Properties

Label 712.1.y.a.587.1
Level $712$
Weight $1$
Character 712.587
Analytic conductor $0.355$
Analytic rank $0$
Dimension $20$
Projective image $D_{44}$
CM discriminant -8
Inner twists $4$

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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 587.1
Root \(-0.281733 - 0.959493i\) of defining polynomial
Character \(\chi\) \(=\) 712.587
Dual form 712.1.y.a.131.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{2} +(-0.898064 + 0.334961i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.936593 + 0.203743i) q^{6} +(0.142315 - 0.989821i) q^{8} +(-0.0614286 + 0.0532282i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{2} +(-0.898064 + 0.334961i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.936593 + 0.203743i) q^{6} +(0.142315 - 0.989821i) q^{8} +(-0.0614286 + 0.0532282i) q^{9} +(-0.281733 - 1.95949i) q^{11} +(-0.677760 - 0.677760i) q^{12} +(-0.654861 + 0.755750i) q^{16} +(0.909632 + 1.41542i) q^{17} +(0.0804543 - 0.0115676i) q^{18} +(1.59700 + 0.114220i) q^{19} +(-0.822373 + 1.80075i) q^{22} +(0.203743 + 0.936593i) q^{24} +(0.959493 + 0.281733i) q^{25} +(0.496697 - 0.909632i) q^{27} +(0.959493 - 0.281733i) q^{32} +(0.909367 + 1.66538i) q^{33} -1.68251i q^{34} +(-0.0739364 - 0.0337656i) q^{36} +(-1.28173 - 0.959493i) q^{38} +(0.494217 - 1.32505i) q^{41} +(-0.254771 + 0.340335i) q^{43} +(1.66538 - 1.07028i) q^{44} +(0.334961 - 0.898064i) q^{48} +(0.281733 - 0.959493i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(-1.29102 - 0.966443i) q^{51} +(-0.909632 + 0.496697i) q^{54} +(-1.47247 + 0.432356i) q^{57} +(1.83107 + 0.682956i) q^{59} +(-0.959493 - 0.281733i) q^{64} +(0.135365 - 1.89265i) q^{66} +(-0.627899 + 1.37491i) q^{67} +(-0.909632 + 1.41542i) q^{68} +(0.0439442 + 0.0683785i) q^{72} +(-0.368991 + 0.425839i) q^{73} +(-0.956056 + 0.0683785i) q^{75} +(0.559521 + 1.50013i) q^{76} +(-0.129807 + 0.902828i) q^{81} +(-1.13214 + 0.847507i) q^{82} +(-1.83107 - 0.398326i) q^{83} +(0.398326 - 0.148568i) q^{86} -1.97964 q^{88} +(0.959493 - 0.281733i) q^{89} +(-0.767317 + 0.574406i) q^{96} +(0.186393 - 1.29639i) q^{97} +(-0.755750 + 0.654861i) q^{98} +(0.121607 + 0.105373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10}) \) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{39}{44}\right)\)

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
\(3\) −0.898064 + 0.334961i −0.898064 + 0.334961i −0.755750 0.654861i \(-0.772727\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(4\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(5\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(6\) 0.936593 + 0.203743i 0.936593 + 0.203743i
\(7\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(8\) 0.142315 0.989821i 0.142315 0.989821i
\(9\) −0.0614286 + 0.0532282i −0.0614286 + 0.0532282i
\(10\) 0 0
\(11\) −0.281733 1.95949i −0.281733 1.95949i −0.281733 0.959493i \(-0.590909\pi\)
1.00000i \(-0.5\pi\)
\(12\) −0.677760 0.677760i −0.677760 0.677760i
\(13\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(17\) 0.909632 + 1.41542i 0.909632 + 1.41542i 0.909632 + 0.415415i \(0.136364\pi\)
1.00000i \(0.5\pi\)
\(18\) 0.0804543 0.0115676i 0.0804543 0.0115676i
\(19\) 1.59700 + 0.114220i 1.59700 + 0.114220i 0.841254 0.540641i \(-0.181818\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.822373 + 1.80075i −0.822373 + 1.80075i
\(23\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(24\) 0.203743 + 0.936593i 0.203743 + 0.936593i
\(25\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(26\) 0 0
\(27\) 0.496697 0.909632i 0.496697 0.909632i
\(28\) 0 0
\(29\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(30\) 0 0
\(31\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(32\) 0.959493 0.281733i 0.959493 0.281733i
\(33\) 0.909367 + 1.66538i 0.909367 + 1.66538i
