0.104251\pi\)
\(740\) 0 0
\(741\) 20.0622 + 4.96410i 0.737003 + 0.182361i
\(742\) 0.803848 0.0295102
\(743\) 9.46410 5.46410i 0.347204 0.200458i −0.316249 0.948676i \(-0.602424\pi\)
0.663453 + 0.748218i \(0.269090\pi\)
\(744\) −2.46410 4.26795i −0.0903383 0.156471i
\(745\) 0 0
\(746\) 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 0
\(751\) 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
\(755\) 0 0
\(756\) −2.59808 + 1.50000i −0.0944911 + 0.0545545i
\(757\) 10.8660 + 18.8205i 0.394932 + 0.684043i 0.993093 0.117334i \(-0.0374347\pi\)
−0.598160 + 0.801377i \(0.704101\pi\)
\(758\) 4.86603 8.42820i 0.176742 0.306126i
\(759\) 0.928203i 0.0336916i
\(760\) 0 0
\(761\) 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
\(765\) 0 0
\(766\) 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 0
\(771\) 7.26795 12.5885i 0.261749 0.453362i
\(772\) 9.85641i 0.354740i
\(773\) 28.2391 + 16.3038i 1.01569 + 0.586409i 0.912852 0.408290i \(-0.133875\pi\)
0.102837 + 0.994698i \(0.467208\pi\)
\(774\) −5.19615 3.00000i −0.186772 0.107833i
\(775\) 0 0
\(776\) 4.19615 7.26795i 0.150633 0.260904i
\(777\) 8.89230 + 15.4019i 0.319010 + 0.552541i
\(778\) −15.4641 + 8.92820i −0.554415 + 0.320092i
\(779\) −22.9282 −0.821488
\(780\) 0 0
\(781\) −3.46410 −0.123955
\(782\) −12.0000 + 6.92820i −0.429119 + 0.247752i
\(783\) −0.732051 1.26795i −0.026161