Properties

Label 945.2.a.b.1.1
Level 945
Weight 2
Character 945.1
Self dual Yes
Analytic conductor 7.546
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.54586299101\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\)
Character \(\chi\) = 945.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.41421 q^{2}\) \(+3.82843 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(-4.41421 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.41421 q^{2}\) \(+3.82843 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(-4.41421 q^{8}\) \(+2.41421 q^{10}\) \(-0.414214 q^{11}\) \(+2.41421 q^{13}\) \(+2.41421 q^{14}\) \(+3.00000 q^{16}\) \(-4.82843 q^{17}\) \(+1.58579 q^{19}\) \(-3.82843 q^{20}\) \(+1.00000 q^{22}\) \(+0.828427 q^{23}\) \(+1.00000 q^{25}\) \(-5.82843 q^{26}\) \(-3.82843 q^{28}\) \(+4.00000 q^{29}\) \(+6.00000 q^{31}\) \(+1.58579 q^{32}\) \(+11.6569 q^{34}\) \(+1.00000 q^{35}\) \(-8.48528 q^{37}\) \(-3.82843 q^{38}\) \(+4.41421 q^{40}\) \(+7.82843 q^{41}\) \(-6.65685 q^{43}\) \(-1.58579 q^{44}\) \(-2.00000 q^{46}\) \(-7.48528 q^{47}\) \(+1.00000 q^{49}\) \(-2.41421 q^{50}\) \(+9.24264 q^{52}\) \(+10.8995 q^{53}\) \(+0.414214 q^{55}\) \(+4.41421 q^{56}\) \(-9.65685 q^{58}\) \(+6.48528 q^{59}\) \(-8.48528 q^{61}\) \(-14.4853 q^{62}\) \(-9.82843 q^{64}\) \(-2.41421 q^{65}\) \(+7.82843 q^{67}\) \(-18.4853 q^{68}\) \(-2.41421 q^{70}\) \(-2.00000 q^{71}\) \(-2.07107 q^{73}\) \(+20.4853 q^{74}\) \(+6.07107 q^{76}\) \(+0.414214 q^{77}\) \(+14.8284 q^{79}\) \(-3.00000 q^{80}\) \(-18.8995 q^{82}\) \(+7.48528 q^{83}\) \(+4.82843 q^{85}\) \(+16.0711 q^{86}\) \(+1.82843 q^{88}\) \(+8.65685 q^{89}\) \(-2.41421 q^{91}\) \(+3.17157 q^{92}\) \(+18.0711 q^{94}\) \(-1.58579 q^{95}\) \(+14.1421 q^{97}\) \(-2.41421 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 2q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 6q^{32} \) \(\mathstrut +\mathstrut 12q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 14q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 20q^{68} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 24q^{74} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 18q^{86} \) \(\mathstrut -\mathstrut 2q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 22q^{94} \) \(\mathstrut -\mathstrut 6q^{95} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41421 −1.70711 −0.853553 0.521005i \(-0.825557\pi\)
−0.853553 + 0.521005i \(0.825557\pi\)
\(3\) 0 0
\(4\) 3.82843 1.91421
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −4.41421 −1.56066
\(9\) 0 0
\(10\) 2.41421 0.763441
\(11\) −0.414214 −0.124890 −0.0624450 0.998048i \(-0.519890\pi\)
−0.0624450 + 0.998048i \(0.519890\pi\)
\(12\) 0 0
\(13\) 2.41421 0.669582 0.334791 0.942292i \(-0.391334\pi\)
0.334791 + 0.942292i \(0.391334\pi\)
\(14\) 2.41421 0.645226
\(15\) 0 0
\(16\) 3.00000 0.750000
\(17\) −4.82843 −1.17107 −0.585533 0.810649i \(-0.699115\pi\)
−0.585533 + 0.810649i \(0.699115\pi\)
\(18\) 0 0
\(19\) 1.58579 0.363804 0.181902 0.983317i \(-0.441775\pi\)
0.181902 + 0.983317i \(0.441775\pi\)
\(20\) −3.82843 −0.856062
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 0.828427 0.172739 0.0863695 0.996263i \(-0.472473\pi\)
0.0863695 + 0.996263i \(0.472473\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −5.82843 −1.14305
\(27\) 0 0
\(28\) −3.82843 −0.723505
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 1.58579 0.280330
\(33\) 0 0
\(34\) 11.6569 1.99913
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −8.48528 −1.39497 −0.697486 0.716599i \(-0.745698\pi\)
−0.697486 + 0.716599i \(0.745698\pi\)
\(38\) −3.82843 −0.621053
\(39\) 0 0
\(40\) 4.41421 0.697948
\(41\) 7.82843 1.22259 0.611297 0.791401i \(-0.290648\pi\)
0.611297 + 0.791401i \(0.290648\pi\)
\(42\) 0 0
\(43\) −6.65685 −1.01516 −0.507580 0.861604i \(-0.669460\pi\)
−0.507580 + 0.861604i \(0.669460\pi\)
\(44\) −1.58579 −0.239066
\(45\) 0 0
\(46\) −2.00000 −0.294884
\(47\) −7.48528 −1.09184 −0.545920 0.837837i \(-0.683820\pi\)
−0.545920 + 0.837837i \(0.683820\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −2.41421 −0.341421
\(51\) 0 0
\(52\) 9.24264 1.28172
\(53\) 10.8995 1.49716 0.748580 0.663044i \(-0.230736\pi\)
0.748580 + 0.663044i \(0.230736\pi\)
\(54\) 0 0
\(55\) 0.414214 0.0558525
\(56\) 4.41421 0.589874
\(57\) 0 0
\(58\) −9.65685 −1.26801
\(59\) 6.48528 0.844312 0.422156 0.906523i \(-0.361273\pi\)
0.422156 + 0.906523i \(0.361273\pi\)
\(60\) 0 0
\(61\) −8.48528 −1.08643 −0.543214 0.839594i \(-0.682793\pi\)
