Properties

Label 712.1.y.a.307.1
Level $712$
Weight $1$
Character 712.307
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 307.1
Root \(0.755750 - 0.654861i\) of defining polynomial
Character \(\chi\) \(=\) 712.307
Dual form 712.1.y.a.603.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.142315 + 0.989821i) q^{2} +(0.956056 + 1.75089i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.59700 + 1.19550i) q^{6} +(-0.415415 - 0.909632i) q^{8} +(-1.61092 + 2.50664i) q^{9} +O(q^{10})\) \(q+(0.142315 + 0.989821i) q^{2} +(0.956056 + 1.75089i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.59700 + 1.19550i) q^{6} +(-0.415415 - 0.909632i) q^{8} +(-1.61092 + 2.50664i) q^{9} +(0.755750 - 1.65486i) q^{11} +(-1.41061 - 1.41061i) q^{12} +(0.841254 - 0.540641i) q^{16} +(0.281733 + 0.0405070i) q^{17} +(-2.71038 - 1.23779i) q^{18} +(-0.682956 + 0.148568i) q^{19} +(1.74557 + 0.512546i) q^{22} +(1.19550 - 1.59700i) q^{24} +(0.654861 - 0.755750i) q^{25} +(-3.93914 - 0.281733i) q^{27} +(0.654861 + 0.755750i) q^{32} +(3.62001 - 0.258908i) q^{33} +0.284630i q^{34} +(0.839462 - 2.85895i) q^{36} +(-0.244250 - 0.654861i) q^{38} +(1.24123 + 0.677760i) q^{41} +(-1.12299 + 0.418852i) q^{43} +(-0.258908 + 1.80075i) q^{44} +(1.75089 + 0.956056i) q^{48} +(-0.755750 - 0.654861i) q^{49} +(0.841254 + 0.540641i) q^{50} +(0.198429 + 0.532008i) q^{51} +(-0.281733 - 3.93914i) q^{54} +(-0.913069 - 1.05374i) q^{57} +(0.767317 - 1.40524i) q^{59} +(-0.654861 + 0.755750i) q^{64} +(0.771454 + 3.54632i) q^{66} +(-1.03748 - 0.304632i) q^{67} +(-0.281733 + 0.0405070i) q^{68} +(2.94931 + 0.424047i) q^{72} +(-1.27155 + 0.817178i) q^{73} +(1.94931 + 0.424047i) q^{75} +(0.613435 - 0.334961i) q^{76} +(-2.03496 - 4.45595i) q^{81} +(-0.494217 + 1.32505i) q^{82} +(-0.767317 + 0.574406i) q^{83} +(-0.574406 - 1.05195i) q^{86} -1.81926 q^{88} +(0.654861 + 0.755750i) q^{89} +(-0.697148 + 1.86912i) q^{96} +(0.698939 + 1.53046i) q^{97} +(0.540641 - 0.841254i) q^{98} +(2.93068 + 4.56023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} + O(q^{10}) \) \( 20q + 2q^{2} - 2q^{3} - 2q^{4} + 2q^{6} + 2q^{8} - 2q^{12} - 2q^{16} - 2q^{19} + 2q^{24} + 2q^{25} - 22q^{27} + 2q^{32} - 20q^{38} + 2q^{41} + 2q^{43} - 2q^{48} - 2q^{50} + 4q^{51} - 4q^{57} - 2q^{59} - 2q^{64} + 22q^{72} + 2q^{75} - 2q^{76} - 2q^{81} - 2q^{82} + 2q^{83} - 2q^{86} + 2q^{89} + 2q^{96} - 4q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(357\) \(535\) \(537\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{15}{44}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(3\) 0.956056 + 1.75089i 0.956056 + 1.75089i 0.540641 + 0.841254i \(0.318182\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(4\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(5\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(6\) −1.59700 + 1.19550i −1.59700 + 1.19550i
\(7\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(8\) −0.415415 0.909632i −0.415415 0.909632i
\(9\) −1.61092 + 2.50664i −1.61092 + 2.50664i
\(10\) 0 0
\(11\) 0.755750 1.65486i 0.755750 1.65486i 1.00000i \(-0.5\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(12\) −1.41061 1.41061i −1.41061 1.41061i
\(13\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.841254 0.540641i 0.841254 0.540641i
\(17\) 0.281733 + 0.0405070i 0.281733 + 0.0405070i 0.281733 0.959493i \(-0.409091\pi\)
1.00000i \(0.5\pi\)
\(18\) −2.71038 1.23779i −2.71038 1.23779i
\(19\) −0.682956 + 0.148568i −0.682956 + 0.148568i −0.540641 0.841254i \(-0.681818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.74557 + 0.512546i 1.74557 + 0.512546i
\(23\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(24\) 1.19550 1.59700i 1.19550 1.59700i
\(25\) 0.654861 0.755750i 0.654861 0.755750i
\(26\) 0 0
\(27\) −3.93914 0.281733i −3.93914 0.281733i
\(28\) 0 0
\(29\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(30\) 0 0
\(31\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(32\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(33\) 3.62001 0.258908i 3.62001 0.258908i
