Properties

Label 712.1.y.a.195.1
Level $712$
Weight $1$
Character 712.195
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 195.1
Root \(0.989821 - 0.142315i\) of defining polynomial
Character \(\chi\) \(=\) 712.195
Dual form 712.1.y.a.555.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.959493 + 0.281733i) q^{2} +(-1.56449 - 0.340335i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-1.40524 - 0.767317i) q^{6} +(0.654861 + 0.755750i) q^{8} +(1.42218 + 0.649487i) q^{9} +O(q^{10})\) \(q+(0.959493 + 0.281733i) q^{2} +(-1.56449 - 0.340335i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-1.40524 - 0.767317i) q^{6} +(0.654861 + 0.755750i) q^{8} +(1.42218 + 0.649487i) q^{9} +(0.989821 - 1.14231i) q^{11} +(-1.13214 - 1.13214i) q^{12} +(0.415415 + 0.909632i) q^{16} +(0.540641 + 1.84125i) q^{17} +(1.18159 + 1.02385i) q^{18} +(-0.0498610 - 0.133682i) q^{19} +(1.27155 - 0.817178i) q^{22} +(-0.767317 - 1.40524i) q^{24} +(0.142315 - 0.989821i) q^{25} +(-0.722212 - 0.540641i) q^{27} +(0.142315 + 0.989821i) q^{32} +(-1.93734 + 1.45027i) q^{33} +1.91899i q^{34} +(0.845273 + 1.31527i) q^{36} +(-0.0101786 - 0.142315i) q^{38} +(-0.300613 - 1.38189i) q^{41} +(-0.956056 + 0.0683785i) q^{43} +(1.45027 - 0.425839i) q^{44} +(-0.340335 - 1.56449i) q^{48} +(-0.989821 - 0.142315i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-0.219186 - 3.06463i) q^{51} +(-0.540641 - 0.722212i) q^{54} +(0.0325104 + 0.226115i) q^{57} +(-1.71524 + 0.373128i) q^{59} +(-0.142315 + 0.989821i) q^{64} +(-2.26745 + 0.845715i) q^{66} +(-1.53046 + 0.983568i) q^{67} +(-0.540641 + 1.84125i) q^{68} +(0.440479 + 1.50013i) q^{72} +(-0.822373 - 1.80075i) q^{73} +(-0.559521 + 1.50013i) q^{75} +(0.0303285 - 0.139418i) q^{76} +(-0.0779559 - 0.0899659i) q^{81} +(0.100889 - 1.41061i) q^{82} +(1.71524 + 0.936593i) q^{83} +(-0.936593 - 0.203743i) q^{86} +1.51150 q^{88} +(0.142315 + 0.989821i) q^{89} +(0.114220 - 1.59700i) q^{96} +(-0.544078 - 0.627899i) q^{97} +(-0.909632 - 0.415415i) q^{98} +(2.14962 - 0.981699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10}) \) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{44}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(3\) −1.56449 0.340335i −1.56449 0.340335i −0.654861 0.755750i \(-0.727273\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(4\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(5\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(6\) −1.40524 0.767317i −1.40524 0.767317i
\(7\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(8\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(9\) 1.42218 + 0.649487i 1.42218 + 0.649487i
\(10\) 0 0
\(11\) 0.989821 1.14231i 0.989821 1.14231i 1.00000i \(-0.5\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(12\) −1.13214 1.13214i −1.13214 1.13214i
\(13\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(17\) 0.540641 + 1.84125i 0.540641 + 1.84125i 0.540641 + 0.841254i \(0.318182\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.18159 + 1.02385i 1.18159 + 1.02385i
\(19\) −0.0498610 0.133682i −0.0498610 0.133682i 0.909632 0.415415i \(-0.136364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.27155 0.817178i 1.27155 0.817178i
\(23\) 0 0 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(24\) −0.767317 1.40524i −0.767317 1.40524i
\(25\) 0.142315 0.989821i 0.142315 0.989821i
\(26\) 0 0
\(27\) −0.722212 0.540641i −0.722212 0.540641i
\(28\) 0 0
\(29\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(30\) 0 0
\(31\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(32\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(33\) −1.93734 + 1.45027i −1.93734 + 1.45027i
\(34\) 1.91899i 1.91899i
\(35\) 0 0
\(36\) 0.845273 + 1.31527i 0.845273 + 1.31527i
