Properties

Label 712.1.y.a.403.1
Level $712$
Weight $1$
Character 712.403
Analytic conductor $0.355$
Analytic rank $0$
Dimension $20$
Projective image $D_{44}$
CM discriminant -8
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 712 = 2^{3} \cdot 89 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 712.y (of order \(44\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.355334288995\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{44})\)
Defining polynomial: \(x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{44}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{44} - \cdots)\)

Embedding invariants

Embedding label 403.1
Root \(0.281733 - 0.959493i\) of defining polynomial
Character \(\chi\) \(=\) 712.403
Dual form 712.1.y.a.659.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.841254 + 0.540641i) q^{2} +(0.613435 - 1.64468i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.373128 + 1.71524i) q^{6} +(0.142315 + 0.989821i) q^{8} +(-1.57293 - 1.36295i) q^{9} +O(q^{10})\) \(q+(-0.841254 + 0.540641i) q^{2} +(0.613435 - 1.64468i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.373128 + 1.71524i) q^{6} +(0.142315 + 0.989821i) q^{8} +(-1.57293 - 1.36295i) q^{9} +(0.281733 - 1.95949i) q^{11} +(-1.24123 - 1.24123i) q^{12} +(-0.654861 - 0.755750i) q^{16} +(-0.909632 + 1.41542i) q^{17} +(2.06010 + 0.296197i) q^{18} +(0.0855040 + 1.19550i) q^{19} +(0.822373 + 1.80075i) q^{22} +(1.71524 + 0.373128i) q^{24} +(0.959493 - 0.281733i) q^{25} +(-1.66587 + 0.909632i) q^{27} +(0.959493 + 0.281733i) q^{32} +(-3.04992 - 1.66538i) q^{33} -1.68251i q^{34} +(-1.89320 + 0.864596i) q^{36} +(-0.718267 - 0.959493i) q^{38} +(-1.32505 + 0.494217i) q^{41} +(1.56449 - 1.17116i) q^{43} +(-1.66538 - 1.07028i) q^{44} +(-1.64468 + 0.613435i) q^{48} +(-0.281733 - 0.959493i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(1.76991 + 2.36432i) q^{51} +(0.909632 - 1.66587i) q^{54} +(2.01867 + 0.592735i) q^{57} +(-0.148568 - 0.398326i) q^{59} +(-0.959493 + 0.281733i) q^{64} +(3.46613 - 0.247902i) q^{66} +(0.627899 + 1.37491i) q^{67} +(0.909632 + 1.41542i) q^{68} +(1.12523 - 1.75089i) q^{72} +(0.368991 + 0.425839i) q^{73} +(0.125226 - 1.75089i) q^{75} +(1.12299 + 0.418852i) q^{76} +(0.177958 + 1.23772i) q^{81} +(0.847507 - 1.13214i) q^{82} +(0.148568 + 0.682956i) q^{83} +(-0.682956 + 1.83107i) q^{86} +1.97964 q^{88} +(0.959493 + 0.281733i) q^{89} +(1.05195 - 1.40524i) q^{96} +(0.186393 + 1.29639i) q^{97} +(0.755750 + 0.654861i) q^{98} +(-3.11384 + 2.69815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10}) \) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/712\mathbb{Z}\right)^\times\).

