Properties

Label 712.1.y.a.347.1
Level $712$
Weight $1$
Character 712.347
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 347.1
Root \(0.540641 + 0.841254i\) of defining polynomial
Character \(\chi\) \(=\) 712.347
Dual form 712.1.y.a.435.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 - 0.909632i) q^{2} +(0.0303285 - 0.424047i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.398326 + 0.148568i) q^{6} +(0.959493 + 0.281733i) q^{8} +(0.810925 + 0.116593i) q^{9} +O(q^{10})\) \(q+(-0.415415 - 0.909632i) q^{2} +(0.0303285 - 0.424047i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.398326 + 0.148568i) q^{6} +(0.959493 + 0.281733i) q^{8} +(0.810925 + 0.116593i) q^{9} +(0.540641 - 0.158746i) q^{11} +(0.300613 + 0.300613i) q^{12} +(-0.142315 - 0.989821i) q^{16} +(0.755750 + 0.345139i) q^{17} +(-0.230813 - 0.786078i) q^{18} +(-0.574406 - 0.767317i) q^{19} +(-0.368991 - 0.425839i) q^{22} +(0.148568 - 0.398326i) q^{24} +(-0.841254 - 0.540641i) q^{25} +(0.164403 - 0.755750i) q^{27} +(-0.841254 + 0.540641i) q^{32} +(-0.0509192 - 0.234072i) q^{33} -0.830830i q^{34} +(-0.619158 + 0.536504i) q^{36} +(-0.459359 + 0.841254i) q^{38} +(1.41061 - 0.100889i) q^{41} +(-0.613435 - 0.334961i) q^{43} +(-0.234072 + 0.512546i) q^{44} +(-0.424047 + 0.0303285i) q^{48} +(-0.540641 + 0.841254i) q^{49} +(-0.142315 + 0.989821i) q^{50} +(0.169276 - 0.310006i) q^{51} +(-0.755750 + 0.164403i) q^{54} +(-0.342800 + 0.220304i) q^{57} +(0.133682 + 1.86912i) q^{59} +(0.841254 + 0.540641i) q^{64} +(-0.191767 + 0.143555i) q^{66} +(-1.29639 - 1.49611i) q^{67} +(-0.755750 + 0.345139i) q^{68} +(0.745229 + 0.340335i) q^{72} +(0.153882 + 1.07028i) q^{73} +(-0.254771 + 0.340335i) q^{75} +(0.956056 + 0.0683785i) q^{76} +(0.470591 + 0.138178i) q^{81} +(-0.677760 - 1.24123i) q^{82} +(-0.133682 + 0.0498610i) q^{83} +(-0.0498610 + 0.697148i) q^{86} +0.563465 q^{88} +(-0.841254 + 0.540641i) q^{89} +(0.203743 + 0.373128i) q^{96} +(0.273100 + 0.0801894i) q^{97} +(0.989821 + 0.142315i) q^{98} +(0.456928 - 0.0656963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10}) \) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{23}{44}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.415415 0.909632i −0.415415 0.909632i
\(3\) 0.0303285 0.424047i 0.0303285 0.424047i −0.959493 0.281733i \(-0.909091\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(4\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(5\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(6\) −0.398326 + 0.148568i −0.398326 + 0.148568i
\(7\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(8\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(9\) 0.810925 + 0.116593i 0.810925 + 0.116593i
\(10\) 0 0
\(11\) 0.540641 0.158746i 0.540641 0.158746i 1.00000i \(-0.5\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(12\) 0.300613 + 0.300613i 0.300613 + 0.300613i
\(13\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.142315 0.989821i −0.142315 0.989821i
\(17\) 0.755750 + 0.345139i 0.755750 + 0.345139i 0.755750 0.654861i \(-0.227273\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.230813 0.786078i −0.230813 0.786078i
\(19\) −0.574406 0.767317i −0.574406 0.767317i 0.415415 0.909632i \(-0.363636\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.368991 0.425839i −0.368991 0.425839i
\(23\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(24\) 0.148568 0.398326i 0.148568 0.398326i
\(25\) −0.841254 0.540641i −0.841254 0.540641i
\(26\) 0 0
\(27\) 0.164403 0.755750i 0.164403 0.755750i
\(28\) 0 0
\(29\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(30\) 0 0
\(31\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(32\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(33\) −0.0509192 0.234072i −0.0509192 0.234072i
\(34\) 0.830830i 0.830830i
\(35\) 0 0
\(36\) −0.619158 + 0.536504i −0.619158 + 0.536504i