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) −0.0101786 0.142315i −0.0101786 0.142315i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.300613 1.38189i −0.300613 1.38189i −0.841254 0.540641i \(-0.818182\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(42\) 0 0
\(43\) −0.956056 + 0.0683785i −0.956056 + 0.0683785i −0.540641 0.841254i \(-0.681818\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(44\) 1.45027 0.425839i 1.45027 0.425839i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(48\) −0.340335 1.56449i −0.340335 1.56449i
\(49\) −0.989821 0.142315i −0.989821 0.142315i
\(50\) 0.415415 0.909632i 0.415415 0.909632i
\(51\) −0.219186 3.06463i −0.219186 3.06463i
\(52\) 0 0
\(53\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(54\) −0.540641 0.722212i −0.540641 0.722212i
\(55\) 0 0
\(56\) 0 0
\(57\) 0.0325104 + 0.226115i 0.0325104 + 0.226115i
\(58\) 0 0
\(59\) −1.71524 + 0.373128i −1.71524 + 0.373128i −0.959493 0.281733i \(-0.909091\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(60\) 0 0
\(61\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(65\) 0 0
\(66\) −2.26745 + 0.845715i −2.26745 + 0.845715i
\(67\) −1.53046 + 0.983568i −1.53046 + 0.983568i −0.540641 + 0.841254i \(0.681818\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(68\) −0.540641 + 1.84125i −0.540641 + 1.84125i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(72\) 0.440479 + 1.50013i 0.440479 + 1.50013i
\(73\) −0.822373 1.80075i −0.822373 1.80075i −0.540641 0.841254i \(-0.681818\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(74\) 0 0
\(75\) −0.559521 + 1.50013i −0.559521 + 1.50013i
\(76\) 0.0303285 0.139418i 0.0303285 0.139418i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(80\) 0 0
\(81\) −0.0779559 0.0899659i −0.0779559 0.0899659i
\(82\) 0.100889 1.41061i 0.100889 1.41061i
\(83\) 1.71524 + 0.936593i 1.71524 + 0.936593i 0.959493 + 0.281733i \(0.0909091\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.936593 0.203743i −0.936593 0.203743i
\(87\) 0 0
\(88\) 1.51150 1.51150
\(89\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.114220 1.59700i 0.114220 1.59700i
\(97\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(98\) −0.909632 0.415415i −0.909632 0.415415i
\(99\) 2.14962 0.981699i 2.14962 0.981699i
\(100\) 0.654861 0.755750i 0.654861 0.755750i
\(101\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(102\) 0.653097 3.00224i 0.653097 3.00224i
\(103\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(108\) −0.315271 0.845273i −0.315271 0.845273i
\(109\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.936593 + 1.71524i 0.936593 + 1.71524i 0.654861 + 0.755750i \(0.272727\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(114\) −0.0325104 + 0.226115i −0.0325104 + 0.226115i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.75089 0.125226i −1.75089 0.125226i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.182822 1.27155i −0.182822 1.27155i
\(122\) 0 0
\(123\) 2.26427i 2.26427i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(128\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(129\) 1.51901 + 0.218401i 1.51901 + 0.218401i
\(130\) 0 0
\(131\) −0.153882 + 0.239446i −0.153882 + 0.239446i −0.909632 0.415415i \(-0.863636\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(132\) −2.41387 + 0.172643i −2.41387 + 0.172643i
\(133\) 0 0
\(134\) −1.74557 + 0.512546i −1.74557 + 0.512546i
\(135\) 0 0
\(136\) −1.03748 + 1.61435i −1.03748 + 1.61435i
\(137\) −0.373128 1.71524i −0.373128 1.71524i −0.654861 0.755750i \(-0.727273\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(138\) 0 0
\(139\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.56347i 1.56347i
\(145\) 0 0
\(146\) −0.281733 1.95949i −0.281733 1.95949i
\(147\) 1.50013 + 0.559521i 1.50013 + 0.559521i
\(148\) 0 0
\(149\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(150\) −0.959493 + 1.28173i −0.959493 + 1.28173i