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{27}{44}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(3\) 0.613435 1.64468i 0.613435 1.64468i −0.142315 0.989821i \(-0.545455\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(4\) 0.415415 0.909632i 0.415415 0.909632i
\(5\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(6\) 0.373128 + 1.71524i 0.373128 + 1.71524i
\(7\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(8\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(9\) −1.57293 1.36295i −1.57293 1.36295i
\(10\) 0 0
\(11\) 0.281733 1.95949i 0.281733 1.95949i 1.00000i \(-0.5\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(12\) −1.24123 1.24123i −1.24123 1.24123i
\(13\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.654861 0.755750i −0.654861 0.755750i
\(17\) −0.909632 + 1.41542i −0.909632 + 1.41542i 1.00000i \(0.5\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(18\) 2.06010 + 0.296197i 2.06010 + 0.296197i
\(19\) 0.0855040 + 1.19550i 0.0855040 + 1.19550i 0.841254 + 0.540641i \(0.181818\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.822373 + 1.80075i 0.822373 + 1.80075i
\(23\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(24\) 1.71524 + 0.373128i 1.71524 + 0.373128i
\(25\) 0.959493 0.281733i 0.959493 0.281733i
\(26\) 0 0
\(27\) −1.66587 + 0.909632i −1.66587 + 0.909632i
\(28\) 0 0
\(29\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(30\) 0 0
\(31\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(32\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(33\) −3.04992 1.66538i −3.04992 1.66538i
\(34\) 1.68251i 1.68251i
\(35\) 0 0
\(36\) −1.89320 + 0.864596i −1.89320 + 0.864596i
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) −0.718267 0.959493i −0.718267 0.959493i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.32505 + 0.494217i −1.32505 + 0.494217i −0.909632 0.415415i \(-0.863636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(42\) 0 0
\(43\) 1.56449 1.17116i 1.56449 1.17116i 0.654861 0.755750i \(-0.272727\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(44\) −1.66538 1.07028i −1.66538 1.07028i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(48\) −1.64468 + 0.613435i −1.64468 + 0.613435i
\(49\) −0.281733 0.959493i −0.281733 0.959493i
\(50\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(51\) 1.76991 + 2.36432i 1.76991 + 2.36432i
\(52\) 0 0
\(53\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(54\) 0.909632 1.66587i 0.909632 1.66587i
\(55\) 0 0
\(56\) 0 0
\(57\) 2.01867 + 0.592735i 2.01867 + 0.592735i
\(58\) 0 0
\(59\) −0.148568 0.398326i −0.148568 0.398326i 0.841254 0.540641i \(-0.181818\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(60\) 0 0
\(61\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(65\) 0 0
\(66\) 3.46613 0.247902i 3.46613 0.247902i
\(67\) 0.627899 + 1.37491i 0.627899 + 1.37491i 0.909632 + 0.415415i \(0.136364\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(68\) 0.909632 + 1.41542i 0.909632 + 1.41542i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(72\) 1.12523 1.75089i 1.12523 1.75089i
\(73\) 0.368991 + 0.425839i 0.368991 + 0.425839i 0.909632 0.415415i \(-0.136364\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(74\) 0 0
\(75\) 0.125226 1.75089i 0.125226 1.75089i
\(76\) 1.12299 + 0.418852i 1.12299 + 0.418852i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(80\) 0 0
\(81\) 0.177958 + 1.23772i 0.177958 + 1.23772i
\(82\) 0.847507 1.13214i 0.847507 1.13214i
\(83\) 0.148568 + 0.682956i 0.148568 + 0.682956i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.682956 + 1.83107i −0.682956 + 1.83107i
\(87\) 0 0
\(88\) 1.97964 1.97964
\(89\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.05195 1.40524i 1.05195 1.40524i
\(97\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(98\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(99\) −3.11384 + 2.69815i −3.11384 + 2.69815i
\(100\) 0.142315 0.989821i 0.142315 0.989821i
\(101\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(102\) −2.76719 1.03211i −2.76719 1.03211i