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) −0.459359 + 0.841254i −0.459359 + 0.841254i
\(39\) 0 0
\(40\) 0 0
\(41\) 1.41061 0.100889i 1.41061 0.100889i 0.654861 0.755750i \(-0.272727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(42\) 0 0
\(43\) −0.613435 0.334961i −0.613435 0.334961i 0.142315 0.989821i \(-0.454545\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(44\) −0.234072 + 0.512546i −0.234072 + 0.512546i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(48\) −0.424047 + 0.0303285i −0.424047 + 0.0303285i
\(49\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(50\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(51\) 0.169276 0.310006i 0.169276 0.310006i
\(52\) 0 0
\(53\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(54\) −0.755750 + 0.164403i −0.755750 + 0.164403i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.342800 + 0.220304i −0.342800 + 0.220304i
\(58\) 0 0
\(59\) 0.133682 + 1.86912i 0.133682 + 1.86912i 0.415415 + 0.909632i \(0.363636\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(60\) 0 0
\(61\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(65\) 0 0
\(66\) −0.191767 + 0.143555i −0.191767 + 0.143555i
\(67\) −1.29639 1.49611i −1.29639 1.49611i −0.755750 0.654861i \(-0.772727\pi\)
−0.540641 0.841254i \(-0.681818\pi\)
\(68\) −0.755750 + 0.345139i −0.755750 + 0.345139i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(72\) 0.745229 + 0.340335i 0.745229 + 0.340335i
\(73\) 0.153882 + 1.07028i 0.153882 + 1.07028i 0.909632 + 0.415415i \(0.136364\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(74\) 0 0
\(75\) −0.254771 + 0.340335i −0.254771 + 0.340335i
\(76\) 0.956056 + 0.0683785i 0.956056 + 0.0683785i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(80\) 0 0
\(81\) 0.470591 + 0.138178i 0.470591 + 0.138178i
\(82\) −0.677760 1.24123i −0.677760 1.24123i
\(83\) −0.133682 + 0.0498610i −0.133682 + 0.0498610i −0.415415 0.909632i \(-0.636364\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.0498610 + 0.697148i −0.0498610 + 0.697148i
\(87\) 0 0
\(88\) 0.563465 0.563465
\(89\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.203743 + 0.373128i 0.203743 + 0.373128i
\(97\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(98\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(99\) 0.456928 0.0656963i 0.456928 0.0656963i
\(100\) 0.959493 0.281733i 0.959493 0.281733i
\(101\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(102\) −0.352311 0.0251978i −0.352311 0.0251978i
\(103\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(108\) 0.463496 + 0.619158i 0.463496 + 0.619158i
\(109\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.0498610 0.133682i 0.0498610 0.133682i −0.909632 0.415415i \(-0.863636\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(114\) 0.342800 + 0.220304i 0.342800 + 0.220304i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.64468 0.898064i 1.64468 0.898064i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.574161 + 0.368991i −0.574161 + 0.368991i
\(122\) 0 0
\(123\) 0.601225i 0.601225i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(128\) 0.142315 0.989821i 0.142315 0.989821i
\(129\) −0.160644 + 0.249967i −0.160644 + 0.249967i
\(130\) 0 0
\(131\) 1.27155 + 1.10181i 1.27155 + 1.10181i 0.989821 + 0.142315i \(0.0454545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(132\) 0.210245 + 0.114802i 0.210245 + 0.114802i
\(133\) 0 0
\(134\) −0.822373 + 1.80075i −0.822373 + 1.80075i
\(135\) 0 0
\(136\) 0.627899 + 0.544078i 0.627899 + 0.544078i
\(137\) −1.86912 + 0.133682i −1.86912 + 0.133682i −0.959493 0.281733i \(-0.909091\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(138\) 0 0
\(139\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.819264i 0.819264i
\(145\) 0 0
\(146\) 0.909632 0.584585i 0.909632 0.584585i
\(147\) 0.340335 + 0.254771i 0.340335 + 0.254771i
\(148\) 0 0
\(149\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(150\) 0.415415 + 0.0903680i 0.415415 + 0.0903680i