\(34\) 1.68251i 1.68251i
\(35\) 0 0
\(36\) −0.0739364 0.0337656i −0.0739364 0.0337656i
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) −1.28173 0.959493i −1.28173 0.959493i
\(39\) 0 0
\(40\) 0 0
\(41\) 0.494217 1.32505i 0.494217 1.32505i −0.415415 0.909632i \(-0.636364\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(42\) 0 0
\(43\) −0.254771 + 0.340335i −0.254771 + 0.340335i −0.909632 0.415415i \(-0.863636\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(44\) 1.66538 1.07028i 1.66538 1.07028i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(48\) 0.334961 0.898064i 0.334961 0.898064i
\(49\) 0.281733 0.959493i 0.281733 0.959493i
\(50\) −0.654861 0.755750i −0.654861 0.755750i
\(51\) −1.29102 0.966443i −1.29102 0.966443i
\(52\) 0 0
\(53\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(54\) −0.909632 + 0.496697i −0.909632 + 0.496697i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.47247 + 0.432356i −1.47247 + 0.432356i
\(58\) 0 0
\(59\) 1.83107 + 0.682956i 1.83107 + 0.682956i 0.989821 + 0.142315i \(0.0454545\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(60\) 0 0
\(61\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.959493 0.281733i −0.959493 0.281733i
\(65\) 0 0
\(66\) 0.135365 1.89265i 0.135365 1.89265i
\(67\) −0.627899 + 1.37491i −0.627899 + 1.37491i 0.281733 + 0.959493i \(0.409091\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(68\) −0.909632 + 1.41542i −0.909632 + 1.41542i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(72\) 0.0439442 + 0.0683785i 0.0439442 + 0.0683785i
\(73\) −0.368991 + 0.425839i −0.368991 + 0.425839i −0.909632 0.415415i \(-0.863636\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(74\) 0 0
\(75\) −0.956056 + 0.0683785i −0.956056 + 0.0683785i
\(76\) 0.559521 + 1.50013i 0.559521 + 1.50013i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(80\) 0 0
\(81\) −0.129807 + 0.902828i −0.129807 + 0.902828i
\(82\) −1.13214 + 0.847507i −1.13214 + 0.847507i
\(83\) −1.83107 0.398326i −1.83107 0.398326i −0.841254 0.540641i \(-0.818182\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.398326 0.148568i 0.398326 0.148568i
\(87\) 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
\(96\) −0.767317 + 0.574406i −0.767317 + 0.574406i
\(97\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(98\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(99\) 0.121607 + 0.105373i 0.121607 + 0.105373i
\(100\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(101\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(102\) 0.563574 + 1.51100i 0.563574 + 1.51100i
\(103\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(108\) 1.03377 + 0.0739364i 1.03377 + 0.0739364i
\(109\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.398326 1.83107i −0.398326 1.83107i −0.540641 0.841254i \(-0.681818\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(114\) 1.47247 + 0.432356i 1.47247 + 0.432356i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.17116 1.56449i −1.17116 1.56449i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.80075 + 0.822373i −2.80075 + 0.822373i
\(122\) 0 0
\(123\) 1.35552i 1.35552i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(128\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(129\) 0.114802 0.390981i 0.114802 0.390981i
\(130\) 0 0
\(131\) −1.74557 + 0.797176i −1.74557 + 0.797176i −0.755750 + 0.654861i \(0.772727\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(132\) −1.13712 + 1.51901i −1.13712 + 1.51901i
\(133\) 0 0
\(134\) 1.27155 0.817178i 1.27155 0.817178i
\(135\) 0 0
\(136\) 1.53046 0.698939i 1.53046 0.698939i
\(137\) −0.682956 + 1.83107i −0.682956 + 1.83107i −0.142315 + 0.989821i \(0.545455\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(138\) 0 0
\(139\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.0812816i 0.0812816i
\(145\) 0 0