−0.543214 + 0.839594i \(0.682793\pi\)
\(62\) −14.4853 −1.83963
\(63\) 0 0
\(64\) −9.82843 −1.22855
\(65\) −2.41421 −0.299446
\(66\) 0 0
\(67\) 7.82843 0.956395 0.478197 0.878252i \(-0.341290\pi\)
0.478197 + 0.878252i \(0.341290\pi\)
\(68\) −18.4853 −2.24167
\(69\) 0 0
\(70\) −2.41421 −0.288554
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −2.07107 −0.242400 −0.121200 0.992628i \(-0.538674\pi\)
−0.121200 + 0.992628i \(0.538674\pi\)
\(74\) 20.4853 2.38137
\(75\) 0 0
\(76\) 6.07107 0.696399
\(77\) 0.414214 0.0472040
\(78\) 0 0
\(79\) 14.8284 1.66833 0.834164 0.551516i \(-0.185951\pi\)
0.834164 + 0.551516i \(0.185951\pi\)
\(80\) −3.00000 −0.335410
\(81\) 0 0
\(82\) −18.8995 −2.08710
\(83\) 7.48528 0.821616 0.410808 0.911722i \(-0.365247\pi\)
0.410808 + 0.911722i \(0.365247\pi\)
\(84\) 0 0
\(85\) 4.82843 0.523716
\(86\) 16.0711 1.73299
\(87\) 0 0
\(88\) 1.82843 0.194911
\(89\) 8.65685 0.917625 0.458812 0.888533i \(-0.348275\pi\)
0.458812 + 0.888533i \(0.348275\pi\)
\(90\) 0 0
\(91\) −2.41421 −0.253078
\(92\) 3.17157 0.330659
\(93\) 0 0
\(94\) 18.0711 1.86389
\(95\) −1.58579 −0.162698
\(96\) 0 0
\(97\) 14.1421 1.43592 0.717958 0.696086i \(-0.245077\pi\)
0.717958 + 0.696086i \(0.245077\pi\)
\(98\) −2.41421 −0.243872
\(99\) 0 0
\(100\) 3.82843 0.382843
\(101\) 19.8284 1.97300 0.986501 0.163755i \(-0.0523605\pi\)
0.986501 + 0.163755i \(0.0523605\pi\)
\(102\) 0 0
\(103\) 10.8284 1.06696 0.533478 0.845814i \(-0.320885\pi\)
0.533478 + 0.845814i \(0.320885\pi\)
\(104\) −10.6569 −1.04499
\(105\) 0 0
\(106\) −26.3137 −2.55581
\(107\) 10.4853 1.01365 0.506825 0.862049i \(-0.330819\pi\)
0.506825 + 0.862049i \(0.330819\pi\)
\(108\) 0 0
\(109\) 3.48528 0.333829 0.166915 0.985971i \(-0.446620\pi\)
0.166915 + 0.985971i \(0.446620\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 0 0
\(112\) −3.00000 −0.283473
\(113\) −2.75736 −0.259391 −0.129695 0.991554i \(-0.541400\pi\)
−0.129695 + 0.991554i \(0.541400\pi\)
\(114\) 0 0
\(115\) −0.828427 −0.0772512
\(116\) 15.3137 1.42184
\(117\) 0 0
\(118\) −15.6569 −1.44133
\(119\) 4.82843 0.442621
\(120\) 0 0
\(121\) −10.8284 −0.984402
\(122\) 20.4853 1.85465
\(123\) 0 0
\(124\) 22.9706 2.06282
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.6569 1.47806 0.739028 0.673674i \(-0.235285\pi\)
0.739028 + 0.673674i \(0.235285\pi\)
\(128\) 20.5563 1.81694
\(129\) 0 0
\(130\) 5.82843 0.511187
\(131\) −12.1421 −1.06086 −0.530432 0.847728i \(-0.677970\pi\)
−0.530432 + 0.847728i \(0.677970\pi\)
\(132\) 0 0
\(133\) −1.58579 −0.137505
\(134\) −18.8995 −1.63267
\(135\) 0 0
\(136\) 21.3137 1.82764
\(137\) 8.41421 0.718875 0.359437 0.933169i \(-0.382969\pi\)
0.359437 + 0.933169i \(0.382969\pi\)
\(138\) 0 0
\(139\) 21.3137 1.80781 0.903903 0.427738i \(-0.140690\pi\)
0.903903 + 0.427738i \(0.140690\pi\)
\(140\) 3.82843 0.323561
\(141\) 0 0
\(142\) 4.82843 0.405193
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −4.00000 −0.332182
\(146\) 5.00000 0.413803
\(147\) 0 0
\(148\) −32.4853 −2.67027
\(149\) −17.7990 −1.45815 −0.729075 0.684434i \(-0.760049\pi\)
−0.729075 + 0.684434i \(0.760049\pi\)
\(150\) 0 0
\(151\) −23.3137 −1.89724 −0.948621 0.316414i \(-0.897521\pi\)
−0.948621 + 0.316414i \(0.897521\pi\)
\(152\) −7.00000 −0.567775
\(153\) 0 0
\(154\) −1.00000 −0.0805823
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) 14.8284 1.18344 0.591719 0.806145i \(-0.298450\pi\)
0.591719 + 0.806145i \(0.298450\pi\)
\(158\) −35.7990 −2.84801
\(159\) 0 0
\(160\) −1.58579 −0.125367
\(161\) −0.828427 −0.0652892
\(162\) 0 0
\(163\) 6.34315 0.496834 0.248417 0.968653i \(-0.420090\pi\)
0.248417 + 0.968653i \(0.420090\pi\)
\(164\) 29.9706 2.34031
\(165\) 0 0
\(166\) −18.0711 −1.40259
\(167\) 11.3137 0.875481 0.437741 0.899101i \(-0.355779\pi\)
0.437741 + 0.899101i \(0.355779\pi\)
\(168\) 0 0
\(169\) −7.17157 −0.551659
\(170\) −11.6569 −0.894040
\(171\) 0 0
\(172\) −25.4853 −1.94323
\(173\) −15.3137 −1.16428 −0.582140 0.813089i \(-0.697784\pi\)
−0.582140 + 0.813089i \(0.697784\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) −1.24264 −0.0936676
\(177\) 0 0
\(178\) −20.8995 −1.56648
\(179\) 13.7279 1.02607 0.513037 0.858367i \(-0.328521\pi\)
0.513037 + 0.858367i \(0.328521\pi\)
\(180\) 0 0
\(181\) 5.65685 0.420471 0.210235 0.977651i \(-0.432577\pi\)
0.210235 + 0.977651i \(0.432577\pi\)
\(182\) 5.82843 0.432032
\(183\) 0 0
\(184\) −3.65685 −0.269587
\(185\) 8.48528 0.623850
\(186\) 0 0
\(187\) 2.00000 0.146254
\(188\) −28.6569 −2.09002