\(103\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) 0.135404 + 1.89320i 0.135404 + 1.89320i
\(109\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.682956 + 0.148568i 0.682956 + 0.148568i 0.540641 0.841254i \(-0.318182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(114\) −2.01867 + 0.592735i −2.01867 + 0.592735i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.340335 + 0.254771i 0.340335 + 0.254771i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.80075 0.822373i −2.80075 0.822373i
\(122\) 0 0
\(123\) 2.48245i 2.48245i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(128\) 0.654861 0.755750i 0.654861 0.755750i
\(129\) −0.966479 3.29153i −0.966479 3.29153i
\(130\) 0 0
\(131\) 1.74557 + 0.797176i 1.74557 + 0.797176i 0.989821 + 0.142315i \(0.0454545\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(132\) −2.78187 + 2.08248i −2.78187 + 2.08248i
\(133\) 0 0
\(134\) −1.27155 0.817178i −1.27155 0.817178i
\(135\) 0 0
\(136\) −1.53046 0.698939i −1.53046 0.698939i
\(137\) 0.398326 0.148568i 0.398326 0.148568i −0.142315 0.989821i \(-0.545455\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(138\) 0 0
\(139\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 2.08128i 2.08128i
\(145\) 0 0
\(146\) −0.540641 0.158746i −0.540641 0.158746i
\(147\) −1.75089 0.125226i −1.75089 0.125226i
\(148\) 0 0
\(149\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(150\) 0.841254 + 1.54064i 0.841254 + 1.54064i
\(151\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(152\) −1.17116 + 0.254771i −1.17116 + 0.254771i
\(153\) 3.35992 0.986563i 3.35992 0.986563i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.818872 0.945028i −0.818872 0.945028i
\(163\) 0.203743 0.936593i 0.203743 0.936593i −0.755750 0.654861i \(-0.772727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(164\) −0.100889 + 1.41061i −0.100889 + 1.41061i
\(165\) 0 0
\(166\) −0.494217 0.494217i −0.494217 0.494217i
\(167\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(168\) 0 0
\(169\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(170\) 0 0
\(171\) 1.49492 1.99698i 1.49492 1.99698i
\(172\) −0.415415 1.90963i −0.415415 1.90963i
\(173\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.66538 + 1.07028i −1.66538 + 1.07028i
\(177\) −0.746256 −0.746256
\(178\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(179\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 0 0
\(181\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.51722 + 2.18119i 2.51722 + 2.18119i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(192\) −0.125226 + 1.75089i −0.125226 + 1.75089i
\(193\) −0.424047 + 1.94931i −0.424047 + 1.94931i −0.142315 + 0.989821i \(0.545455\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(194\) −0.857685 0.989821i −0.857685 0.989821i
\(195\) 0 0
\(196\) −0.989821 0.142315i −0.989821 0.142315i
\(197\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(198\) 1.16079 3.95330i 1.16079 3.95330i
\(199\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(200\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(201\) 2.64646 0.189279i 2.64646 0.189279i
\(202\) 0 0
\(203\) 0 0
\(204\) 2.88591 0.627791i 2.88591 0.627791i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.36667 + 0.169267i 2.36667 + 0.169267i
\(210\) 0 0
\(211\) −1.71524 0.936593i −1.71524 0.936593i −0.959493 0.281733i \(-0.909091\pi\)
−0.755750 0.654861i \(-0.772727\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) −1.13745 1.51946i −1.13745 1.51946i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.926721 0.345649i 0.926721 0.345649i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(224\) 0 0
\(225\) −1.89320 0.864596i −1.89320 0.864596i
\(226\) −0.654861 + 0.244250i −0.654861 + 0.244250i
\(227\) −0.158746 0.540641i −0.158746 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
−1.00000 \(\pi\)
\(228\) 1.37776 1.59002i 1.37776 1.59002i
\(229\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.830830i 0.830830i 0.909632 + 0.415415i \(0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.424047 0.0303285i −0.424047 0.0303285i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(240\) 0 0