\(146\) 0.540641 0.158746i 0.540641 0.158746i
\(147\) 0.0683785 + 0.956056i 0.0683785 + 0.956056i
\(148\) 0 0
\(149\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(150\) 0.841254 + 0.459359i 0.841254 + 0.459359i
\(151\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(152\) 0.340335 1.56449i 0.340335 1.56449i
\(153\) −0.131217 0.0385289i −0.131217 0.0385289i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.597306 0.689328i 0.597306 0.689328i
\(163\) 1.71524 0.373128i 1.71524 0.373128i 0.755750 0.654861i \(-0.227273\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(164\) 1.41061 0.100889i 1.41061 0.100889i
\(165\) 0 0
\(166\) 1.32505 + 1.32505i 1.32505 + 1.32505i
\(167\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(168\) 0 0
\(169\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(170\) 0 0
\(171\) −0.104181 + 0.0779892i −0.104181 + 0.0779892i
\(172\) −0.415415 0.0903680i −0.415415 0.0903680i
\(173\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.66538 + 1.07028i 1.66538 + 1.07028i
\(177\) −1.87319 −1.87319
\(178\) −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 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(182\) 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 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(192\) 0.956056 0.0683785i 0.956056 0.0683785i
\(193\) 0.139418 0.0303285i 0.139418 0.0303285i −0.142315 0.989821i \(-0.545455\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(194\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(195\) 0 0
\(196\) 0.989821 0.142315i 0.989821 0.142315i
\(197\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(198\) −0.0453332 0.154391i −0.0453332 0.154391i
\(199\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(200\) 0.415415 0.909632i 0.415415 0.909632i
\(201\) 0.103354 1.44508i 0.103354 1.44508i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.342800 1.57582i 0.342800 1.57582i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.226115 3.16150i −0.226115 3.16150i
\(210\) 0 0
\(211\) −0.203743 0.373128i −0.203743 0.373128i 0.755750 0.654861i \(-0.227273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) −0.829686 0.621095i −0.829686 0.621095i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.188739 0.506028i 0.188739 0.506028i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(224\) 0 0
\(225\) −0.0739364 + 0.0337656i −0.0739364 + 0.0337656i
\(226\) −0.654861 + 1.75575i −0.654861 + 1.75575i
\(227\) −0.158746 + 0.540641i −0.158746 + 0.540641i 0.841254 + 0.540641i \(0.181818\pi\)
−1.00000 \(\pi\)
\(228\) −1.00497 1.15980i −1.00497 1.15980i
\(229\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(230\) 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
\(236\) 0.139418 + 1.94931i 0.139418 + 1.94931i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(240\) 0 0
\(241\) 0.148568 0.682956i 0.148568 0.682956i −0.841254 0.540641i \(-0.818182\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(242\) 2.80075 + 0.822373i 2.80075 + 0.822373i
\(243\) 0.0344673 + 0.158443i 0.0344673 + 0.158443i
\(244\) 0 0
\(245\) 0 0
\(246\) 0.732850 1.14034i 0.732850 1.14034i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.77785 0.255616i 1.77785 0.255616i
\(250\) 0 0
\(251\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(252\) 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 \(-0.227273\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(258\) −0.307958 + 0.266847i −0.307958 + 0.266847i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.89945 + 0.273100i 1.89945 + 0.273100i
\(263\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(264\) 1.77785 0.663103i 1.77785 0.663103i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.767317 + 0.574406i −0.767317 + 0.574406i
\(268\) −1.51150 −1.51150