\(151\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(152\) −0.334961 0.898064i −0.334961 0.898064i
\(153\) 0.572615 + 0.367998i 0.572615 + 0.367998i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.0697994 0.485465i −0.0697994 0.485465i
\(163\) −1.83107 0.682956i −1.83107 0.682956i −0.989821 0.142315i \(-0.954545\pi\)
−0.841254 0.540641i \(-0.818182\pi\)
\(164\) −0.847507 + 1.13214i −0.847507 + 1.13214i
\(165\) 0 0
\(166\) 0.100889 + 0.100889i 0.100889 + 0.100889i
\(167\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(168\) 0 0
\(169\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(170\) 0 0
\(171\) −0.376336 0.689209i −0.376336 0.689209i
\(172\) 0.654861 0.244250i 0.654861 0.244250i
\(173\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.234072 0.512546i −0.234072 0.512546i
\(177\) 0.796652 0.796652
\(178\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(179\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(180\) 0 0
\(181\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.463379 + 0.0666238i 0.463379 + 0.0666238i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(192\) 0.254771 0.340335i 0.254771 0.340335i
\(193\) −1.50013 0.559521i −1.50013 0.559521i −0.540641 0.841254i \(-0.681818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) −0.0405070 0.281733i −0.0405070 0.281733i
\(195\) 0 0
\(196\) −0.281733 0.959493i −0.281733 0.959493i
\(197\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(198\) −0.249574 0.388345i −0.249574 0.388345i
\(199\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(200\) −0.654861 0.755750i −0.654861 0.755750i
\(201\) −0.673741 + 0.504356i −0.673741 + 0.504356i
\(202\) 0 0
\(203\) 0 0
\(204\) 0.123435 + 0.330941i 0.123435 + 0.330941i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.432356 0.323658i −0.432356 0.323658i
\(210\) 0 0
\(211\) −0.148568 0.682956i −0.148568 0.682956i −0.989821 0.142315i \(-0.954545\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0.370663 0.678819i 0.370663 0.678819i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.458515 0.0327936i 0.458515 0.0327936i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(224\) 0 0
\(225\) −0.619158 0.536504i −0.619158 0.536504i
\(226\) −0.142315 + 0.0101786i −0.142315 + 0.0101786i
\(227\) −0.584585 + 0.909632i −0.584585 + 0.909632i 0.415415 + 0.909632i \(0.363636\pi\)
−1.00000 \(1.00000\pi\)
\(228\) 0.0579914 0.403339i 0.0579914 0.403339i
\(229\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.30972i 1.30972i −0.755750 0.654861i \(-0.772727\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.50013 1.12299i −1.50013 1.12299i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(240\) 0 0
\(241\) −0.697148 1.86912i −0.697148 1.86912i −0.415415 0.909632i \(-0.636364\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(242\) 0.574161 + 0.368991i 0.574161 + 0.368991i
\(243\) 0.343150 0.920022i 0.343150 0.920022i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.546894 + 0.249758i −0.546894 + 0.249758i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.0170890 + 0.0581999i 0.0170890 + 0.0581999i
\(250\) 0 0
\(251\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(257\) −1.89945 + 0.273100i −1.89945 + 0.273100i −0.989821 0.142315i \(-0.954545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(258\) 0.294111 + 0.0422868i 0.294111 + 0.0422868i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.474017 1.61435i 0.474017 1.61435i
\(263\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(264\) 0.0170890 0.238936i 0.0170890 0.238936i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.203743 + 0.373128i 0.203743 + 0.373128i
\(268\) 1.97964 1.97964
\(269\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(270\) 0 0
\(271\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(272\) 0.234072 0.797176i 0.234072 0.797176i