\(151\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(152\) 0.0683785 0.125226i 0.0683785 0.125226i
\(153\) −0.426983 + 2.96973i −0.426983 + 2.96973i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.0494518 0.108284i −0.0494518 0.108284i
\(163\) 1.05195 0.574406i 1.05195 0.574406i 0.142315 0.989821i \(-0.454545\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(164\) 0.494217 1.32505i 0.494217 1.32505i
\(165\) 0 0
\(166\) 1.38189 + 1.38189i 1.38189 + 1.38189i
\(167\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(168\) 0 0
\(169\) −0.909632 0.415415i −0.909632 0.415415i
\(170\) 0 0
\(171\) 0.0159138 0.222504i 0.0159138 0.222504i
\(172\) −0.841254 0.459359i −0.841254 0.459359i
\(173\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.45027 + 0.425839i 1.45027 + 0.425839i
\(177\) 2.81047 2.81047
\(178\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(179\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0 0
\(181\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.63843 + 1.20493i 2.63843 + 1.20493i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(192\) 0.559521 1.50013i 0.559521 1.50013i
\(193\) −1.64468 + 0.898064i −1.64468 + 0.898064i −0.654861 + 0.755750i \(0.727273\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(194\) −0.345139 0.755750i −0.345139 0.755750i
\(195\) 0 0
\(196\) −0.755750 0.654861i −0.755750 0.654861i
\(197\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(198\) 2.33912 0.336315i 2.33912 0.336315i
\(199\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(200\) 0.841254 0.540641i 0.841254 0.540641i
\(201\) 2.72914 1.01792i 2.72914 1.01792i
\(202\) 0 0
\(203\) 0 0
\(204\) 1.47247 2.69663i 1.47247 2.69663i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.202061 0.0753648i −0.202061 0.0753648i
\(210\) 0 0
\(211\) 0.767317 0.574406i 0.767317 0.574406i −0.142315 0.989821i \(-0.545455\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) −0.0643589 0.899856i −0.0643589 0.899856i
\(217\) 0 0
\(218\) 0 0
\(219\) 0.673741 + 3.09714i 0.673741 + 3.09714i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(224\) 0 0
\(225\) 0.845273 1.31527i 0.845273 1.31527i
\(226\) 0.415415 + 1.90963i 0.415415 + 1.90963i
\(227\) −1.95949 0.281733i −1.95949 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
−1.00000 \(\pi\)
\(228\) −0.0948973 + 0.207796i −0.0948973 + 0.207796i
\(229\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.68251i 1.68251i 0.540641 + 0.841254i \(0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.64468 0.613435i −1.64468 0.613435i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(240\) 0 0
\(241\) 0.203743 0.373128i 0.203743 0.373128i −0.755750 0.654861i \(-0.772727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(242\) 0.182822 1.27155i 0.182822 1.27155i
\(243\) 0.523699 + 0.959084i 0.523699 + 0.959084i
\(244\) 0 0
\(245\) 0 0
\(246\) −0.637919 + 2.17255i −0.637919 + 2.17255i
\(247\) 0 0
\(248\) 0 0
\(249\) −2.36473 2.04905i −2.36473 2.04905i
\(250\) 0 0
\(251\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(257\) 1.19136 0.544078i 1.19136 0.544078i 0.281733 0.959493i \(-0.409091\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(258\) 1.39595 + 0.637510i 1.39595 + 0.637510i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.215109 + 0.186393i −0.215109 + 0.186393i
\(263\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) −2.36473 0.514415i −2.36473 0.514415i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.114220 1.59700i 0.114220 1.59700i
\(268\) −1.81926 −1.81926
\(269\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(270\) 0 0
\(271\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(272\) −1.45027 + 1.25667i −1.45027 + 1.25667i
\(273\) 0 0
\(274\) 0.125226 1.75089i 0.125226 1.75089i