\(269\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(270\) 0 0
\(271\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(272\) −1.66538 0.239446i −1.66538 0.239446i
\(273\) 0 0
\(274\) 1.56449 1.17116i 1.56449 1.17116i
\(275\) 0.281733 1.95949i 0.281733 1.95949i
\(276\) 0 0
\(277\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(278\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.19550 0.0855040i 1.19550 0.0855040i 0.540641 0.841254i \(-0.318182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(282\) 0 0
\(283\) 1.19136 1.37491i 1.19136 1.37491i 0.281733 0.959493i \(-0.409091\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.0439442 + 0.0683785i −0.0439442 + 0.0683785i
\(289\) −0.760554 + 1.66538i −0.760554 + 1.66538i
\(290\) 0 0
\(291\) 0.266847 + 1.22668i 0.266847 + 1.22668i
\(292\) −0.540641 0.158746i −0.540641 0.158746i
\(293\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(294\) 0.459359 0.841254i 0.459359 0.841254i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.92235 0.717001i −1.92235 0.717001i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.459359 0.841254i −0.459359 0.841254i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.13214 + 1.13214i −1.13214 + 1.13214i
\(305\) 0 0
\(306\) 0.0895567 + 0.103354i 0.0895567 + 0.103354i
\(307\) 0.234072 0.797176i 0.234072 0.797176i −0.755750 0.654861i \(-0.772727\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(312\) 0 0
\(313\) −0.0855040 + 0.114220i −0.0855040 + 0.114220i −0.841254 0.540641i \(-0.818182\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.29102 + 2.36432i 1.29102 + 2.36432i
\(324\) −0.875165 + 0.256972i −0.875165 + 0.256972i
\(325\) 0 0
\(326\) −1.64468 0.613435i −1.64468 0.613435i
\(327\) 0 0
\(328\) −1.24123 0.677760i −1.24123 0.677760i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(332\) −0.398326 1.83107i −0.398326 1.83107i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.19550 + 0.0855040i 1.19550 + 0.0855040i 0.654861 0.755750i \(-0.272727\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(338\) 0.989821 0.142315i 0.989821 0.142315i
\(339\) 0.971061 + 1.51100i 0.971061 + 1.51100i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.129807 0.00928398i 0.129807 0.00928398i
\(343\) 0 0
\(344\) 0.300613 + 0.300613i 0.300613 + 0.300613i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.37491 + 1.19136i −1.37491 + 1.19136i −0.415415 + 0.909632i \(0.636364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(348\) 0 0
\(349\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.822373 1.80075i −0.822373 1.80075i
\(353\) −0.133682 + 0.0498610i −0.133682 + 0.0498610i −0.415415 0.909632i \(-0.636364\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(354\) 1.57582 + 1.01272i 1.57582 + 1.01272i
\(355\) 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 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(360\) 0 0
\(361\) 1.54755 + 0.222504i 1.54755 + 0.222504i
\(362\) 0 0
\(363\) 2.23979 1.67668i 2.23979 1.67668i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(368\) 0 0
\(369\) 0.0401708 + 0.107702i 0.0401708 + 0.107702i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(374\) −3.29686 + 0.474017i −3.29686 + 0.474017i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.142315 + 1.98982i −0.142315 + 1.98982i 1.00000i \(0.5\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(384\) −0.841254 0.459359i −0.841254 0.459359i
\(385\) 0 0
\(386\) −0.133682 0.0498610i −0.133682 0.0498610i
\(387\) −0.00246515 0.0344673i −0.00246515 0.0344673i
\(388\) 1.25667 0.368991i 1.25667 0.368991i
\(389\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.909632 0.415415i −0.909632 0.415415i
\(393\) 1.30061 1.30061i 1.30061 1.30061i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.0453332 + 0.154391i −0.0453332 + 0.154391i