\(273\) 0 0
\(274\) 0.898064 + 1.64468i 0.898064 + 1.64468i
\(275\) −0.540641 0.158746i −0.540641 0.158746i
\(276\) 0 0
\(277\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(278\) 1.84125 0.540641i 1.84125 0.540641i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.05195 1.40524i 1.05195 1.40524i 0.142315 0.989821i \(-0.454545\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(282\) 0 0
\(283\) 0.215109 + 1.49611i 0.215109 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.745229 + 0.340335i −0.745229 + 0.340335i
\(289\) −0.202824 0.234072i −0.202824 0.234072i
\(290\) 0 0
\(291\) 0.0422868 0.113375i 0.0422868 0.113375i
\(292\) −0.909632 0.584585i −0.909632 0.584585i
\(293\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(294\) 0.0903680 0.415415i 0.0903680 0.415415i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.0310895 0.434688i −0.0310895 0.434688i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.0903680 0.415415i −0.0903680 0.415415i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.677760 + 0.677760i −0.677760 + 0.677760i
\(305\) 0 0
\(306\) 0.0968693 0.673741i 0.0968693 0.673741i
\(307\) 0.708089 1.10181i 0.708089 1.10181i −0.281733 0.959493i \(-0.590909\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(312\) 0 0
\(313\) −1.40524 0.767317i −1.40524 0.767317i −0.415415 0.909632i \(-0.636364\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.169276 0.778150i −0.169276 0.778150i
\(324\) −0.412599 + 0.265161i −0.412599 + 0.265161i
\(325\) 0 0
\(326\) 0.139418 + 1.94931i 0.139418 + 1.94931i
\(327\) 0 0
\(328\) 1.38189 + 0.300613i 1.38189 + 0.300613i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(332\) 0.0498610 0.133682i 0.0498610 0.133682i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.05195 + 1.40524i 1.05195 + 1.40524i 0.909632 + 0.415415i \(0.136364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(338\) −0.281733 0.959493i −0.281733 0.959493i
\(339\) −0.0551755 0.0251978i −0.0551755 0.0251978i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.470591 + 0.628635i −0.470591 + 0.628635i
\(343\) 0 0
\(344\) −0.494217 0.494217i −0.494217 0.494217i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.49611 + 0.215109i 1.49611 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(348\) 0 0
\(349\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.368991 + 0.425839i −0.368991 + 0.425839i
\(353\) 0.114220 1.59700i 0.114220 1.59700i −0.540641 0.841254i \(-0.681818\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(354\) −0.330941 0.724660i −0.330941 0.724660i
\(355\) 0 0
\(356\) 0.142315 0.989821i 0.142315 0.989821i
\(357\) 0 0
\(358\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(359\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(360\) 0 0
\(361\) 0.0228997 0.0779892i 0.0228997 0.0779892i
\(362\) 0 0
\(363\) 0.139056 + 0.254663i 0.139056 + 0.254663i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(368\) 0 0
\(369\) 1.15566 + 0.0826546i 1.15566 + 0.0826546i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(374\) −0.131891 0.449181i −0.131891 0.449181i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.959493 + 0.718267i −0.959493 + 0.718267i −0.959493 0.281733i \(-0.909091\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(384\) −0.415415 0.0903680i −0.415415 0.0903680i
\(385\) 0 0
\(386\) 0.114220 + 1.59700i 0.114220 + 1.59700i
\(387\) −0.458395 0.343150i −0.458395 0.343150i
\(388\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(389\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(393\) 0.505783 0.505783i 0.505783 0.505783i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.249574 + 0.388345i −0.249574 + 0.388345i
\(397\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(401\) 0.822373 1.80075i 0.822373 1.80075i 0.281733 0.959493i \(-0.409091\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(402\) 0.738661 + 0.403339i 0.738661 + 0.403339i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.249758 0.249758i 0.249758 0.249758i