\(189\) 0 0
\(190\) 3.82843 0.277743
\(191\) 20.0711 1.45229 0.726146 0.687541i \(-0.241310\pi\)
0.726146 + 0.687541i \(0.241310\pi\)
\(192\) 0 0
\(193\) −5.51472 −0.396958 −0.198479 0.980105i \(-0.563600\pi\)
−0.198479 + 0.980105i \(0.563600\pi\)
\(194\) −34.1421 −2.45126
\(195\) 0 0
\(196\) 3.82843 0.273459
\(197\) −12.8995 −0.919051 −0.459525 0.888165i \(-0.651981\pi\)
−0.459525 + 0.888165i \(0.651981\pi\)
\(198\) 0 0
\(199\) −2.41421 −0.171139 −0.0855695 0.996332i \(-0.527271\pi\)
−0.0855695 + 0.996332i \(0.527271\pi\)
\(200\) −4.41421 −0.312132
\(201\) 0 0
\(202\) −47.8701 −3.36813
\(203\) −4.00000 −0.280745
\(204\) 0 0
\(205\) −7.82843 −0.546761
\(206\) −26.1421 −1.82141
\(207\) 0 0
\(208\) 7.24264 0.502187
\(209\) −0.656854 −0.0454356
\(210\) 0 0
\(211\) 2.48528 0.171094 0.0855469 0.996334i \(-0.472736\pi\)
0.0855469 + 0.996334i \(0.472736\pi\)
\(212\) 41.7279 2.86589
\(213\) 0 0
\(214\) −25.3137 −1.73041
\(215\) 6.65685 0.453994
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) −8.41421 −0.569882
\(219\) 0 0
\(220\) 1.58579 0.106914
\(221\) −11.6569 −0.784125
\(222\) 0 0
\(223\) −5.65685 −0.378811 −0.189405 0.981899i \(-0.560656\pi\)
−0.189405 + 0.981899i \(0.560656\pi\)
\(224\) −1.58579 −0.105955
\(225\) 0 0
\(226\) 6.65685 0.442807
\(227\) −9.48528 −0.629560 −0.314780 0.949165i \(-0.601931\pi\)
−0.314780 + 0.949165i \(0.601931\pi\)
\(228\) 0 0
\(229\) 6.34315 0.419167 0.209583 0.977791i \(-0.432789\pi\)
0.209583 + 0.977791i \(0.432789\pi\)
\(230\) 2.00000 0.131876
\(231\) 0 0
\(232\) −17.6569 −1.15923
\(233\) 14.5563 0.953618 0.476809 0.879007i \(-0.341793\pi\)
0.476809 + 0.879007i \(0.341793\pi\)
\(234\) 0 0
\(235\) 7.48528 0.488286
\(236\) 24.8284 1.61619
\(237\) 0 0
\(238\) −11.6569 −0.755602
\(239\) −24.6274 −1.59302 −0.796508 0.604629i \(-0.793322\pi\)
−0.796508 + 0.604629i \(0.793322\pi\)
\(240\) 0 0
\(241\) −15.7990 −1.01770 −0.508851 0.860854i \(-0.669930\pi\)
−0.508851 + 0.860854i \(0.669930\pi\)
\(242\) 26.1421 1.68048
\(243\) 0 0
\(244\) −32.4853 −2.07966
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 3.82843 0.243597
\(248\) −26.4853 −1.68182
\(249\) 0 0
\(250\) 2.41421 0.152688
\(251\) 1.85786 0.117267 0.0586337 0.998280i \(-0.481326\pi\)
0.0586337 + 0.998280i \(0.481326\pi\)
\(252\) 0 0
\(253\) −0.343146 −0.0215734
\(254\) −40.2132 −2.52320
\(255\) 0 0
\(256\) −29.9706 −1.87316
\(257\) −6.34315 −0.395675 −0.197837 0.980235i \(-0.563392\pi\)
−0.197837 + 0.980235i \(0.563392\pi\)
\(258\) 0 0
\(259\) 8.48528 0.527250
\(260\) −9.24264 −0.573204
\(261\) 0 0
\(262\) 29.3137 1.81101
\(263\) −3.65685 −0.225491 −0.112746 0.993624i \(-0.535965\pi\)
−0.112746 + 0.993624i \(0.535965\pi\)
\(264\) 0 0
\(265\) −10.8995 −0.669551
\(266\) 3.82843 0.234736
\(267\) 0 0
\(268\) 29.9706 1.83074
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) 12.7574 0.774954 0.387477 0.921879i \(-0.373347\pi\)
0.387477 + 0.921879i \(0.373347\pi\)
\(272\) −14.4853 −0.878299
\(273\) 0 0
\(274\) −20.3137 −1.22720
\(275\) −0.414214 −0.0249780
\(276\) 0 0
\(277\) −4.34315 −0.260954 −0.130477 0.991451i \(-0.541651\pi\)
−0.130477 + 0.991451i \(0.541651\pi\)
\(278\) −51.4558 −3.08612
\(279\) 0 0
\(280\) −4.41421 −0.263800
\(281\) −27.6569 −1.64987 −0.824935 0.565228i \(-0.808788\pi\)
−0.824935 + 0.565228i \(0.808788\pi\)
\(282\) 0 0
\(283\) −12.4853 −0.742173 −0.371086 0.928598i \(-0.621015\pi\)
−0.371086 + 0.928598i \(0.621015\pi\)
\(284\) −7.65685 −0.454351
\(285\) 0 0
\(286\) 2.41421 0.142755
\(287\) −7.82843 −0.462097
\(288\) 0 0
\(289\) 6.31371 0.371395
\(290\) 9.65685 0.567070
\(291\) 0 0
\(292\) −7.92893 −0.464006
\(293\) 18.4853 1.07992 0.539961 0.841690i \(-0.318439\pi\)
0.539961 + 0.841690i \(0.318439\pi\)
\(294\) 0 0
\(295\) −6.48528 −0.377588
\(296\) 37.4558 2.17708
\(297\) 0 0
\(298\) 42.9706 2.48922
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) 6.65685 0.383695
\(302\) 56.2843 3.23880
\(303\) 0 0
\(304\) 4.75736 0.272853
\(305\) 8.48528 0.485866
\(306\) 0 0
\(307\) −14.4853 −0.826719 −0.413359 0.910568i \(-0.635645\pi\)
−0.413359 + 0.910568i \(0.635645\pi\)
\(308\) 1.58579 0.0903586
\(309\) 0 0
\(310\) 14.4853 0.822709
\(311\) −14.3431 −0.813325 −0.406663 0.913578i \(-0.633308\pi\)
−0.406663 + 0.913578i \(0.633308\pi\)
\(312\) 0 0
\(313\) 27.3848 1.54788 0.773940 0.633259i \(-0.218283\pi\)
0.773940 + 0.633259i \(0.218283\pi\)
\(314\) −35.7990 −2.02025
\(315\) 0 0
\(316\) 56.7696 3.19354
\(317\) −28.4142 −1.59590 −0.797951 0.602723i \(-0.794082\pi\)