\(275\) −0.989821 1.14231i −0.989821 1.14231i
\(276\) 0 0
\(277\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(278\) 0.857685 0.989821i 0.857685 0.989821i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.697148 + 1.86912i −0.697148 + 1.86912i −0.281733 + 0.959493i \(0.590909\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(282\) 0 0
\(283\) −0.449181 0.983568i −0.449181 0.983568i −0.989821 0.142315i \(-0.954545\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.440479 + 1.50013i −0.440479 + 1.50013i
\(289\) −2.25667 + 1.45027i −2.25667 + 1.45027i
\(290\) 0 0
\(291\) 0.637510 + 1.16751i 0.637510 + 1.16751i
\(292\) 0.281733 1.95949i 0.281733 1.95949i
\(293\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(294\) 1.28173 + 0.959493i 1.28173 + 0.959493i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.33244 + 0.289855i −1.33244 + 0.289855i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.28173 + 0.959493i −1.28173 + 0.959493i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.100889 0.100889i 0.100889 0.100889i
\(305\) 0 0
\(306\) −1.24636 + 2.72914i −1.24636 + 2.72914i
\(307\) −1.66538 0.239446i −1.66538 0.239446i −0.755750 0.654861i \(-0.772727\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) 0 0
\(313\) 1.86912 0.133682i 1.86912 0.133682i 0.909632 0.415415i \(-0.136364\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.219186 0.164081i 0.219186 0.164081i
\(324\) −0.0169414 0.117830i −0.0169414 0.117830i
\(325\) 0 0
\(326\) 1.17116 0.254771i 1.17116 0.254771i
\(327\) 0 0
\(328\) 0.847507 1.13214i 0.847507 1.13214i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(332\) 0.936593 + 1.71524i 0.936593 + 1.71524i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.697148 1.86912i −0.697148 1.86912i −0.415415 0.909632i \(-0.636364\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(338\) −0.755750 0.654861i −0.755750 0.654861i
\(339\) −0.881537 3.00224i −0.881537 3.00224i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.0779559 0.209008i 0.0779559 0.209008i
\(343\) 0 0
\(344\) −0.677760 0.677760i −0.677760 0.677760i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.983568 0.449181i −0.983568 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(348\) 0 0
\(349\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.27155 + 0.817178i 1.27155 + 0.817178i
\(353\) −1.83107 0.398326i −1.83107 0.398326i −0.841254 0.540641i \(-0.818182\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(354\) 2.69663 + 0.791802i 2.69663 + 0.791802i
\(355\) 0 0
\(356\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(357\) 0 0
\(358\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(359\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(360\) 0 0
\(361\) 0.740365 0.641530i 0.740365 0.641530i
\(362\) 0 0
\(363\) −0.146730 + 2.05156i −0.146730 + 2.05156i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(368\) 0 0
\(369\) 0.469997 2.16054i 0.469997 2.16054i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(374\) 2.19209 + 1.89945i 2.19209 + 1.89945i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.654861 + 0.244250i −0.654861 + 0.244250i −0.654861 0.755750i \(-0.727273\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(384\) 0.959493 1.28173i 0.959493 1.28173i
\(385\) 0 0
\(386\) −1.83107 + 0.398326i −1.83107 + 0.398326i
\(387\) −1.40409 0.523699i −1.40409 0.523699i
\(388\) −0.118239 0.822373i −0.118239 0.822373i
\(389\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.540641 0.841254i −0.540641 0.841254i
\(393\) 0.322240 0.322240i 0.322240 0.322240i
\(394\) 0 0
\(395\) 0 0
\(396\) 2.33912 + 0.336315i 2.33912 + 0.336315i
\(397\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.959493 0.281733i 0.959493 0.281733i