\(409\) −0.215109 + 0.186393i −0.215109 + 0.186393i −0.755750 0.654861i \(-0.772727\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(410\) 0 0
\(411\) 0.796652i 0.796652i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.797176 + 0.173415i 0.797176 + 0.173415i
\(418\) −0.114802 + 0.527738i −0.114802 + 0.527738i
\(419\) −0.559521 1.50013i −0.559521 1.50013i −0.841254 0.540641i \(-0.818182\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(420\) 0 0
\(421\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(422\) −0.559521 + 0.418852i −0.559521 + 0.418852i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.449181 0.698939i −0.449181 0.698939i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(432\) −0.771454 0.0551755i −0.771454 0.0551755i
\(433\) 1.38189 + 1.38189i 1.38189 + 1.38189i 0.841254 + 0.540641i \(0.181818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.220304 0.403457i −0.220304 0.403457i
\(439\) 0 0 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(440\) 0 0
\(441\) −0.536504 + 0.619158i −0.536504 + 0.619158i
\(442\) 0 0
\(443\) 0.627899 + 1.37491i 0.627899 + 1.37491i 0.909632 + 0.415415i \(0.136364\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.989821 + 1.14231i −0.989821 + 1.14231i 1.00000i \(0.5\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(450\) −0.230813 + 0.786078i −0.230813 + 0.786078i
\(451\) 0.746618 0.278474i 0.746618 0.278474i
\(452\) 0.0683785 + 0.125226i 0.0683785 + 0.125226i
\(453\) 0 0
\(454\) 1.07028 + 0.153882i 1.07028 + 0.153882i
\(455\) 0 0
\(456\) −0.390981 + 0.114802i −0.390981 + 0.114802i
\(457\) 0.847507 + 0.847507i 0.847507 + 0.847507i 0.989821 0.142315i \(-0.0454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(458\) 0 0
\(459\) 0.385087 0.514415i 0.385087 0.514415i
\(460\) 0 0
\(461\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(462\) 0 0
\(463\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.19136 + 0.544078i −1.19136 + 0.544078i
\(467\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.398326 + 1.83107i −0.398326 + 1.83107i
\(473\) −0.384822 0.0837128i −0.384822 0.0837128i
\(474\) 0 0
\(475\) 0.0683785 + 0.956056i 0.0683785 + 0.956056i
\(476\) 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
\(482\) −1.41061 + 1.41061i −1.41061 + 1.41061i
\(483\) 0 0
\(484\) 0.0971309 0.675560i 0.0971309 0.675560i
\(485\) 0 0
\(486\) −0.979431 + 0.0700503i −0.979431 + 0.0700503i
\(487\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(488\) 0 0
\(489\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(490\) 0 0
\(491\) 1.54064 + 0.841254i 1.54064 + 0.841254i 1.00000 \(0\)
0.540641 + 0.841254i \(0.318182\pi\)
\(492\) 0.454376 + 0.393719i 0.454376 + 0.393719i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.0458415 0.0397218i 0.0458415 0.0397218i
\(499\) −1.94931 + 0.424047i −1.94931 + 0.424047i −0.959493 + 0.281733i \(0.909091\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.10181 0.708089i 1.10181 0.708089i
\(503\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.0903680 0.415415i 0.0903680 0.415415i
\(508\) 0 0
\(509\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(513\) −0.674334 + 0.307958i −0.674334 + 0.307958i
\(514\) 1.03748 + 1.61435i 1.03748 + 1.61435i
\(515\) 0 0
\(516\) −0.0837128 0.285100i −0.0837128 0.285100i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.697148 0.0498610i −0.697148 0.0498610i −0.281733 0.959493i \(-0.590909\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(522\) 0 0
\(523\) 1.03748 0.304632i 1.03748 0.304632i 0.281733 0.959493i \(-0.409091\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(524\) −1.66538 + 0.239446i −1.66538 + 0.239446i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.224443 + 0.0837128i −0.224443 + 0.0837128i