−0.797951 + 0.602723i \(0.794082\pi\)
\(318\) 0 0
\(319\) −1.65685 −0.0927660
\(320\) 9.82843 0.549426
\(321\) 0 0
\(322\) 2.00000 0.111456
\(323\) −7.65685 −0.426039
\(324\) 0 0
\(325\) 2.41421 0.133916
\(326\) −15.3137 −0.848148
\(327\) 0 0
\(328\) −34.5563 −1.90806
\(329\) 7.48528 0.412677
\(330\) 0 0
\(331\) 6.00000 0.329790 0.164895 0.986311i \(-0.447272\pi\)
0.164895 + 0.986311i \(0.447272\pi\)
\(332\) 28.6569 1.57275
\(333\) 0 0
\(334\) −27.3137 −1.49454
\(335\) −7.82843 −0.427713
\(336\) 0 0
\(337\) 28.6274 1.55943 0.779717 0.626132i \(-0.215363\pi\)
0.779717 + 0.626132i \(0.215363\pi\)
\(338\) 17.3137 0.941742
\(339\) 0 0
\(340\) 18.4853 1.00251
\(341\) −2.48528 −0.134586
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 29.3848 1.58432
\(345\) 0 0
\(346\) 36.9706 1.98755
\(347\) −3.17157 −0.170259 −0.0851295 0.996370i \(-0.527130\pi\)
−0.0851295 + 0.996370i \(0.527130\pi\)
\(348\) 0 0
\(349\) −25.7990 −1.38099 −0.690494 0.723338i \(-0.742607\pi\)
−0.690494 + 0.723338i \(0.742607\pi\)
\(350\) 2.41421 0.129045
\(351\) 0 0
\(352\) −0.656854 −0.0350104
\(353\) −26.1421 −1.39141 −0.695703 0.718330i \(-0.744907\pi\)
−0.695703 + 0.718330i \(0.744907\pi\)
\(354\) 0 0
\(355\) 2.00000 0.106149
\(356\) 33.1421 1.75653
\(357\) 0 0
\(358\) −33.1421 −1.75162
\(359\) −28.6985 −1.51465 −0.757324 0.653039i \(-0.773494\pi\)
−0.757324 + 0.653039i \(0.773494\pi\)
\(360\) 0 0
\(361\) −16.4853 −0.867646
\(362\) −13.6569 −0.717788
\(363\) 0 0
\(364\) −9.24264 −0.484446
\(365\) 2.07107 0.108405
\(366\) 0 0
\(367\) 26.0000 1.35719 0.678594 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 2.48528 0.129554
\(369\) 0 0
\(370\) −20.4853 −1.06498
\(371\) −10.8995 −0.565874
\(372\) 0 0
\(373\) 18.9706 0.982259 0.491129 0.871087i \(-0.336584\pi\)
0.491129 + 0.871087i \(0.336584\pi\)
\(374\) −4.82843 −0.249672
\(375\) 0 0
\(376\) 33.0416 1.70399
\(377\) 9.65685 0.497353
\(378\) 0 0
\(379\) 22.2843 1.14467 0.572333 0.820021i \(-0.306038\pi\)
0.572333 + 0.820021i \(0.306038\pi\)
\(380\) −6.07107 −0.311439
\(381\) 0 0
\(382\) −48.4558 −2.47922
\(383\) −10.3431 −0.528510 −0.264255 0.964453i \(-0.585126\pi\)
−0.264255 + 0.964453i \(0.585126\pi\)
\(384\) 0 0
\(385\) −0.414214 −0.0211103
\(386\) 13.3137 0.677650
\(387\) 0 0
\(388\) 54.1421 2.74865
\(389\) 17.3137 0.877840 0.438920 0.898526i \(-0.355361\pi\)
0.438920 + 0.898526i \(0.355361\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) −4.41421 −0.222951
\(393\) 0 0
\(394\) 31.1421 1.56892
\(395\) −14.8284 −0.746099
\(396\) 0 0
\(397\) 14.8284 0.744217 0.372109 0.928189i \(-0.378635\pi\)
0.372109 + 0.928189i \(0.378635\pi\)
\(398\) 5.82843 0.292153
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) −5.79899 −0.289588 −0.144794 0.989462i \(-0.546252\pi\)
−0.144794 + 0.989462i \(0.546252\pi\)
\(402\) 0 0
\(403\) 14.4853 0.721563
\(404\) 75.9117 3.77675
\(405\) 0 0
\(406\) 9.65685 0.479262
\(407\) 3.51472 0.174218
\(408\) 0 0
\(409\) −3.31371 −0.163852 −0.0819262 0.996638i \(-0.526107\pi\)
−0.0819262 + 0.996638i \(0.526107\pi\)
\(410\) 18.8995 0.933380
\(411\) 0 0
\(412\) 41.4558 2.04238
\(413\) −6.48528 −0.319120
\(414\) 0 0
\(415\) −7.48528 −0.367438
\(416\) 3.82843 0.187704
\(417\) 0 0
\(418\) 1.58579 0.0775634
\(419\) 3.17157 0.154941 0.0774707 0.996995i \(-0.475316\pi\)
0.0774707 + 0.996995i \(0.475316\pi\)
\(420\) 0 0
\(421\) −7.00000 −0.341159 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(422\) −6.00000 −0.292075
\(423\) 0 0
\(424\) −48.1127 −2.33656
\(425\) −4.82843 −0.234213
\(426\) 0 0
\(427\) 8.48528 0.410632
\(428\) 40.1421 1.94034
\(429\) 0 0
\(430\) −16.0711 −0.775016
\(431\) 36.4142 1.75401 0.877005 0.480480i \(-0.159538\pi\)
0.877005 + 0.480480i \(0.159538\pi\)
\(432\) 0 0
\(433\) −29.8701 −1.43546 −0.717732 0.696320i \(-0.754820\pi\)
−0.717732 + 0.696320i \(0.754820\pi\)
\(434\) 14.4853 0.695316
\(435\) 0 0
\(436\) 13.3431 0.639021
\(437\) 1.31371 0.0628432
\(438\) 0 0
\(439\) 10.7574 0.513421 0.256710 0.966488i \(-0.417361\pi\)
0.256710 + 0.966488i \(0.417361\pi\)
\(440\) −1.82843 −0.0871668
\(441\) 0 0
\(442\) 28.1421 1.33858
\(443\) −7.02944 −0.333979 −0.166989 0.985959i \(-0.553405\pi\)
−0.166989 + 0.985959i \(0.553405\pi\)
\(444\) 0 0
\(445\) −8.65685 −0.410374
\(446\) 13.6569 0.646671
\(447\) 0 0
\(448\) 9.82843 0.464350
\(449\) 11.1716 0.527219 0.263610 0.964629i \(-0.415087\pi\)
0.263610 + 0.964629i \(0.415087\pi\)
\(450\) 0 0
\(451\) −3.24264 −0.152690