\(34\) 0.284630i 0.284630i
\(35\) 0 0
\(36\) 0.839462 2.85895i 0.839462 2.85895i
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) −0.244250 0.654861i −0.244250 0.654861i
\(39\) 0 0
\(40\) 0 0
\(41\) 1.24123 + 0.677760i 1.24123 + 0.677760i 0.959493 0.281733i \(-0.0909091\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(42\) 0 0
\(43\) −1.12299 + 0.418852i −1.12299 + 0.418852i −0.841254 0.540641i \(-0.818182\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(44\) −0.258908 + 1.80075i −0.258908 + 1.80075i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(48\) 1.75089 + 0.956056i 1.75089 + 0.956056i
\(49\) −0.755750 0.654861i −0.755750 0.654861i
\(50\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(51\) 0.198429 + 0.532008i 0.198429 + 0.532008i
\(52\) 0 0
\(53\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(54\) −0.281733 3.93914i −0.281733 3.93914i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.913069 1.05374i −0.913069 1.05374i
\(58\) 0 0
\(59\) 0.767317 1.40524i 0.767317 1.40524i −0.142315 0.989821i \(-0.545455\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(60\) 0 0
\(61\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(65\) 0 0
\(66\) 0.771454 + 3.54632i 0.771454 + 3.54632i
\(67\) −1.03748 0.304632i −1.03748 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(68\) −0.281733 + 0.0405070i −0.281733 + 0.0405070i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(72\) 2.94931 + 0.424047i 2.94931 + 0.424047i
\(73\) −1.27155 + 0.817178i −1.27155 + 0.817178i −0.989821 0.142315i \(-0.954545\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(74\) 0 0
\(75\) 1.94931 + 0.424047i 1.94931 + 0.424047i
\(76\) 0.613435 0.334961i 0.613435 0.334961i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(80\) 0 0
\(81\) −2.03496 4.45595i −2.03496 4.45595i
\(82\) −0.494217 + 1.32505i −0.494217 + 1.32505i
\(83\) −0.767317 + 0.574406i −0.767317 + 0.574406i −0.909632 0.415415i \(-0.863636\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.574406 1.05195i −0.574406 1.05195i
\(87\) 0 0
\(88\) −1.81926 −1.81926
\(89\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.697148 + 1.86912i −0.697148 + 1.86912i
\(97\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(98\) 0.540641 0.841254i 0.540641 0.841254i
\(99\) 2.93068 + 4.56023i 2.93068 + 4.56023i
\(100\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(101\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(102\) −0.498354 + 0.272122i −0.498354 + 0.272122i
\(103\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(108\) 3.85895 0.839462i 3.85895 0.839462i
\(109\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.574406 0.767317i 0.574406 0.767317i −0.415415 0.909632i \(-0.636364\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(114\) 0.913069 1.05374i 0.913069 1.05374i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.50013 + 0.559521i 1.50013 + 0.559521i
\(119\) 0 0
\(120\) 0 0
\(121\) −1.51255 1.74557i −1.51255 1.74557i
\(122\) 0 0
\(123\) 2.82122i 2.82122i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(128\) −0.841254 0.540641i −0.841254 0.540641i
\(129\) −1.80700 1.56577i −1.80700 1.56577i
\(130\) 0 0
\(131\) −0.368991 1.25667i −0.368991 1.25667i −0.909632 0.415415i \(-0.863636\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(132\) −3.40043 + 1.26830i −3.40043 + 1.26830i
\(133\) 0 0
\(134\) 0.153882 1.07028i 0.153882 1.07028i
\(135\) 0 0
\(136\) −0.0801894 0.273100i −0.0801894 0.273100i
\(137\) 1.40524 + 0.767317i 1.40524 + 0.767317i 0.989821 0.142315i \(-0.0454545\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(138\) 0 0
\(139\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 2.97964i 2.97964i
\(145\) 0 0
\(146\) −0.989821 1.14231i −0.989821 1.14231i
\(147\) 0.424047 1.94931i 0.424047 1.94931i
\(148\) 0 0
\(149\) 0 0 −0.936950 0.349464i \(-0.886364\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(150\) −0.142315 + 1.98982i −0.142315 + 1.98982i