\(529\) 0.281733 0.959493i 0.281733 0.959493i
\(530\) 0 0
\(531\) −0.109521 + 1.53131i −0.109521 + 1.53131i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.254771 0.340335i 0.254771 0.340335i
\(535\) 0 0
\(536\) −0.822373 1.80075i −0.822373 1.80075i
\(537\) −0.00863238 + 0.120696i −0.00863238 + 0.120696i
\(538\) 0 0
\(539\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(540\) 0 0
\(541\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.822373 + 0.118239i −0.822373 + 0.118239i
\(545\) 0 0
\(546\) 0 0
\(547\) 1.75089 + 0.125226i 1.75089 + 0.125226i 0.909632 0.415415i \(-0.136364\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(548\) 1.12299 1.50013i 1.12299 1.50013i
\(549\) 0 0
\(550\) 0.0801894 + 0.557730i 0.0801894 + 0.557730i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.25667 1.45027i −1.25667 1.45027i
\(557\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0.0423052 0.194474i 0.0423052 0.194474i
\(562\) −1.71524 0.373128i −1.71524 0.373128i
\(563\) 1.54064 0.841254i 1.54064 0.841254i 0.540641 0.841254i \(-0.318182\pi\)
1.00000 \(0\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.27155 0.817178i 1.27155 0.817178i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.17116 0.254771i 1.17116 0.254771i 0.415415 0.909632i \(-0.363636\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(570\) 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
\(576\) 0.619158 + 0.536504i 0.619158 + 0.536504i
\(577\) −0.841254 0.459359i −0.841254 0.459359i 1.00000i \(-0.5\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(578\) −0.128663 + 0.281733i −0.128663 + 0.281733i
\(579\) −0.282760 + 0.619158i −0.282760 + 0.619158i
\(580\) 0 0
\(581\) 0 0
\(582\) −0.120696 + 0.00863238i −0.120696 + 0.00863238i
\(583\) 0 0
\(584\) −0.153882 + 1.07028i −0.153882 + 1.07028i
\(585\) 0 0
\(586\) 0 0
\(587\) 1.45027 1.25667i 1.45027 1.25667i 0.540641 0.841254i \(-0.318182\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(588\) −0.415415 + 0.0903680i −0.415415 + 0.0903680i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.0855040 + 1.19550i 0.0855040 + 1.19550i 0.841254 + 0.540641i \(0.181818\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(594\) −0.382491 + 0.208856i −0.382491 + 0.208856i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(600\) −0.340335 + 0.254771i −0.340335 + 0.254771i
\(601\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(602\) 0 0
\(603\) −0.876838 1.36439i −0.876838 1.36439i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(608\) 0.898064 + 0.334961i 0.898064 + 0.334961i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.653097 + 0.191767i −0.653097 + 0.191767i
\(613\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(614\) −1.29639 0.186393i −1.29639 0.186393i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.83107 0.682956i 1.83107 0.682956i 0.841254 0.540641i \(-0.181818\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(618\) 0 0
\(619\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(626\) −0.114220 + 1.59700i −0.114220 + 1.59700i
\(627\) −0.150359 + 0.173524i −0.150359 + 0.173524i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(632\) 0 0
\(633\) −0.294111 + 0.0422868i −0.294111 + 0.0422868i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.474017 1.61435i −0.474017 1.61435i −0.755750 0.654861i \(-0.772727\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(642\) 0 0
\(643\) −0.153882 0.239446i −0.153882 0.239446i 0.755750 0.654861i \(-0.227273\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.637510 + 0.477234i −0.637510 + 0.477234i
\(647\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(648\) 0.412599 + 0.265161i 0.412599 + 0.265161i
\(649\) 0.368991 + 0.989304i 0.368991 + 0.989304i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.71524 0.936593i 1.71524 0.936593i