\(452\) −10.5563 −0.496529
\(453\) 0 0
\(454\) 22.8995 1.07473
\(455\) 2.41421 0.113180
\(456\) 0 0
\(457\) −30.1421 −1.40999 −0.704995 0.709212i \(-0.749051\pi\)
−0.704995 + 0.709212i \(0.749051\pi\)
\(458\) −15.3137 −0.715563
\(459\) 0 0
\(460\) −3.17157 −0.147875
\(461\) 13.6274 0.634692 0.317346 0.948310i \(-0.397208\pi\)
0.317346 + 0.948310i \(0.397208\pi\)
\(462\) 0 0
\(463\) 22.6569 1.05295 0.526477 0.850190i \(-0.323513\pi\)
0.526477 + 0.850190i \(0.323513\pi\)
\(464\) 12.0000 0.557086
\(465\) 0 0
\(466\) −35.1421 −1.62793
\(467\) −1.65685 −0.0766701 −0.0383350 0.999265i \(-0.512205\pi\)
−0.0383350 + 0.999265i \(0.512205\pi\)
\(468\) 0 0
\(469\) −7.82843 −0.361483
\(470\) −18.0711 −0.833556
\(471\) 0 0
\(472\) −28.6274 −1.31768
\(473\) 2.75736 0.126784
\(474\) 0 0
\(475\) 1.58579 0.0727609
\(476\) 18.4853 0.847271
\(477\) 0 0
\(478\) 59.4558 2.71945
\(479\) 26.1421 1.19446 0.597232 0.802068i \(-0.296267\pi\)
0.597232 + 0.802068i \(0.296267\pi\)
\(480\) 0 0
\(481\) −20.4853 −0.934048
\(482\) 38.1421 1.73733
\(483\) 0 0
\(484\) −41.4558 −1.88436
\(485\) −14.1421 −0.642161
\(486\) 0 0
\(487\) 30.3137 1.37365 0.686823 0.726825i \(-0.259005\pi\)
0.686823 + 0.726825i \(0.259005\pi\)
\(488\) 37.4558 1.69555
\(489\) 0 0
\(490\) 2.41421 0.109063
\(491\) 12.6274 0.569867 0.284934 0.958547i \(-0.408028\pi\)
0.284934 + 0.958547i \(0.408028\pi\)
\(492\) 0 0
\(493\) −19.3137 −0.869846
\(494\) −9.24264 −0.415846
\(495\) 0 0
\(496\) 18.0000 0.808224
\(497\) 2.00000 0.0897123
\(498\) 0 0
\(499\) 0.201010 0.00899845 0.00449922 0.999990i \(-0.498568\pi\)
0.00449922 + 0.999990i \(0.498568\pi\)
\(500\) −3.82843 −0.171212
\(501\) 0 0
\(502\) −4.48528 −0.200188
\(503\) 35.6274 1.58855 0.794274 0.607560i \(-0.207851\pi\)
0.794274 + 0.607560i \(0.207851\pi\)
\(504\) 0 0
\(505\) −19.8284 −0.882353
\(506\) 0.828427 0.0368281
\(507\) 0 0
\(508\) 63.7696 2.82932
\(509\) −4.34315 −0.192507 −0.0962533 0.995357i \(-0.530686\pi\)
−0.0962533 + 0.995357i \(0.530686\pi\)
\(510\) 0 0
\(511\) 2.07107 0.0916186
\(512\) 31.2426 1.38074
\(513\) 0 0
\(514\) 15.3137 0.675459
\(515\) −10.8284 −0.477158
\(516\) 0 0
\(517\) 3.10051 0.136360
\(518\) −20.4853 −0.900072
\(519\) 0 0
\(520\) 10.6569 0.467334
\(521\) −27.4853 −1.20415 −0.602076 0.798439i \(-0.705660\pi\)
−0.602076 + 0.798439i \(0.705660\pi\)
\(522\) 0 0
\(523\) 21.1716 0.925768 0.462884 0.886419i \(-0.346815\pi\)
0.462884 + 0.886419i \(0.346815\pi\)
\(524\) −46.4853 −2.03072
\(525\) 0 0
\(526\) 8.82843 0.384938
\(527\) −28.9706 −1.26198
\(528\) 0 0
\(529\) −22.3137 −0.970161
\(530\) 26.3137 1.14299
\(531\) 0 0
\(532\) −6.07107 −0.263214
\(533\) 18.8995 0.818628
\(534\) 0 0
\(535\) −10.4853 −0.453318
\(536\) −34.5563 −1.49261
\(537\) 0 0
\(538\) −33.7990 −1.45718
\(539\) −0.414214 −0.0178414
\(540\) 0 0
\(541\) −27.6274 −1.18780 −0.593898 0.804541i \(-0.702412\pi\)
−0.593898 + 0.804541i \(0.702412\pi\)
\(542\) −30.7990 −1.32293
\(543\) 0 0
\(544\) −7.65685 −0.328285
\(545\) −3.48528 −0.149293
\(546\) 0 0
\(547\) −40.2843 −1.72243 −0.861216 0.508240i \(-0.830296\pi\)
−0.861216 + 0.508240i \(0.830296\pi\)
\(548\) 32.2132 1.37608
\(549\) 0 0
\(550\) 1.00000 0.0426401
\(551\) 6.34315 0.270227
\(552\) 0 0
\(553\) −14.8284 −0.630569
\(554\) 10.4853 0.445477
\(555\) 0 0
\(556\) 81.5980 3.46053
\(557\) −43.7990 −1.85582 −0.927911 0.372801i \(-0.878397\pi\)
−0.927911 + 0.372801i \(0.878397\pi\)
\(558\) 0 0
\(559\) −16.0711 −0.679734
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) 66.7696 2.81650
\(563\) −27.9706 −1.17882 −0.589409 0.807835i \(-0.700639\pi\)
−0.589409 + 0.807835i \(0.700639\pi\)
\(564\) 0 0
\(565\) 2.75736 0.116003
\(566\) 30.1421 1.26697
\(567\) 0 0
\(568\) 8.82843 0.370433
\(569\) −8.68629 −0.364148 −0.182074 0.983285i \(-0.558281\pi\)
−0.182074 + 0.983285i \(0.558281\pi\)
\(570\) 0 0
\(571\) −43.7990 −1.83293 −0.916465 0.400114i \(-0.868970\pi\)
−0.916465 + 0.400114i \(0.868970\pi\)
\(572\) −3.82843 −0.160075
\(573\) 0 0
\(574\) 18.8995 0.788850
\(575\) 0.828427 0.0345478
\(576\) 0 0
\(577\) 5.72792 0.238457 0.119228 0.992867i \(-0.461958\pi\)
0.119228 + 0.992867i \(0.461958\pi\)
\(578\) −15.2426 −0.634010
\(579\) 0 0
\(580\) −15.3137 −0.635867
\(581\) −7.48528 −0.310542
\(582\) 0 0
\(583\) −4.51472 −0.186981
\(584\) 9.14214 0.378304
\(585\) 0 0
\(586\) −44.6274 −1.84354
\(587\) −12.6863 −0.523619 −0.261810 0.965120i \(-0.584319\pi\)
−0.261810 + 0.965120i \(0.584319\pi\)
\(588\) 0 0
\(589\) 9.51472 0.392047
\(590\) 15.6569 0.644582