\(401\) 1.74557 0.512546i 1.74557 0.512546i 0.755750 0.654861i \(-0.227273\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(402\) 2.90537 0.207796i 2.90537 0.207796i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 2.17255 2.17255i 2.17255 2.17255i
\(409\) 0.449181 + 0.698939i 0.449181 + 0.698939i 0.989821 0.142315i \(-0.0454545\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(410\) 0 0
\(411\) 2.81047i 2.81047i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.25667 + 1.67871i −1.25667 + 1.67871i
\(418\) −0.172643 0.129239i −0.172643 0.129239i
\(419\) 0.898064 1.64468i 0.898064 1.64468i 0.142315 0.989821i \(-0.454545\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(420\) 0 0
\(421\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(422\) 0.898064 0.334961i 0.898064 0.334961i
\(423\) 0 0
\(424\) 0 0
\(425\) 1.89945 0.273100i 1.89945 0.273100i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(432\) 0.191767 0.881537i 0.191767 0.881537i
\(433\) 0.847507 + 0.847507i 0.847507 + 0.847507i 0.989821 0.142315i \(-0.0454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.226115 + 3.16150i −0.226115 + 3.16150i
\(439\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(440\) 0 0
\(441\) −1.31527 0.845273i −1.31527 0.845273i
\(442\) 0 0
\(443\) −1.03748 0.304632i −1.03748 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.909632 + 0.584585i 0.909632 + 0.584585i 0.909632 0.415415i \(-0.136364\pi\)
1.00000i \(0.5\pi\)
\(450\) 1.18159 1.02385i 1.18159 1.02385i
\(451\) −1.87611 1.02443i −1.87611 1.02443i
\(452\) −0.139418 + 1.94931i −0.139418 + 1.94931i
\(453\) 0 0
\(454\) −1.80075 0.822373i −1.80075 0.822373i
\(455\) 0 0
\(456\) −0.149596 + 0.172643i −0.149596 + 0.172643i
\(457\) −0.494217 0.494217i −0.494217 0.494217i 0.415415 0.909632i \(-0.363636\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(458\) 0 0
\(459\) 0.605000 1.62207i 0.605000 1.62207i
\(460\) 0 0
\(461\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(462\) 0 0
\(463\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.474017 + 1.61435i −0.474017 + 1.61435i
\(467\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.40524 1.05195i −1.40524 1.05195i
\(473\) −0.868215 + 1.15980i −0.868215 + 1.15980i
\(474\) 0 0
\(475\) −0.139418 + 0.0303285i −0.139418 + 0.0303285i
\(476\) 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
\(482\) 0.300613 0.300613i 0.300613 0.300613i
\(483\) 0 0
\(484\) 0.533654 1.16854i 0.533654 1.16854i
\(485\) 0 0
\(486\) 0.232281 + 1.06778i 0.232281 + 1.06778i
\(487\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(488\) 0 0
\(489\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(490\) 0 0
\(491\) 1.98982 0.142315i 1.98982 0.142315i 0.989821 0.142315i \(-0.0454545\pi\)
1.00000 \(0\)
\(492\) −1.22416 + 1.90483i −1.22416 + 1.90483i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.69166 2.63227i −1.69166 2.63227i
\(499\) 0.254771 + 0.340335i 0.254771 + 0.340335i 0.909632 0.415415i \(-0.136364\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(503\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.28173 + 0.959493i 1.28173 + 0.959493i
\(508\) 0 0
\(509\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(513\) −0.0362640 + 0.123504i −0.0362640 + 0.123504i
\(514\) 1.29639 0.186393i 1.29639 0.186393i
\(515\) 0 0
\(516\) 1.15980 + 1.00497i 1.15980 + 1.00497i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.203743 0.936593i 0.203743 0.936593i −0.755750 0.654861i \(-0.772727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(522\) 0 0
\(523\) 1.29639 1.49611i 1.29639 1.49611i 0.540641 0.841254i \(-0.318182\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(524\) −0.258908 + 0.118239i −0.258908 + 0.118239i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −2.12401 1.15980i −2.12401 1.15980i
\(529\) 0.755750 0.654861i 0.755750 0.654861i