\(397\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(398\) 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 \(-0.954545\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(402\) −0.868215 + 1.15980i −0.868215 + 1.15980i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −1.14034 + 1.14034i −1.14034 + 1.14034i
\(409\) −1.19136 0.544078i −1.19136 0.544078i −0.281733 0.959493i \(-0.590909\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(410\) 0 0
\(411\) 1.87319i 1.87319i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.239446 + 0.130747i 0.239446 + 0.130747i
\(418\) −1.51901 + 2.78187i −1.51901 + 2.78187i
\(419\) −0.0303285 + 0.139418i −0.0303285 + 0.139418i −0.989821 0.142315i \(-0.954545\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(420\) 0 0
\(421\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(422\) −0.0303285 + 0.424047i −0.0303285 + 0.424047i
\(423\) 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 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(432\) 0.362187 + 0.971061i 0.362187 + 0.971061i
\(433\) −1.24123 1.24123i −1.24123 1.24123i −0.959493 0.281733i \(-0.909091\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.432356 + 0.323658i −0.432356 + 0.323658i
\(439\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(440\) 0 0
\(441\) 0.0337656 + 0.0739364i 0.0337656 + 0.0739364i
\(442\) 0 0
\(443\) 1.53046 + 0.983568i 1.53046 + 0.983568i 0.989821 + 0.142315i \(0.0454545\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.755750 + 1.65486i 0.755750 + 1.65486i 0.755750 + 0.654861i \(0.227273\pi\)
1.00000i \(0.5\pi\)
\(450\) 0.0804543 + 0.0115676i 0.0804543 + 0.0115676i
\(451\) −2.73566 0.595106i −2.73566 0.595106i
\(452\) 1.50013 1.12299i 1.50013 1.12299i
\(453\) 0 0
\(454\) 0.425839 0.368991i 0.425839 0.368991i
\(455\) 0 0
\(456\) 0.218401 + 1.51901i 0.218401 + 1.51901i
\(457\) −1.41061 1.41061i −1.41061 1.41061i −0.755750 0.654861i \(-0.772727\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(458\) 0 0
\(459\) 1.73932 0.124398i 1.73932 0.124398i
\(460\) 0 0
\(461\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(462\) 0 0
\(463\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.449181 0.698939i 0.449181 0.698939i
\(467\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.936593 1.71524i 0.936593 1.71524i
\(473\) 0.738661 + 0.403339i 0.738661 + 0.403339i
\(474\) 0 0
\(475\) 1.50013 + 0.559521i 1.50013 + 0.559521i
\(476\) 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
\(482\) −0.494217 + 0.494217i −0.494217 + 0.494217i
\(483\) 0 0
\(484\) −1.91153 2.20602i −1.91153 2.20602i
\(485\) 0 0
\(486\) 0.0566653 0.151926i 0.0566653 0.151926i
\(487\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(488\) 0 0
\(489\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(490\) 0 0
\(491\) 0.718267 0.959493i 0.718267 0.959493i −0.281733 0.959493i \(-0.590909\pi\)
1.00000 \(0\)
\(492\) −1.23303 + 0.563104i −1.23303 + 0.563104i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.63382 0.746139i −1.63382 0.746139i
\(499\) 0.613435 0.334961i 0.613435 0.334961i −0.142315 0.989821i \(-0.545455\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.797176 0.234072i 0.797176 0.234072i
\(503\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.459359 0.841254i 0.459359 0.841254i
\(508\) 0 0
\(509\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(513\) 0.897124 1.39595i 0.897124 1.39595i
\(514\) −0.0801894 0.273100i −0.0801894 0.273100i
\(515\) 0 0
\(516\) 0.403339 0.0579914i 0.403339 0.0579914i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.148568 + 0.398326i 0.148568 + 0.398326i 0.989821 0.142315i \(-0.0454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(522\) 0 0
\(523\) −0.0801894 0.557730i −0.0801894 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(524\) −1.45027 1.25667i −1.45027 1.25667i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.85412 0.403339i −1.85412 0.403339i