\(591\) 0 0
\(592\) −25.4558 −1.04623
\(593\) 9.85786 0.404814 0.202407 0.979301i \(-0.435124\pi\)
0.202407 + 0.979301i \(0.435124\pi\)
\(594\) 0 0
\(595\) −4.82843 −0.197946
\(596\) −68.1421 −2.79121
\(597\) 0 0
\(598\) −4.82843 −0.197449
\(599\) −5.10051 −0.208401 −0.104200 0.994556i \(-0.533228\pi\)
−0.104200 + 0.994556i \(0.533228\pi\)
\(600\) 0 0
\(601\) 24.6274 1.00457 0.502287 0.864701i \(-0.332492\pi\)
0.502287 + 0.864701i \(0.332492\pi\)
\(602\) −16.0711 −0.655008
\(603\) 0 0
\(604\) −89.2548 −3.63173
\(605\) 10.8284 0.440238
\(606\) 0 0
\(607\) 40.4853 1.64325 0.821623 0.570031i \(-0.193069\pi\)
0.821623 + 0.570031i \(0.193069\pi\)
\(608\) 2.51472 0.101985
\(609\) 0 0
\(610\) −20.4853 −0.829425
\(611\) −18.0711 −0.731077
\(612\) 0 0
\(613\) 37.9411 1.53243 0.766214 0.642586i \(-0.222138\pi\)
0.766214 + 0.642586i \(0.222138\pi\)
\(614\) 34.9706 1.41130
\(615\) 0 0
\(616\) −1.82843 −0.0736694
\(617\) −24.7696 −0.997185 −0.498592 0.866837i \(-0.666150\pi\)
−0.498592 + 0.866837i \(0.666150\pi\)
\(618\) 0 0
\(619\) −26.2132 −1.05360 −0.526799 0.849990i \(-0.676608\pi\)
−0.526799 + 0.849990i \(0.676608\pi\)
\(620\) −22.9706 −0.922520
\(621\) 0 0
\(622\) 34.6274 1.38843
\(623\) −8.65685 −0.346830
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −66.1127 −2.64239
\(627\) 0 0
\(628\) 56.7696 2.26535
\(629\) 40.9706 1.63360
\(630\) 0 0
\(631\) 1.37258 0.0546417 0.0273208 0.999627i \(-0.491302\pi\)
0.0273208 + 0.999627i \(0.491302\pi\)
\(632\) −65.4558 −2.60369
\(633\) 0 0
\(634\) 68.5980 2.72437
\(635\) −16.6569 −0.661007
\(636\) 0 0
\(637\) 2.41421 0.0956546
\(638\) 4.00000 0.158362
\(639\) 0 0
\(640\) −20.5563 −0.812561
\(641\) 0.485281 0.0191675 0.00958373 0.999954i \(-0.496949\pi\)
0.00958373 + 0.999954i \(0.496949\pi\)
\(642\) 0 0
\(643\) 28.7696 1.13456 0.567280 0.823525i \(-0.307996\pi\)
0.567280 + 0.823525i \(0.307996\pi\)
\(644\) −3.17157 −0.124977
\(645\) 0 0
\(646\) 18.4853 0.727294
\(647\) 25.3431 0.996342 0.498171 0.867079i \(-0.334005\pi\)
0.498171 + 0.867079i \(0.334005\pi\)
\(648\) 0 0
\(649\) −2.68629 −0.105446
\(650\) −5.82843 −0.228610
\(651\) 0 0
\(652\) 24.2843 0.951045
\(653\) 8.20101 0.320930 0.160465 0.987042i \(-0.448701\pi\)
0.160465 + 0.987042i \(0.448701\pi\)
\(654\) 0 0
\(655\) 12.1421 0.474432
\(656\) 23.4853 0.916946
\(657\) 0 0
\(658\) −18.0711 −0.704484
\(659\) 12.3431 0.480821 0.240410 0.970671i \(-0.422718\pi\)
0.240410 + 0.970671i \(0.422718\pi\)
\(660\) 0 0
\(661\) −8.20101 −0.318982 −0.159491 0.987199i \(-0.550985\pi\)
−0.159491 + 0.987199i \(0.550985\pi\)
\(662\) −14.4853 −0.562986
\(663\) 0 0
\(664\) −33.0416 −1.28226
\(665\) 1.58579 0.0614942
\(666\) 0 0
\(667\) 3.31371 0.128307
\(668\) 43.3137 1.67586
\(669\) 0 0
\(670\) 18.8995 0.730151
\(671\) 3.51472 0.135684
\(672\) 0 0
\(673\) 3.17157 0.122255 0.0611276 0.998130i \(-0.480530\pi\)
0.0611276 + 0.998130i \(0.480530\pi\)
\(674\) −69.1127 −2.66212
\(675\) 0 0
\(676\) −27.4558 −1.05599
\(677\) −13.8579 −0.532601 −0.266300 0.963890i \(-0.585801\pi\)
−0.266300 + 0.963890i \(0.585801\pi\)
\(678\) 0 0
\(679\) −14.1421 −0.542725
\(680\) −21.3137 −0.817343
\(681\) 0 0
\(682\) 6.00000 0.229752
\(683\) 15.5147 0.593654 0.296827 0.954931i \(-0.404071\pi\)
0.296827 + 0.954931i \(0.404071\pi\)
\(684\) 0 0
\(685\) −8.41421 −0.321491
\(686\) 2.41421 0.0921751
\(687\) 0 0
\(688\) −19.9706 −0.761371
\(689\) 26.3137 1.00247
\(690\) 0 0
\(691\) 28.5563 1.08633 0.543167 0.839624i \(-0.317225\pi\)
0.543167 + 0.839624i \(0.317225\pi\)
\(692\) −58.6274 −2.22868
\(693\) 0 0
\(694\) 7.65685 0.290650
\(695\) −21.3137 −0.808475
\(696\) 0 0
\(697\) −37.7990 −1.43174
\(698\) 62.2843 2.35749
\(699\) 0 0
\(700\) −3.82843 −0.144701
\(701\) −28.3431 −1.07051 −0.535253 0.844692i \(-0.679784\pi\)
−0.535253 + 0.844692i \(0.679784\pi\)
\(702\) 0 0
\(703\) −13.4558 −0.507497
\(704\) 4.07107 0.153434
\(705\) 0 0
\(706\) 63.1127 2.37528
\(707\) −19.8284 −0.745725
\(708\) 0 0
\(709\) 1.62742 0.0611189 0.0305595 0.999533i \(-0.490271\pi\)
0.0305595 + 0.999533i \(0.490271\pi\)
\(710\) −4.82843 −0.181208
\(711\) 0 0
\(712\) −38.2132 −1.43210
\(713\) 4.97056 0.186149
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) 52.5563 1.96412
\(717\) 0 0
\(718\) 69.2843 2.58567
\(719\) 35.7990 1.33508 0.667539 0.744575i \(-0.267348\pi\)
0.667539 + 0.744575i \(0.267348\pi\)
\(720\) 0 0
\(721\) −10.8284 −0.403272
\(722\) 39.7990 1.48117
\(723\) 0 0
\(724\) 21.6569 0.804871
\(725\) 4.00000 0.148556