\(151\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(152\) 0.418852 + 0.559521i 0.418852 + 0.559521i
\(153\) −0.555384 + 0.640947i −0.555384 + 0.640947i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 4.12099 2.64840i 4.12099 2.64840i
\(163\) 0.114220 + 0.0855040i 0.114220 + 0.0855040i 0.654861 0.755750i \(-0.272727\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(164\) −1.38189 0.300613i −1.38189 0.300613i
\(165\) 0 0
\(166\) −0.677760 0.677760i −0.677760 0.677760i
\(167\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(168\) 0 0
\(169\) 0.540641 0.841254i 0.540641 0.841254i
\(170\) 0 0
\(171\) 0.727779 1.95125i 0.727779 1.95125i
\(172\) 0.959493 0.718267i 0.959493 0.718267i
\(173\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.258908 1.80075i −0.258908 1.80075i
\(177\) 3.19401 3.19401
\(178\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(179\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(180\) 0 0
\(181\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.279953 0.435615i 0.279953 0.435615i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.877679 0.479249i \(-0.159091\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(192\) −1.94931 0.424047i −1.94931 0.424047i
\(193\) −0.340335 0.254771i −0.340335 0.254771i 0.415415 0.909632i \(-0.363636\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(194\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(195\) 0 0
\(196\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(197\) 0 0 0.977147 0.212565i \(-0.0681818\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(198\) −4.09673 + 3.54984i −4.09673 + 3.54984i
\(199\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(200\) −0.959493 0.281733i −0.959493 0.281733i
\(201\) −0.458515 2.10776i −0.458515 2.10776i
\(202\) 0 0
\(203\) 0 0
\(204\) −0.340275 0.454554i −0.340275 0.454554i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.270284 + 1.24248i −0.270284 + 1.24248i
\(210\) 0 0
\(211\) −1.19550 + 0.0855040i −1.19550 + 0.0855040i −0.654861 0.755750i \(-0.727273\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 1.38010 + 3.70020i 1.38010 + 3.70020i
\(217\) 0 0
\(218\) 0 0
\(219\) −2.64646 1.44508i −2.64646 1.44508i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(224\) 0 0
\(225\) 0.839462 + 2.85895i 0.839462 + 2.85895i
\(226\) 0.841254 + 0.459359i 0.841254 + 0.459359i
\(227\) −1.14231 0.989821i −1.14231 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
−1.00000 \(\pi\)
\(228\) 1.17296 + 0.753813i 1.17296 + 0.753813i
\(229\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.91899i 1.91899i −0.281733 0.959493i \(-0.590909\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.340335 + 1.56449i −0.340335 + 1.56449i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(240\) 0 0
\(241\) 1.05195 + 1.40524i 1.05195 + 1.40524i 0.909632 + 0.415415i \(0.136364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(242\) 1.51255 1.74557i 1.51255 1.74557i
\(243\) 3.48965 4.66163i 3.48965 4.66163i
\(244\) 0 0
\(245\) 0 0
\(246\) −2.79250 + 0.401502i −2.79250 + 0.401502i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.73932 0.794320i −1.73932 0.794320i
\(250\) 0 0
\(251\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.415415 0.909632i 0.415415 0.909632i
\(257\) 0.449181 + 0.698939i 0.449181 + 0.698939i 0.989821 0.142315i \(-0.0454545\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(258\) 1.29267 2.01144i 1.29267 2.01144i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.19136 0.544078i 1.19136 0.544078i
\(263\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(264\) −1.73932 3.18532i −1.73932 3.18532i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.697148 + 1.86912i −0.697148 + 1.86912i
\(268\) 1.08128 1.08128
\(269\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(270\) 0 0
\(271\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(272\) 0.258908 0.118239i 0.258908 0.118239i
\(273\) 0 0
\(274\) −0.559521 + 1.50013i −0.559521 + 1.50013i