\(241\) −1.83107 + 0.398326i −1.83107 + 0.398326i −0.989821 0.142315i \(-0.954545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(242\) 2.80075 0.822373i 2.80075 0.822373i
\(243\) 0.290168 + 0.0631221i 0.290168 + 0.0631221i
\(244\) 0 0
\(245\) 0 0
\(246\) −1.34211 2.08837i −1.34211 2.08837i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.21438 + 0.174602i 1.21438 + 0.174602i
\(250\) 0 0
\(251\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(257\) −0.215109 + 0.186393i −0.215109 + 0.186393i −0.755750 0.654861i \(-0.772727\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(258\) 2.59259 + 2.24649i 2.59259 + 2.24649i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.89945 + 0.273100i −1.89945 + 0.273100i
\(263\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(264\) 1.21438 3.25588i 1.21438 3.25588i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.05195 1.40524i 1.05195 1.40524i
\(268\) 1.51150 1.51150
\(269\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(270\) 0 0
\(271\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(272\) 1.66538 0.239446i 1.66538 0.239446i
\(273\) 0 0
\(274\) −0.254771 + 0.340335i −0.254771 + 0.340335i
\(275\) −0.281733 1.95949i −0.281733 1.95949i
\(276\) 0 0
\(277\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(278\) 0.0405070 0.281733i 0.0405070 0.281733i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.114220 1.59700i 0.114220 1.59700i −0.540641 0.841254i \(-0.681818\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(282\) 0 0
\(283\) −1.19136 1.37491i −1.19136 1.37491i −0.909632 0.415415i \(-0.863636\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.12523 1.75089i −1.12523 1.75089i
\(289\) −0.760554 1.66538i −0.760554 1.66538i
\(290\) 0 0
\(291\) 2.24649 + 0.488694i 2.24649 + 0.488694i
\(292\) 0.540641 0.158746i 0.540641 0.158746i
\(293\) 0 0 0.977147 0.212565i \(-0.0681818\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(294\) 1.54064 0.841254i 1.54064 0.841254i
\(295\) 0 0
\(296\) 0 0
\(297\) 1.31309 + 3.52053i 1.31309 + 3.52053i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.54064 0.841254i −1.54064 0.841254i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.847507 0.847507i 0.847507 0.847507i
\(305\) 0 0
\(306\) −2.29317 + 2.64646i −2.29317 + 2.64646i
\(307\) −0.234072 0.797176i −0.234072 0.797176i −0.989821 0.142315i \(-0.954545\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(312\) 0 0
\(313\) −1.59700 + 1.19550i −1.59700 + 1.19550i −0.755750 + 0.654861i \(0.772727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.76991 0.966443i −1.76991 0.966443i
\(324\) 1.19980 + 0.352293i 1.19980 + 0.352293i
\(325\) 0 0
\(326\) 0.334961 + 0.898064i 0.334961 + 0.898064i
\(327\) 0 0
\(328\) −0.677760 1.24123i −0.677760 1.24123i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(332\) 0.682956 + 0.148568i 0.682956 + 0.148568i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.114220 + 1.59700i 0.114220 + 1.59700i 0.654861 + 0.755750i \(0.272727\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(338\) −0.989821 0.142315i −0.989821 0.142315i
\(339\) 0.663296 1.03211i 0.663296 1.03211i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.177958 + 2.48818i −0.177958 + 2.48818i
\(343\) 0 0
\(344\) 1.38189 + 1.38189i 1.38189 + 1.38189i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.37491 1.19136i −1.37491 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(348\) 0 0
\(349\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.822373 1.80075i 0.822373 1.80075i
\(353\) −0.697148 + 1.86912i −0.697148 + 1.86912i −0.281733 + 0.959493i \(0.590909\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(354\) 0.627791 0.403457i 0.627791 0.403457i
\(355\) 0 0
\(356\) 0.654861 0.755750i 0.654861 0.755750i
\(357\) 0 0
\(358\) 1.10181 0.708089i 1.10181 0.708089i
\(359\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(360\) 0 0
\(361\) −0.432092 + 0.0621254i −0.432092 + 0.0621254i
\(362\) 0 0