\(530\) 0 0
\(531\) −2.68172 0.583373i −2.68172 0.583373i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.559521 1.50013i 0.559521 1.50013i
\(535\) 0 0
\(536\) −1.74557 0.512546i −1.74557 0.512546i
\(537\) −1.29983 0.282760i −1.29983 0.282760i
\(538\) 0 0
\(539\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(540\) 0 0
\(541\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.74557 + 0.797176i −1.74557 + 0.797176i
\(545\) 0 0
\(546\) 0 0
\(547\) −0.424047 + 1.94931i −0.424047 + 1.94931i −0.142315 + 0.989821i \(0.545455\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(548\) 0.613435 1.64468i 0.613435 1.64468i
\(549\) 0 0
\(550\) −0.627899 1.37491i −0.627899 1.37491i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.10181 0.708089i 1.10181 0.708089i
\(557\) 0 0 0.936950 0.349464i \(-0.113636\pi\)
−0.936950 + 0.349464i \(0.886364\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −3.71772 2.78305i −3.71772 2.78305i
\(562\) −1.19550 + 1.59700i −1.19550 + 1.59700i
\(563\) 1.98982 + 0.142315i 1.98982 + 0.142315i 1.00000 \(0\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.153882 1.07028i −0.153882 1.07028i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.418852 0.559521i −0.418852 0.559521i 0.540641 0.841254i \(-0.318182\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(570\) 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
\(576\) −0.845273 + 1.31527i −0.845273 + 1.31527i
\(577\) 0.142315 0.0101786i 0.142315 0.0101786i 1.00000i \(-0.5\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(578\) −2.57385 + 0.755750i −2.57385 + 0.755750i
\(579\) 2.87874 0.845273i 2.87874 0.845273i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.282760 + 1.29983i 0.282760 + 1.29983i
\(583\) 0 0
\(584\) 0.822373 1.80075i 0.822373 1.80075i
\(585\) 0 0
\(586\) 0 0
\(587\) 0.708089 + 1.10181i 0.708089 + 1.10181i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(588\) 0.959493 + 1.28173i 0.959493 + 1.28173i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.682956 + 0.148568i −0.682956 + 0.148568i −0.540641 0.841254i \(-0.681818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(594\) −1.36013 0.0972785i −1.36013 0.0972785i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(600\) −1.50013 + 0.559521i −1.50013 + 0.559521i
\(601\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 0 0
\(603\) −2.81540 + 0.404794i −2.81540 + 0.404794i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(608\) 0.125226 0.0683785i 0.125226 0.0683785i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1.96476 + 2.26745i −1.96476 + 2.26745i
\(613\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(614\) −1.53046 0.698939i −1.53046 0.698939i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.05195 0.574406i −1.05195 0.574406i −0.142315 0.989821i \(-0.545455\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(618\) 0 0
\(619\) 0.239446 + 0.153882i 0.239446 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.959493 0.281733i −0.959493 0.281733i
\(626\) 1.83107 + 0.398326i 1.83107 + 0.398326i
\(627\) 0.290474 + 0.186676i 0.290474 + 0.186676i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(632\) 0 0
\(633\) −1.39595 + 0.637510i −1.39595 + 0.637510i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.215109 + 0.186393i 0.215109 + 0.186393i 0.755750 0.654861i \(-0.227273\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(642\) 0 0
\(643\) 0.822373 0.118239i 0.822373 0.118239i 0.281733 0.959493i \(-0.409091\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.256535 0.0956825i 0.256535 0.0956825i
\(647\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(648\) 0.0169414 0.117830i 0.0169414 0.117830i
\(649\) −1.27155 + 2.32868i −1.27155 + 2.32868i
\(650\) 0 0
\(651\) 0 0
\(652\) 1.19550 + 0.0855040i 1.19550 + 0.0855040i