\(726\) 0 0
\(727\) 48.0833 1.78331 0.891655 0.452716i \(-0.149545\pi\)
0.891655 + 0.452716i \(0.149545\pi\)
\(728\) 10.6569 0.394969
\(729\) 0 0
\(730\) −5.00000 −0.185058
\(731\) 32.1421 1.18882
\(732\) 0 0
\(733\) −41.2426 −1.52333 −0.761666 0.647970i \(-0.775618\pi\)
−0.761666 + 0.647970i \(0.775618\pi\)
\(734\) −62.7696 −2.31687
\(735\) 0 0
\(736\) 1.31371 0.0484239
\(737\) −3.24264 −0.119444
\(738\) 0 0
\(739\) −35.1716 −1.29381 −0.646904 0.762572i \(-0.723936\pi\)
−0.646904 + 0.762572i \(0.723936\pi\)
\(740\) 32.4853 1.19418
\(741\) 0 0
\(742\) 26.3137 0.966007
\(743\) −11.6569 −0.427649 −0.213824 0.976872i \(-0.568592\pi\)
−0.213824 + 0.976872i \(0.568592\pi\)
\(744\) 0 0
\(745\) 17.7990 0.652105
\(746\) −45.7990 −1.67682
\(747\) 0 0
\(748\) 7.65685 0.279962
\(749\) −10.4853 −0.383124
\(750\) 0 0
\(751\) −20.8284 −0.760040 −0.380020 0.924978i \(-0.624083\pi\)
−0.380020 + 0.924978i \(0.624083\pi\)
\(752\) −22.4558 −0.818880
\(753\) 0 0
\(754\) −23.3137 −0.849035
\(755\) 23.3137 0.848473
\(756\) 0 0
\(757\) −38.4853 −1.39877 −0.699386 0.714744i \(-0.746543\pi\)
−0.699386 + 0.714744i \(0.746543\pi\)
\(758\) −53.7990 −1.95407
\(759\) 0 0
\(760\) 7.00000 0.253917
\(761\) 24.6274 0.892743 0.446372 0.894848i \(-0.352716\pi\)
0.446372 + 0.894848i \(0.352716\pi\)
\(762\) 0 0
\(763\) −3.48528 −0.126176
\(764\) 76.8406 2.78000
\(765\) 0 0
\(766\) 24.9706 0.902223
\(767\) 15.6569 0.565336
\(768\) 0 0
\(769\) 46.7696 1.68655 0.843277 0.537480i \(-0.180624\pi\)
0.843277 + 0.537480i \(0.180624\pi\)
\(770\) 1.00000 0.0360375
\(771\) 0 0
\(772\) −21.1127 −0.759863
\(773\) 44.1421 1.58768 0.793841 0.608125i \(-0.208078\pi\)
0.793841 + 0.608125i \(0.208078\pi\)
\(774\) 0 0
\(775\) 6.00000 0.215526
\(776\) −62.4264 −2.24098
\(777\) 0 0
\(778\) −41.7990 −1.49857
\(779\) 12.4142 0.444785
\(780\) 0 0
\(781\) 0.828427 0.0296435
\(782\) 9.65685 0.345328
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −14.8284 −0.529249
\(786\) 0 0
\(787\) 3.79899 0.135419 0.0677097 0.997705i \(-0.478431\pi\)
0.0677097 + 0.997705i \(0.478431\pi\)
\(788\) −49.3848 −1.75926
\(789\) 0 0
\(790\) 35.7990 1.27367
\(791\) 2.75736 0.0980404
\(792\) 0 0
\(793\) −20.4853 −0.727454
\(794\) −35.7990 −1.27046
\(795\) 0 0
\(796\) −9.24264 −0.327597
\(797\) −16.0000 −0.566749 −0.283375 0.959009i \(-0.591454\pi\)
−0.283375 + 0.959009i \(0.591454\pi\)
\(798\) 0 0
\(799\) 36.1421 1.27862
\(800\) 1.58579 0.0560660
\(801\) 0 0
\(802\) 14.0000 0.494357
\(803\) 0.857864 0.0302734
\(804\) 0 0
\(805\) 0.828427 0.0291982
\(806\) −34.9706 −1.23179
\(807\) 0 0
\(808\) −87.5269 −3.07919
\(809\) −52.0833 −1.83115 −0.915575 0.402147i \(-0.868264\pi\)
−0.915575 + 0.402147i \(0.868264\pi\)
\(810\) 0 0
\(811\) −19.3848 −0.680692 −0.340346 0.940300i \(-0.610544\pi\)
−0.340346 + 0.940300i \(0.610544\pi\)
\(812\) −15.3137 −0.537406
\(813\) 0 0
\(814\) −8.48528 −0.297409
\(815\) −6.34315 −0.222191
\(816\) 0 0
\(817\) −10.5563 −0.369320
\(818\) 8.00000 0.279713
\(819\) 0 0
\(820\) −29.9706 −1.04662
\(821\) −9.02944 −0.315130 −0.157565 0.987509i \(-0.550364\pi\)
−0.157565 + 0.987509i \(0.550364\pi\)
\(822\) 0 0
\(823\) 29.2843 1.02079 0.510393 0.859941i \(-0.329500\pi\)
0.510393 + 0.859941i \(0.329500\pi\)
\(824\) −47.7990 −1.66516
\(825\) 0 0
\(826\) 15.6569 0.544772
\(827\) −36.4853 −1.26872 −0.634359 0.773039i \(-0.718736\pi\)
−0.634359 + 0.773039i \(0.718736\pi\)
\(828\) 0 0
\(829\) −21.1716 −0.735319 −0.367660 0.929960i \(-0.619841\pi\)
−0.367660 + 0.929960i \(0.619841\pi\)
\(830\) 18.0711 0.627256
\(831\) 0 0
\(832\) −23.7279 −0.822618
\(833\) −4.82843 −0.167295
\(834\) 0 0
\(835\) −11.3137 −0.391527
\(836\) −2.51472 −0.0869734
\(837\) 0 0
\(838\) −7.65685 −0.264502
\(839\) 25.7990 0.890680 0.445340 0.895362i \(-0.353083\pi\)
0.445340 + 0.895362i \(0.353083\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 16.8995 0.582395
\(843\) 0 0
\(844\) 9.51472 0.327510
\(845\) 7.17157 0.246710
\(846\) 0 0
\(847\) 10.8284 0.372069
\(848\) 32.6985 1.12287
\(849\) 0 0
\(850\) 11.6569 0.399827
\(851\) −7.02944 −0.240966
\(852\) 0 0
\(853\) −4.48528 −0.153573 −0.0767866 0.997048i \(-0.524466\pi\)
−0.0767866 + 0.997048i \(0.524466\pi\)
\(854\) −20.4853 −0.700992
\(855\) 0 0
\(856\) −46.2843 −1.58196
\(857\) −17.3137 −0.591425 −0.295713 0.955277i \(-0.595557\pi\)
−0.295713 + 0.955277i \(0.595557\pi\)
\(858\) 0 0
\(859\) −38.3553 −1.30867 −0.654334 0.756206i \(-0.727051\pi\)
−0.654334 + 0.756206i \(0.727051\pi\)
\(860\) 25.4853 0.869041