\(275\) −0.755750 1.65486i −0.755750 1.65486i
\(276\) 0 0
\(277\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(278\) 0.345139 0.755750i 0.345139 0.755750i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.83107 0.398326i −1.83107 0.398326i −0.841254 0.540641i \(-0.818182\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(282\) 0 0
\(283\) −0.474017 + 0.304632i −0.474017 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −2.94931 + 0.424047i −2.94931 + 0.424047i
\(289\) −0.881761 0.258908i −0.881761 0.258908i
\(290\) 0 0
\(291\) −2.01144 + 2.68697i −2.01144 + 2.68697i
\(292\) 0.989821 1.14231i 0.989821 1.14231i
\(293\) 0 0 −0.599278 0.800541i \(-0.704545\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(294\) 1.98982 + 0.142315i 1.98982 + 0.142315i
\(295\) 0 0
\(296\) 0 0
\(297\) −3.44323 + 6.30580i −3.44323 + 6.30580i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.98982 + 0.142315i −1.98982 + 0.142315i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.494217 + 0.494217i −0.494217 + 0.494217i
\(305\) 0 0
\(306\) −0.713463 0.458515i −0.713463 0.458515i
\(307\) 1.45027 + 1.25667i 1.45027 + 1.25667i 0.909632 + 0.415415i \(0.136364\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(312\) 0 0
\(313\) −0.398326 + 0.148568i −0.398326 + 0.148568i −0.540641 0.841254i \(-0.681818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.198429 + 0.0141919i −0.198429 + 0.0141919i
\(324\) 3.20792 + 3.70214i 3.20792 + 3.70214i
\(325\) 0 0
\(326\) −0.0683785 + 0.125226i −0.0683785 + 0.125226i
\(327\) 0 0
\(328\) 0.100889 1.41061i 0.100889 1.41061i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.544078 0.627899i 0.544078 0.627899i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(332\) 0.574406 0.767317i 0.574406 0.767317i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.83107 + 0.398326i −1.83107 + 0.398326i −0.989821 0.142315i \(-0.954545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(338\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(339\) 1.89265 + 0.272122i 1.89265 + 0.272122i
\(340\) 0 0
\(341\) 0 0
\(342\) 2.03496 + 0.442679i 2.03496 + 0.442679i
\(343\) 0 0
\(344\) 0.847507 + 0.847507i 0.847507 + 0.847507i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.304632 0.474017i 0.304632 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(348\) 0 0
\(349\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.74557 0.512546i 1.74557 0.512546i
\(353\) 0.203743 + 0.373128i 0.203743 + 0.373128i 0.959493 0.281733i \(-0.0909091\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(354\) 0.454554 + 3.16150i 0.454554 + 3.16150i
\(355\) 0 0
\(356\) −0.841254 0.540641i −0.841254 0.540641i
\(357\) 0 0
\(358\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(359\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(360\) 0 0
\(361\) −0.465276 + 0.212484i −0.465276 + 0.212484i
\(362\) 0 0
\(363\) 1.61022 4.31716i 1.61022 4.31716i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(368\) 0 0
\(369\) −3.69841 + 2.01948i −3.69841 + 2.01948i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(374\) 0.471022 + 0.215109i 0.471022 + 0.215109i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.415415 + 1.90963i 0.415415 + 1.90963i 0.415415 + 0.909632i \(0.363636\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.997452 0.0713392i \(-0.977273\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(384\) 0.142315 1.98982i 0.142315 1.98982i
\(385\) 0 0
\(386\) 0.203743 0.373128i 0.203743 0.373128i
\(387\) 0.759127 3.48965i 0.759127 3.48965i
\(388\) −1.10181 1.27155i −1.10181 1.27155i
\(389\) 0 0 0.997452 0.0713392i \(-0.0227273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(393\) 1.84751 1.84751i 1.84751 1.84751i
\(394\) 0 0
\(395\) 0 0
\(396\) −4.09673 3.54984i −4.09673 3.54984i
\(397\) 0 0 −0.877679 0.479249i \(-0.840909\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.142315 0.989821i 0.142315 0.989821i