\(653\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.300613 1.38189i −0.300613 1.38189i
\(657\) 0.885855i 0.885855i
\(658\) 0 0
\(659\) 1.27155 1.10181i 1.27155 1.10181i 0.281733 0.959493i \(-0.409091\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(660\) 0 0
\(661\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(662\) 0.273100 1.89945i 0.273100 1.89945i
\(663\) 0 0
\(664\) −0.142315 + 0.0101786i −0.142315 + 0.0101786i
\(665\) 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 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(674\) 0.841254 1.54064i 0.841254 1.54064i
\(675\) −0.546894 + 0.546894i −0.546894 + 0.546894i
\(676\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(677\) 0 0 0.977147 0.212565i \(-0.0681818\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(678\) 0.0606569i 0.0606569i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.367998 + 0.275479i 0.367998 + 0.275479i
\(682\) 0 0
\(683\) −1.71524 + 0.936593i −1.71524 + 0.936593i −0.755750 + 0.654861i \(0.772727\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(684\) 0.767317 + 0.166920i 0.767317 + 0.166920i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.244250 + 0.654861i −0.244250 + 0.654861i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.19136 + 0.544078i −1.19136 + 0.544078i −0.909632 0.415415i \(-0.863636\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.425839 1.45027i −0.425839 1.45027i
\(695\) 0 0
\(696\) 0 0
\(697\) 1.10089 + 0.410610i 1.10089 + 0.410610i
\(698\) 0 0
\(699\) −0.555384 0.0397218i −0.555384 0.0397218i
\(700\) 0 0
\(701\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.540641 + 0.158746i 0.540641 + 0.158746i
\(705\) 0 0
\(706\) −1.50013 + 0.559521i −1.50013 + 0.559521i
\(707\) 0 0
\(708\) −0.521696 + 0.602069i −0.521696 + 0.602069i
\(709\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.186393 0.215109i 0.186393 0.215109i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.0804543 + 0.0115676i −0.0804543 + 0.0115676i
\(723\) −0.813741 + 0.238936i −0.813741 + 0.238936i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.173883 0.232281i 0.173883 0.232281i
\(727\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(728\) 0 0
\(729\) 0.0664101 + 0.0303285i 0.0664101 + 0.0303285i
\(730\) 0 0
\(731\) −0.347995 0.464867i −0.347995 0.464867i
\(732\) 0 0
\(733\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.938384 0.603063i −0.938384 0.603063i
\(738\) −0.404894 1.08556i −0.404894 1.08556i
\(739\) 0.340335 1.56449i 0.340335 1.56449i −0.415415 0.909632i \(-0.636364\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.114220 + 0.0248470i −0.114220 + 0.0248470i
\(748\) −0.353799 + 0.306569i −0.353799 + 0.306569i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(752\) 0 0
\(753\) 0.555384 0.0397218i 0.555384 0.0397218i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(758\) 1.05195 + 0.574406i 1.05195 + 0.574406i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.304632 0.474017i 0.304632 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.0903680 + 0.415415i 0.0903680 + 0.415415i
\(769\) −1.27155 + 0.817178i −1.27155 + 0.817178i −0.989821 0.142315i \(-0.954545\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(770\) 0 0
\(771\) 0.0581999 + 0.813741i 0.0581999 + 0.813741i
\(772\) 1.40524 0.767317i 1.40524 0.767317i
\(773\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(774\) −0.121716 + 0.559521i −0.121716 + 0.559521i
\(775\) 0 0
\(776\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.887677 1.02443i −0.887677 1.02443i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(785\) 0 0
\(786\) −0.670186 0.249967i −0.670186 0.249967i
\(787\) 1.19550 1.59700i 1.19550 1.59700i 0.540641 0.841254i \(-0.318182\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.456928 + 0.0656963i 0.456928 + 0.0656963i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0