\(861\) 0 0
\(862\) −87.9117 −2.99428
\(863\) 39.6569 1.34994 0.674968 0.737847i \(-0.264158\pi\)
0.674968 + 0.737847i \(0.264158\pi\)
\(864\) 0 0
\(865\) 15.3137 0.520682
\(866\) 72.1127 2.45049
\(867\) 0 0
\(868\) −22.9706 −0.779672
\(869\) −6.14214 −0.208358
\(870\) 0 0
\(871\) 18.8995 0.640385
\(872\) −15.3848 −0.520994
\(873\) 0 0
\(874\) −3.17157 −0.107280
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −34.8284 −1.17607 −0.588036 0.808835i \(-0.700099\pi\)
−0.588036 + 0.808835i \(0.700099\pi\)
\(878\) −25.9706 −0.876464
\(879\) 0 0
\(880\) 1.24264 0.0418894
\(881\) 15.6569 0.527493 0.263746 0.964592i \(-0.415042\pi\)
0.263746 + 0.964592i \(0.415042\pi\)
\(882\) 0 0
\(883\) 2.34315 0.0788531 0.0394266 0.999222i \(-0.487447\pi\)
0.0394266 + 0.999222i \(0.487447\pi\)
\(884\) −44.6274 −1.50098
\(885\) 0 0
\(886\) 16.9706 0.570137
\(887\) 17.7696 0.596643 0.298322 0.954465i \(-0.403573\pi\)
0.298322 + 0.954465i \(0.403573\pi\)
\(888\) 0 0
\(889\) −16.6569 −0.558653
\(890\) 20.8995 0.700553
\(891\) 0 0
\(892\) −21.6569 −0.725125
\(893\) −11.8701 −0.397216
\(894\) 0 0
\(895\) −13.7279 −0.458874
\(896\) −20.5563 −0.686739
\(897\) 0 0
\(898\) −26.9706 −0.900019
\(899\) 24.0000 0.800445
\(900\) 0 0
\(901\) −52.6274 −1.75327
\(902\) 7.82843 0.260658
\(903\) 0 0
\(904\) 12.1716 0.404820
\(905\) −5.65685 −0.188040
\(906\) 0 0
\(907\) −26.5147 −0.880407 −0.440203 0.897898i \(-0.645094\pi\)
−0.440203 + 0.897898i \(0.645094\pi\)
\(908\) −36.3137 −1.20511
\(909\) 0 0
\(910\) −5.82843 −0.193210
\(911\) 40.8406 1.35311 0.676555 0.736392i \(-0.263472\pi\)
0.676555 + 0.736392i \(0.263472\pi\)
\(912\) 0 0
\(913\) −3.10051 −0.102612
\(914\) 72.7696 2.40700
\(915\) 0 0
\(916\) 24.2843 0.802375
\(917\) 12.1421 0.400969
\(918\) 0 0
\(919\) 36.7696 1.21292 0.606458 0.795116i \(-0.292590\pi\)
0.606458 + 0.795116i \(0.292590\pi\)
\(920\) 3.65685 0.120563
\(921\) 0 0
\(922\) −32.8995 −1.08349
\(923\) −4.82843 −0.158930
\(924\) 0 0
\(925\) −8.48528 −0.278994
\(926\) −54.6985 −1.79750
\(927\) 0 0
\(928\) 6.34315 0.208224
\(929\) −10.0294 −0.329055 −0.164528 0.986372i \(-0.552610\pi\)
−0.164528 + 0.986372i \(0.552610\pi\)
\(930\) 0 0
\(931\) 1.58579 0.0519721
\(932\) 55.7279 1.82543
\(933\) 0 0
\(934\) 4.00000 0.130884
\(935\) −2.00000 −0.0654070
\(936\) 0 0
\(937\) 18.8995 0.617420 0.308710 0.951156i \(-0.400103\pi\)
0.308710 + 0.951156i \(0.400103\pi\)
\(938\) 18.8995 0.617090
\(939\) 0 0
\(940\) 28.6569 0.934684
\(941\) −3.68629 −0.120170 −0.0600848 0.998193i \(-0.519137\pi\)
−0.0600848 + 0.998193i \(0.519137\pi\)
\(942\) 0 0
\(943\) 6.48528 0.211190
\(944\) 19.4558 0.633234
\(945\) 0 0
\(946\) −6.65685 −0.216433
\(947\) 9.45584 0.307274 0.153637 0.988127i \(-0.450901\pi\)
0.153637 + 0.988127i \(0.450901\pi\)
\(948\) 0 0
\(949\) −5.00000 −0.162307
\(950\) −3.82843 −0.124211
\(951\) 0 0
\(952\) −21.3137 −0.690781
\(953\) 46.1421 1.49469 0.747345 0.664436i \(-0.231328\pi\)
0.747345 + 0.664436i \(0.231328\pi\)
\(954\) 0 0
\(955\) −20.0711 −0.649485
\(956\) −94.2843 −3.04937
\(957\) 0 0
\(958\) −63.1127 −2.03908
\(959\) −8.41421 −0.271709
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 49.4558 1.59452
\(963\) 0 0
\(964\) −60.4853 −1.94810
\(965\) 5.51472 0.177525
\(966\) 0 0
\(967\) 13.8284 0.444692 0.222346 0.974968i \(-0.428629\pi\)
0.222346 + 0.974968i \(0.428629\pi\)
\(968\) 47.7990 1.53632
\(969\) 0 0
\(970\) 34.1421 1.09624
\(971\) −13.4558 −0.431819 −0.215909 0.976413i \(-0.569272\pi\)
−0.215909 + 0.976413i \(0.569272\pi\)
\(972\) 0 0
\(973\) −21.3137 −0.683286
\(974\) −73.1838 −2.34496
\(975\) 0 0
\(976\) −25.4558 −0.814822
\(977\) 43.5269 1.39255 0.696275 0.717775i \(-0.254840\pi\)
0.696275 + 0.717775i \(0.254840\pi\)
\(978\) 0 0
\(979\) −3.58579 −0.114602
\(980\) −3.82843 −0.122295
\(981\) 0 0
\(982\) −30.4853 −0.972824
\(983\) 3.02944 0.0966240 0.0483120 0.998832i \(-0.484616\pi\)
0.0483120 + 0.998832i \(0.484616\pi\)
\(984\) 0 0
\(985\) 12.8995 0.411012
\(986\) 46.6274 1.48492
\(987\) 0 0
\(988\) 14.6569 0.466297
\(989\) −5.51472 −0.175358
\(990\) 0 0
\(991\) 23.1716 0.736069 0.368035 0.929812i \(-0.380031\pi\)
0.368035 + 0.929812i \(0.380031\pi\)
\(992\) 9.51472 0.302093
\(993\) 0 0
\(994\) −4.82843 −0.153148
\(995\) 2.41421 0.0765357
\(996\) 0 0
\(997\) −31.5147 −0.998081 −0.499041 0.866579i \(-0.666314\pi\)
−0.499041 + 0.866579i \(0.666314\pi\)
\(998\) −0.485281 −0.0153613
\(999\) 0 0
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 \(a_p\))