\(401\) −0.153882 + 1.07028i −0.153882 + 1.07028i 0.755750 + 0.654861i \(0.227273\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(402\) 2.02105 0.753813i 2.02105 0.753813i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.401502 0.401502i 0.401502 0.401502i
\(409\) 0.474017 1.61435i 0.474017 1.61435i −0.281733 0.959493i \(-0.590909\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(410\) 0 0
\(411\) 3.19401i 3.19401i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.118239 1.65320i 0.118239 1.65320i
\(418\) −1.26830 0.0907103i −1.26830 0.0907103i
\(419\) −0.254771 0.340335i −0.254771 0.340335i 0.654861 0.755750i \(-0.272727\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(420\) 0 0
\(421\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(422\) −0.254771 1.17116i −0.254771 1.17116i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.215109 0.186393i 0.215109 0.186393i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.977147 0.212565i \(-0.931818\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(432\) −3.46613 + 1.89265i −3.46613 + 1.89265i
\(433\) 0.100889 + 0.100889i 0.100889 + 0.100889i 0.755750 0.654861i \(-0.227273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.05374 2.82518i 1.05374 2.82518i
\(439\) 0 0 0.800541 0.599278i \(-0.204545\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(440\) 0 0
\(441\) 2.85895 0.839462i 2.85895 0.839462i
\(442\) 0 0
\(443\) −0.0801894 0.557730i −0.0801894 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.540641 + 0.158746i −0.540641 + 0.158746i −0.540641 0.841254i \(-0.681818\pi\)
1.00000i \(0.5\pi\)
\(450\) −2.71038 + 1.23779i −2.71038 + 1.23779i
\(451\) 2.05965 1.54184i 2.05965 1.54184i
\(452\) −0.334961 + 0.898064i −0.334961 + 0.898064i
\(453\) 0 0
\(454\) 0.817178 1.27155i 0.817178 1.27155i
\(455\) 0 0
\(456\) −0.579211 + 1.26830i −0.579211 + 1.26830i
\(457\) 1.38189 + 1.38189i 1.38189 + 1.38189i 0.841254 + 0.540641i \(0.181818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(458\) 0 0
\(459\) −1.09837 0.238936i −1.09837 0.238936i
\(460\) 0 0
\(461\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(462\) 0 0
\(463\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.89945 0.273100i 1.89945 0.273100i
\(467\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.59700 0.114220i −1.59700 0.114220i
\(473\) −0.155554 + 2.17493i −0.155554 + 2.17493i
\(474\) 0 0
\(475\) −0.334961 + 0.613435i −0.334961 + 0.613435i
\(476\) 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
\(482\) −1.24123 + 1.24123i −1.24123 + 1.24123i
\(483\) 0 0
\(484\) 1.94306 + 1.24873i 1.94306 + 1.24873i
\(485\) 0 0
\(486\) 5.11081 + 2.79071i 5.11081 + 2.79071i
\(487\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(488\) 0 0
\(489\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(490\) 0 0
\(491\) 1.75575 0.654861i 1.75575 0.654861i 0.755750 0.654861i \(-0.227273\pi\)
1.00000 \(0\)
\(492\) −0.794830 2.70694i −0.794830 2.70694i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.538704 1.83466i 0.538704 1.83466i
\(499\) −0.125226 1.75089i −0.125226 1.75089i −0.540641 0.841254i \(-0.681818\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.25667 1.45027i −1.25667 1.45027i
\(503\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.98982 + 0.142315i 1.98982 + 0.142315i
\(508\) 0 0
\(509\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(513\) 2.73211 0.392818i 2.73211 0.392818i
\(514\) −0.627899 + 0.544078i −0.627899 + 0.544078i
\(515\) 0 0
\(516\) 2.17493 + 0.993259i 2.17493 + 0.993259i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.05195 0.574406i 1.05195 0.574406i 0.142315 0.989821i \(-0.454545\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(522\) 0 0
\(523\) −0.627899 + 1.37491i −0.627899 + 1.37491i 0.281733 + 0.959493i \(0.409091\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(524\) 0.708089 + 1.10181i 0.708089 + 1.10181i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 2.90537 2.17493i 2.90537 2.17493i
\(529\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(530\) 0 0