\(653\) 0 0 0.977147 0.212565i \(-0.0681818\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.13214 0.847507i 1.13214 0.847507i
\(657\) 3.09510i 3.09510i
\(658\) 0 0
\(659\) −0.153882 0.239446i −0.153882 0.239446i 0.755750 0.654861i \(-0.227273\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(660\) 0 0
\(661\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(662\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(663\) 0 0
\(664\) 0.415415 + 1.90963i 0.415415 + 1.90963i
\(665\) 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 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(674\) −0.142315 1.98982i −0.142315 1.98982i
\(675\) −0.637919 + 0.637919i −0.637919 + 0.637919i
\(676\) −0.540641 0.841254i −0.540641 0.841254i
\(677\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(678\) 3.12899i 3.12899i
\(679\) 0 0
\(680\) 0 0
\(681\) 2.96973 + 1.10765i 2.96973 + 1.10765i
\(682\) 0 0
\(683\) −1.19550 0.0855040i −1.19550 0.0855040i −0.540641 0.841254i \(-0.681818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(684\) 0.133682 0.178579i 0.133682 0.178579i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.459359 0.841254i −0.459359 0.841254i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.474017 + 1.61435i −0.474017 + 1.61435i 0.281733 + 0.959493i \(0.409091\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.817178 0.708089i −0.817178 0.708089i
\(695\) 0 0
\(696\) 0 0
\(697\) 2.38189 1.30061i 2.38189 1.30061i
\(698\) 0 0
\(699\) 0.572615 2.63227i 0.572615 2.63227i
\(700\) 0 0
\(701\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.989821 + 1.14231i 0.989821 + 1.14231i
\(705\) 0 0
\(706\) −1.64468 0.898064i −1.64468 0.898064i
\(707\) 0 0
\(708\) 2.36432 + 1.51946i 2.36432 + 1.51946i
\(709\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.891115 0.406958i 0.891115 0.406958i
\(723\) −0.445743 + 0.514415i −0.445743 + 0.514415i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.718777 + 1.92712i −0.718777 + 1.92712i
\(727\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(728\) 0 0
\(729\) −0.459377 1.56449i −0.459377 1.56449i
\(730\) 0 0
\(731\) −0.642785 1.72337i −0.642785 1.72337i
\(732\) 0 0
\(733\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.391340 + 2.72183i −0.391340 + 2.72183i
\(738\) 1.05965 1.94061i 1.05965 1.94061i
\(739\) 1.50013 + 1.12299i 1.50013 + 1.12299i 0.959493 + 0.281733i \(0.0909091\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.83107 + 2.44603i 1.83107 + 2.44603i
\(748\) 1.56815 + 2.44009i 1.56815 + 2.44009i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(752\) 0 0
\(753\) −0.572615 2.63227i −0.572615 2.63227i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(758\) −0.697148 + 0.0498610i −0.697148 + 0.0498610i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.49611 + 0.215109i 1.49611 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.28173 0.959493i 1.28173 0.959493i
\(769\) 0.153882 + 1.07028i 0.153882 + 1.07028i 0.909632 + 0.415415i \(0.136364\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(770\) 0 0
\(771\) −2.04905 + 0.445743i −2.04905 + 0.445743i
\(772\) −1.86912 0.133682i −1.86912 0.133682i
\(773\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(774\) −1.19967 0.898064i −1.19967 0.898064i
\(775\) 0 0
\(776\) 0.118239 0.822373i 0.118239 0.822373i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.169746 + 0.109089i −0.169746 + 0.109089i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.281733 0.959493i −0.281733 0.959493i
\(785\) 0 0
\(786\) 0.399972 0.218401i 0.399972 0.218401i
\(787\) 0.148568 0.398326i 0.148568 0.398326i −0.841254 0.540641i \(-0.818182\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 2.14962 + 0.981699i 2.14962 + 0.981699i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0