\(529\) −0.989821 0.142315i −0.989821 0.142315i
\(530\) 0 0
\(531\) −0.148833 + 0.0555118i −0.148833 + 0.0555118i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.956056 0.0683785i 0.956056 0.0683785i
\(535\) 0 0
\(536\) 1.27155 + 0.817178i 1.27155 + 0.817178i
\(537\) 1.17621 0.438705i 1.17621 0.438705i
\(538\) 0 0
\(539\) −1.95949 0.281733i −1.95949 0.281733i
\(540\) 0 0
\(541\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.27155 + 1.10181i 1.27155 + 1.10181i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.418852 1.12299i −0.418852 1.12299i −0.959493 0.281733i \(-0.909091\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(548\) −1.94931 + 0.139418i −1.94931 + 0.139418i
\(549\) 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 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −1.53002 + 2.80202i −1.53002 + 2.80202i
\(562\) −1.05195 0.574406i −1.05195 0.574406i
\(563\) 0.718267 + 0.959493i 0.718267 + 0.959493i 1.00000 \(0\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.74557 + 0.512546i −1.74557 + 0.512546i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.75089 0.956056i 1.75089 0.956056i 0.841254 0.540641i \(-0.181818\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(570\) 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
\(576\) 0.0739364 0.0337656i 0.0739364 0.0337656i
\(577\) 0.959493 1.28173i 0.959493 1.28173i 1.00000i \(-0.5\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(578\) 1.54019 0.989821i 1.54019 0.989821i
\(579\) −0.115047 + 0.0739364i −0.115047 + 0.0739364i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.438705 1.17621i 0.438705 1.17621i
\(583\) 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 \(-0.318182\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(588\) −0.841254 + 0.459359i −0.841254 + 0.459359i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.86912 0.697148i −1.86912 0.697148i −0.959493 0.281733i \(-0.909091\pi\)
−0.909632 0.415415i \(-0.863636\pi\)
\(594\) 1.22955 + 1.64248i 1.22955 + 1.64248i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(600\) −0.0683785 + 0.956056i −0.0683785 + 0.956056i
\(601\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(602\) 0 0
\(603\) −0.0346129 0.117881i −0.0346129 0.117881i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(608\) 1.56449 0.340335i 1.56449 0.340335i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.0194625 0.135365i −0.0194625 0.135365i
\(613\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(614\) −0.627899 + 0.544078i −0.627899 + 0.544078i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.71524 0.373128i −1.71524 0.373128i −0.755750 0.654861i \(-0.772727\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(618\) 0 0
\(619\) 0.797176 + 1.74557i 0.797176 + 1.74557i 0.654861 + 0.755750i \(0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(626\) 0.133682 0.0498610i 0.133682 0.0498610i
\(627\) 1.26204 + 2.76349i 1.26204 + 2.76349i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(632\) 0 0
\(633\) 0.307958 + 0.266847i 0.307958 + 0.266847i
\(634\) 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 \(-0.954545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(642\) 0 0
\(643\) 0.368991 + 1.25667i 0.368991 + 1.25667i 0.909632 + 0.415415i \(0.136364\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.192176 2.68697i 0.192176 2.68697i
\(647\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(648\) 0.875165 + 0.256972i 0.875165 + 0.256972i
\(649\) 0.822373 3.78039i 0.822373 3.78039i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.05195 + 1.40524i 1.05195 + 1.40524i
\(653\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.677760 + 1.24123i 0.677760 + 1.24123i
\(657\) 0.0457994i 0.0457994i