\(531\) 2.28633 + 4.18710i 2.28633 + 4.18710i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.94931 0.424047i −1.94931 0.424047i
\(535\) 0 0
\(536\) 0.153882 + 1.07028i 0.153882 + 1.07028i
\(537\) 1.60857 + 2.94588i 1.60857 + 2.94588i
\(538\) 0 0
\(539\) −1.65486 + 0.755750i −1.65486 + 0.755750i
\(540\) 0 0
\(541\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.153882 + 0.239446i 0.153882 + 0.239446i
\(545\) 0 0
\(546\) 0 0
\(547\) −1.64468 + 0.898064i −1.64468 + 0.898064i −0.654861 + 0.755750i \(0.727273\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(548\) −1.56449 0.340335i −1.56449 0.340335i
\(549\) 0 0
\(550\) 1.53046 0.983568i 1.53046 0.983568i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(557\) 0 0 −0.212565 0.977147i \(-0.568182\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 1.03036 + 0.0736930i 1.03036 + 0.0736930i
\(562\) 0.133682 1.86912i 0.133682 1.86912i
\(563\) 1.75575 + 0.654861i 1.75575 + 0.654861i 1.00000 \(0\)
0.755750 + 0.654861i \(0.227273\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.368991 0.425839i −0.368991 0.425839i
\(567\) 0 0
\(568\) 0 0
\(569\) 0.139418 + 1.94931i 0.139418 + 1.94931i 0.281733 + 0.959493i \(0.409091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(570\) 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
\(576\) −0.839462 2.85895i −0.839462 2.85895i
\(577\) 0.654861 0.244250i 0.654861 0.244250i 1.00000i \(-0.5\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(578\) 0.130785 0.909632i 0.130785 0.909632i
\(579\) 0.120696 0.839462i 0.120696 0.839462i
\(580\) 0 0
\(581\) 0 0
\(582\) −2.94588 1.60857i −2.94588 1.60857i
\(583\) 0 0
\(584\) 1.27155 + 0.817178i 1.27155 + 0.817178i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.234072 + 0.797176i −0.234072 + 0.797176i 0.755750 + 0.654861i \(0.227273\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(588\) 0.142315 + 1.98982i 0.142315 + 1.98982i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.936593 + 1.71524i −0.936593 + 1.71524i −0.281733 + 0.959493i \(0.590909\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(594\) −6.73164 2.51077i −6.73164 2.51077i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(600\) −0.424047 1.94931i −0.424047 1.94931i
\(601\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 0 0
\(603\) 2.43490 2.10985i 2.43490 2.10985i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(608\) −0.559521 0.418852i −0.559521 0.418852i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.352311 0.771454i 0.352311 0.771454i
\(613\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(614\) −1.03748 + 1.61435i −1.03748 + 1.61435i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.114220 + 0.0855040i −0.114220 + 0.0855040i −0.654861 0.755750i \(-0.727273\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(618\) 0 0
\(619\) −1.25667 + 0.368991i −1.25667 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.142315 0.989821i −0.142315 0.989821i
\(626\) −0.203743 0.373128i −0.203743 0.373128i
\(627\) −2.43384 + 0.714640i −2.43384 + 0.714640i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(632\) 0 0
\(633\) −1.29267 2.01144i −1.29267 2.01144i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.19136 0.544078i −1.19136 0.544078i −0.281733 0.959493i \(-0.590909\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(642\) 0 0
\(643\) 1.27155 1.10181i 1.27155 1.10181i 0.281733 0.959493i \(-0.409091\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.0422868 0.194389i −0.0422868 0.194389i
\(647\) 0 0 0.599278 0.800541i \(-0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(648\) −3.20792 + 3.70214i −3.20792 + 3.70214i
\(649\) −1.74557 2.33181i −1.74557 2.33181i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.133682 0.0498610i −0.133682 0.0498610i
\(653\) 0 0 0.479249 0.877679i \(-0.340909\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.41061 0.100889i 1.41061 0.100889i
\(657\) 4.50373i 4.50373i
\(658\) 0 0