\(363\) −3.07062 + 4.10187i −3.07062 + 4.10187i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(368\) 0 0
\(369\) 2.75780 + 1.02860i 2.75780 + 1.02860i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(374\) −3.29686 0.474017i −3.29686 0.474017i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.142315 + 0.0101786i −0.142315 + 0.0101786i −0.142315 0.989821i \(-0.545455\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(384\) −0.841254 1.54064i −0.841254 1.54064i
\(385\) 0 0
\(386\) −0.697148 1.86912i −0.697148 1.86912i
\(387\) −4.05707 0.290168i −4.05707 0.290168i
\(388\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(389\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.909632 0.415415i 0.909632 0.415415i
\(393\) 2.38189 2.38189i 2.38189 2.38189i
\(394\) 0 0
\(395\) 0 0
\(396\) 1.16079 + 3.95330i 1.16079 + 3.95330i
\(397\) 0 0 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.841254 0.540641i −0.841254 0.540641i
\(401\) 1.27155 + 0.817178i 1.27155 + 0.817178i 0.989821 0.142315i \(-0.0454545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(402\) −2.12401 + 1.59002i −2.12401 + 1.59002i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −2.08837 + 2.08837i −2.08837 + 2.08837i
\(409\) 1.19136 0.544078i 1.19136 0.544078i 0.281733 0.959493i \(-0.409091\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(410\) 0 0
\(411\) 0.746256i 0.746256i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.239446 + 0.438512i 0.239446 + 0.438512i
\(418\) −2.08248 + 1.13712i −2.08248 + 1.13712i
\(419\) 1.94931 0.424047i 1.94931 0.424047i 0.959493 0.281733i \(-0.0909091\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(420\) 0 0
\(421\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(422\) 1.94931 0.139418i 1.94931 0.139418i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.474017 + 1.61435i −0.474017 + 1.61435i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(432\) 1.77836 + 0.663296i 1.77836 + 0.663296i
\(433\) −0.677760 0.677760i −0.677760 0.677760i 0.281733 0.959493i \(-0.409091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.592735 + 0.791802i −0.592735 + 0.791802i
\(439\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(440\) 0 0
\(441\) −0.864596 + 1.89320i −0.864596 + 1.89320i
\(442\) 0 0
\(443\) −1.53046 + 0.983568i −1.53046 + 0.983568i −0.540641 + 0.841254i \(0.681818\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.755750 + 1.65486i −0.755750 + 1.65486i 1.00000i \(0.5\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(450\) 2.06010 0.296197i 2.06010 0.296197i
\(451\) 0.595106 + 2.73566i 0.595106 + 2.73566i
\(452\) 0.418852 0.559521i 0.418852 0.559521i
\(453\) 0 0
\(454\) 0.425839 + 0.368991i 0.425839 + 0.368991i
\(455\) 0 0
\(456\) −0.299415 + 2.08248i −0.299415 + 2.08248i
\(457\) 0.100889 + 0.100889i 0.100889 + 0.100889i 0.755750 0.654861i \(-0.227273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(458\) 0 0
\(459\) 0.227819 3.18532i 0.227819 3.18532i
\(460\) 0 0
\(461\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(462\) 0 0
\(463\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.449181 0.698939i −0.449181 0.698939i
\(467\) −0.698939 1.53046i −0.698939 1.53046i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.373128 0.203743i 0.373128 0.203743i
\(473\) −1.85412 3.39557i −1.85412 3.39557i
\(474\) 0 0
\(475\) 0.418852 + 1.12299i 0.418852 + 1.12299i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.32505 1.32505i 1.32505 1.32505i
\(483\) 0 0
\(484\) −1.91153 + 2.20602i −1.91153 + 2.20602i
\(485\) 0 0
\(486\) −0.278231 + 0.103775i −0.278231 + 0.103775i
\(487\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(488\) 0 0
\(489\) −1.41542 0.909632i −1.41542 0.909632i
\(490\) 0 0
\(491\) 1.28173 0.959493i 1.28173 0.959493i 0.281733 0.959493i \(-0.409091\pi\)
1.00000 \(0\)
\(492\) 2.25812 + 1.03125i 2.25812 + 1.03125i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.11600 + 0.509660i −1.11600 + 0.509660i
\(499\) −0.898064 + 1.64468i −0.898064 + 1.64468i −0.142315 + 0.989821i \(0.545455\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(503\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.54064 0.841254i 1.54064 0.841254i