\(658\) 0 0
\(659\) −1.74557 0.797176i −1.74557 0.797176i −0.989821 0.142315i \(-0.954545\pi\)
−0.755750 0.654861i \(-0.772727\pi\)
\(660\) 0 0
\(661\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(662\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(663\) 0 0
\(664\) −0.654861 + 1.75575i −0.654861 + 1.75575i
\(665\) 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 \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(674\) −0.959493 0.718267i −0.959493 0.718267i
\(675\) 0.732850 0.732850i 0.732850 0.732850i
\(676\) −0.909632 0.415415i −0.909632 0.415415i
\(677\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(678\) 1.79613i 1.79613i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.0385289 0.538704i −0.0385289 0.538704i
\(682\) 0 0
\(683\) −1.05195 1.40524i −1.05195 1.40524i −0.909632 0.415415i \(-0.863636\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(684\) −0.114220 0.0623688i −0.114220 0.0623688i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.0903680 0.415415i −0.0903680 0.415415i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.449181 0.698939i 0.449181 0.698939i −0.540641 0.841254i \(-0.681818\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.80075 0.258908i 1.80075 0.258908i
\(695\) 0 0
\(696\) 0 0
\(697\) 2.32505 0.505783i 2.32505 0.505783i
\(698\) 0 0
\(699\) −0.278295 0.746139i −0.278295 0.746139i
\(700\) 0 0
\(701\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.281733 + 1.95949i −0.281733 + 1.95949i
\(705\) 0 0
\(706\) 0.139418 + 0.0303285i 0.139418 + 0.0303285i
\(707\) 0 0
\(708\) −0.778150 1.70391i −0.778150 1.70391i
\(709\) 0 0 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(710\) 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 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.18159 1.02385i −1.18159 1.02385i
\(723\) 0.0953398 + 0.663103i 0.0953398 + 0.663103i
\(724\) 0 0
\(725\) 0 0
\(726\) −2.79071 + 0.199596i −2.79071 + 0.199596i
\(727\) 0 0 0.977147 0.212565i \(-0.0681818\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(728\) 0 0
\(729\) −0.577151 0.898064i −0.577151 0.898064i
\(730\) 0 0
\(731\) −0.713463 0.0510279i −0.713463 0.0510279i
\(732\) 0 0
\(733\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.87102 + 0.843008i 2.87102 + 0.843008i
\(738\) 0.0244343 0.112323i 0.0244343 0.112323i
\(739\) 0.0683785 0.125226i 0.0683785 0.125226i −0.841254 0.540641i \(-0.818182\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.133682 0.0729961i 0.133682 0.0729961i
\(748\) 3.02977 + 1.38365i 3.02977 + 1.38365i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(752\) 0 0
\(753\) 0.278295 0.746139i 0.278295 0.746139i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(758\) 1.19550 1.59700i 1.19550 1.59700i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.557730 1.89945i 0.557730 1.89945i 0.142315 0.989821i \(-0.454545\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.459359 + 0.841254i 0.459359 + 0.841254i
\(769\) 1.74557 0.512546i 1.74557 0.512546i 0.755750 0.654861i \(-0.227273\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(770\) 0 0
\(771\) −0.255616 0.0953398i −0.255616 0.0953398i
\(772\) 0.0855040 + 0.114220i 0.0855040 + 0.114220i
\(773\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(774\) −0.0165606 + 0.0303285i −0.0165606 + 0.0303285i
\(775\) 0 0
\(776\) −1.25667 0.368991i −1.25667 0.368991i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.940613 2.05965i 0.940613 2.05965i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(785\) 0 0
\(786\) −1.79731 + 0.390981i −1.79731 + 0.390981i
\(787\) −0.697148 + 0.0498610i −0.697148 + 0.0498610i −0.415415 0.909632i \(-0.636364\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.121607 0.105373i 0.121607 0.105373i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0