\(659\) −0.368991 + 1.25667i −0.368991 + 1.25667i 0.540641 + 0.841254i \(0.318182\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(660\) 0 0
\(661\) 0 0 −0.349464 0.936950i \(-0.613636\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(662\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(663\) 0 0
\(664\) 0.841254 + 0.459359i 0.841254 + 0.459359i
\(665\) 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 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(674\) −0.654861 1.75575i −0.654861 1.75575i
\(675\) −2.79250 + 2.79250i −2.79250 + 2.79250i
\(676\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(677\) 0 0 −0.0713392 0.997452i \(-0.522727\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(678\) 1.91211i 1.91211i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.640947 2.94639i 0.640947 2.94639i
\(682\) 0 0
\(683\) 0.133682 + 0.0498610i 0.133682 + 0.0498610i 0.415415 0.909632i \(-0.363636\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(684\) −0.148568 + 2.07725i −0.148568 + 2.07725i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.718267 + 0.959493i −0.718267 + 0.959493i
\(689\) 0 0
\(690\) 0 0
\(691\) 1.89945 0.273100i 1.89945 0.273100i 0.909632 0.415415i \(-0.136364\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.512546 + 0.234072i 0.512546 + 0.234072i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.322240 + 0.241226i 0.322240 + 0.241226i
\(698\) 0 0
\(699\) 3.35992 1.83466i 3.35992 1.83466i
\(700\) 0 0
\(701\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(705\) 0 0
\(706\) −0.340335 + 0.254771i −0.340335 + 0.254771i
\(707\) 0 0
\(708\) −3.06463 + 0.899856i −3.06463 + 0.899856i
\(709\) 0 0 −0.479249 0.877679i \(-0.659091\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.415415 0.909632i 0.415415 0.909632i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.349464 0.936950i \(-0.386364\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.276537 0.430300i −0.276537 0.430300i
\(723\) −1.45469 + 3.18532i −1.45469 + 3.18532i
\(724\) 0 0
\(725\) 0 0
\(726\) 4.50237 + 0.979431i 4.50237 + 0.979431i
\(727\) 0 0 −0.800541 0.599278i \(-0.795455\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(728\) 0 0
\(729\) 6.64951 + 0.956056i 6.64951 + 0.956056i
\(730\) 0 0
\(731\) −0.333348 + 0.0725155i −0.333348 + 0.0725155i
\(732\) 0 0
\(733\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.28820 + 1.48666i −1.28820 + 1.48666i
\(738\) −2.52527 3.37336i −2.52527 3.37336i
\(739\) 0.424047 + 0.0303285i 0.424047 + 0.0303285i 0.281733 0.959493i \(-0.409091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.212565 0.977147i \(-0.431818\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.203743 2.84870i −0.203743 2.84870i
\(748\) −0.145886 + 0.496841i −0.145886 + 0.496841i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(752\) 0 0
\(753\) −3.35992 1.83466i −3.35992 1.83466i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(758\) −1.83107 + 0.682956i −1.83107 + 0.682956i
\(759\) 0 0
\(760\) 0 0
\(761\) −1.37491 1.19136i −1.37491 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.98982 0.142315i 1.98982 0.142315i
\(769\) 0.368991 + 0.425839i 0.368991 + 0.425839i 0.909632 0.415415i \(-0.136364\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(770\) 0 0
\(771\) −0.794320 + 1.45469i −0.794320 + 1.45469i
\(772\) 0.398326 + 0.148568i 0.398326 + 0.148568i
\(773\) 0 0 0.0713392 0.997452i \(-0.477273\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(774\) 3.56217 + 0.254771i 3.56217 + 0.254771i
\(775\) 0 0
\(776\) 1.10181 1.27155i 1.10181 1.27155i
\(777\) 0 0
\(778\) 0 0
\(779\) −0.948395 0.278474i −0.948395 0.278474i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.989821 0.142315i −0.989821 0.142315i
\(785\) 0 0
\(786\) 2.09163 + 1.56577i 2.09163 + 1.56577i
\(787\) 1.71524 + 0.373128i 1.71524 + 0.373128i 0.959493 0.281733i \(-0.0909091\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 2.93068 4.56023i 2.93068 4.56023i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0