\(508\) 0 0
\(509\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.415415 0.909632i −0.415415 0.909632i
\(513\) −1.22990 1.91377i −1.22990 1.91377i
\(514\) 0.0801894 0.273100i 0.0801894 0.273100i
\(515\) 0 0
\(516\) −3.39557 0.488209i −3.39557 0.488209i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.83107 0.682956i −1.83107 0.682956i −0.989821 0.142315i \(-0.954545\pi\)
−0.841254 0.540641i \(-0.818182\pi\)
\(522\) 0 0
\(523\) 0.0801894 0.557730i 0.0801894 0.557730i −0.909632 0.415415i \(-0.863636\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(524\) 1.45027 1.25667i 1.45027 1.25667i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.738661 + 3.39557i 0.738661 + 3.39557i
\(529\) 0.989821 0.142315i 0.989821 0.142315i
\(530\) 0 0
\(531\) −0.309212 + 0.829029i −0.309212 + 0.829029i
\(532\) 0 0
\(533\) 0 0
\(534\) −0.125226 + 1.75089i −0.125226 + 1.75089i
\(535\) 0 0
\(536\) −1.27155 + 0.817178i −1.27155 + 0.817178i
\(537\) −0.803429 + 2.15408i −0.803429 + 2.15408i
\(538\) 0 0
\(539\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(540\) 0 0
\(541\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.27155 + 1.10181i −1.27155 + 1.10181i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.50013 0.559521i −1.50013 0.559521i −0.540641 0.841254i \(-0.681818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(548\) 0.0303285 0.424047i 0.0303285 0.424047i
\(549\) 0 0
\(550\) 1.29639 + 1.49611i 1.29639 + 1.49611i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(557\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 5.13151 2.80202i 5.13151 2.80202i
\(562\) 0.767317 + 1.40524i 0.767317 + 1.40524i
\(563\) 1.28173 + 0.959493i 1.28173 + 0.959493i 1.00000 \(0\)
0.281733 + 0.959493i \(0.409091\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.74557 + 0.512546i 1.74557 + 0.512546i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.0683785 + 0.125226i −0.0683785 + 0.125226i −0.909632 0.415415i \(-0.863636\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(570\) 0 0
\(571\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.89320 + 0.864596i 1.89320 + 0.864596i
\(577\) 0.959493 0.718267i 0.959493 0.718267i 1.00000i \(-0.5\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(578\) 1.54019 + 0.989821i 1.54019 + 0.989821i
\(579\) 2.94588 + 1.89320i 2.94588 + 1.89320i
\(580\) 0 0
\(581\) 0 0
\(582\) −2.15408 + 0.803429i −2.15408 + 0.803429i
\(583\) 0 0
\(584\) −0.368991 + 0.425839i −0.368991 + 0.425839i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.258908 + 0.118239i −0.258908 + 0.118239i −0.540641 0.841254i \(-0.681818\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(588\) −0.841254 + 1.54064i −0.841254 + 1.54064i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.0498610 0.133682i −0.0498610 0.133682i 0.909632 0.415415i \(-0.136364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(594\) −3.00798 2.25175i −3.00798 2.25175i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(600\) 1.75089 0.125226i 1.75089 0.125226i
\(601\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(602\) 0 0
\(603\) 0.886290 3.01843i 0.886290 3.01843i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(608\) −0.254771 + 1.17116i −0.254771 + 1.17116i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.498354 3.46613i 0.498354 3.46613i
\(613\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(614\) 0.627899 + 0.544078i 0.627899 + 0.544078i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.203743 0.936593i −0.203743 0.936593i −0.959493 0.281733i \(-0.909091\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(618\) 0 0
\(619\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.841254 0.540641i 0.841254 0.540641i
\(626\) 0.697148 1.86912i 0.697148 1.86912i
\(627\) 1.73019 3.78858i 1.73019 3.78858i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(632\) 0 0
\(633\) −2.59259 + 2.24649i −2.59259 + 2.24649i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.89945 + 0.273100i 1.89945 + 0.273100i 0.989821 0.142315i \(-0.0454545\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(642\) 0 0
\(643\) −0.368991 + 1.25667i −0.368991 + 1.25667i 0.540641 + 0.841254i \(0.318182\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.01144 0.143861i 2.01144 0.143861i
\(647\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(648\) −1.19980 + 0.352293i −1.19980 + 0.352293i
\(649\) −0.822373 + 0.178896i −0.822373 + 0.178896i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.767317 0.574406i −0.767317 0.574406i
\(653\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.24123 + 0.677760i 1.24123 + 0.677760i
\(657\) 1.17273i 1.17273i
\(658\) 0 0
\(659\) 1.74557 0.797176i 1.74557 0.797176i 0.755750 0.654861i \(-0.227273\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(660\) 0 0
\(661\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(662\) 0.186393 0.215109i 0.186393 0.215109i
\(663\) 0 0
\(664\) −0.654861 + 0.244250i −0.654861 + 0.244250i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(674\) −0.959493 1.28173i −0.959493 1.28173i
\(675\) −1.34211 + 1.34211i −1.34211 + 1.34211i
\(676\) 0.909632 0.415415i 0.909632 0.415415i
\(677\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(678\) 1.22687i 1.22687i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.986563 0.0705604i −0.986563 0.0705604i
\(682\) 0 0
\(683\) 0.767317 + 0.574406i 0.767317 + 0.574406i 0.909632 0.415415i \(-0.136364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(684\) −1.19550 2.18940i −1.19550 2.18940i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.90963 0.415415i −1.90963 0.415415i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.449181 0.698939i −0.449181 0.698939i 0.540641 0.841254i \(-0.318182\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.505783 2.32505i 0.505783 2.32505i
\(698\) 0 0
\(699\) 1.36645 + 0.509660i 1.36645 + 0.509660i
\(700\) 0 0
\(701\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.281733 + 1.95949i 0.281733 + 1.95949i
\(705\) 0 0
\(706\) −0.424047 1.94931i −0.424047 1.94931i
\(707\) 0 0
\(708\) −0.310006 + 0.678819i −0.310006 + 0.678819i
\(709\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.329911 0.285870i 0.329911 0.285870i
\(723\) −0.468125 + 3.25588i −0.468125 + 3.25588i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.365532 5.11081i 0.365532 5.11081i
\(727\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(728\) 0 0
\(729\) −0.394231 + 0.613435i −0.394231 + 0.613435i
\(730\) 0 0
\(731\) 0.234571 + 3.27974i 0.234571 + 3.27974i
\(732\) 0 0
\(733\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.87102 0.843008i 2.87102 0.843008i
\(738\) −2.87611 + 0.625660i −2.87611 + 0.625660i
\(739\) −1.75089 + 0.956056i −1.75089 + 0.956056i −0.841254 + 0.540641i \(0.818182\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.697148 1.27673i 0.697148 1.27673i
\(748\) 3.02977 1.38365i 3.02977 1.38365i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(752\) 0 0
\(753\) −1.36645 + 0.509660i −1.36645 + 0.509660i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(758\) 0.114220 0.0855040i 0.114220 0.0855040i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.557730 + 1.89945i 0.557730 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.54064 + 0.841254i 1.54064 + 0.841254i
\(769\) −1.74557 0.512546i −1.74557 0.512546i −0.755750 0.654861i \(-0.772727\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(770\) 0 0
\(771\) 0.174602 + 0.468125i 0.174602 + 0.468125i
\(772\) 1.59700 + 1.19550i 1.59700 + 1.19550i
\(773\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(774\) 3.56990 1.94931i 3.56990 1.94931i
\(775\) 0 0
\(776\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.704134 1.54184i −0.704134 1.54184i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(785\) 0 0
\(786\) −0.716028 + 3.29153i −0.716028 + 3.29153i
\(787\) −0.133682 + 1.86912i −0.133682 + 1.86912i 0.281733 + 0.959493i \(0.409091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −3.11384 2.69815i −3.11384 2.69815i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0