Properties

Label 9555.2.a.u.1.1
Level $9555$
Weight $2$
Character 9555.1
Self dual yes
Analytic conductor $76.297$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9555.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(76.2970591313\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 195)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9555.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{9} +2.00000 q^{10} +5.00000 q^{11} -2.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} -4.00000 q^{16} +7.00000 q^{17} +2.00000 q^{18} +6.00000 q^{19} +2.00000 q^{20} +10.0000 q^{22} +3.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +2.00000 q^{29} -2.00000 q^{30} -2.00000 q^{31} -8.00000 q^{32} -5.00000 q^{33} +14.0000 q^{34} +2.00000 q^{36} +7.00000 q^{37} +12.0000 q^{38} -1.00000 q^{39} -9.00000 q^{41} -8.00000 q^{43} +10.0000 q^{44} +1.00000 q^{45} +6.00000 q^{46} -10.0000 q^{47} +4.00000 q^{48} +2.00000 q^{50} -7.00000 q^{51} +2.00000 q^{52} +5.00000 q^{53} -2.00000 q^{54} +5.00000 q^{55} -6.00000 q^{57} +4.00000 q^{58} -2.00000 q^{60} -5.00000 q^{61} -4.00000 q^{62} -8.00000 q^{64} +1.00000 q^{65} -10.0000 q^{66} -4.00000 q^{67} +14.0000 q^{68} -3.00000 q^{69} +9.00000 q^{71} +6.00000 q^{73} +14.0000 q^{74} -1.00000 q^{75} +12.0000 q^{76} -2.00000 q^{78} -3.00000 q^{79} -4.00000 q^{80} +1.00000 q^{81} -18.0000 q^{82} +4.00000 q^{83} +7.00000 q^{85} -16.0000 q^{86} -2.00000 q^{87} -11.0000 q^{89} +2.00000 q^{90} +6.00000 q^{92} +2.00000 q^{93} -20.0000 q^{94} +6.00000 q^{95} +8.00000 q^{96} +11.0000 q^{97} +5.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.00000 1.00000
\(5\) 1.00000 0.447214
\(6\) −2.00000 −0.816497
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) −2.00000 −0.577350
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −4.00000 −1.00000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 2.00000 0.471405
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 10.0000 2.13201
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.00000 0.392232
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −2.00000 −0.365148
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −8.00000 −1.41421
\(33\) −5.00000 −0.870388
\(34\) 14.0000 2.40098
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 12.0000 1.94666
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 10.0000 1.50756
\(45\) 1.00000 0.149071
\(46\) 6.00000 0.884652
\(47\) −10.0000 −1.45865 −0.729325 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) 4.00000 0.577350
\(49\) 0 0
\(50\) 2.00000 0.282843
\(51\) −7.00000 −0.980196
\(52\) 2.00000 0.277350
\(53\) 5.00000 0.686803 0.343401 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(54\) −2.00000 −0.272166
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) −6.00000 −0.794719
\(58\) 4.00000 0.525226
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −2.00000 −0.258199
\(61\) −5.00000 −0.640184 −0.320092 0.947386i \(-0.603714\pi\)
−0.320092 + 0.947386i \(0.603714\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 1.00000 0.124035
\(66\) −10.0000 −1.23091
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 14.0000 1.69775
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 14.0000 1.62747
\(75\) −1.00000 −0.115470
\(76\) 12.0000 1.37649
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −3.00000 −0.337526 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) −4.00000 −0.447214
\(81\) 1.00000 0.111111
\(82\) −18.0000 −1.98777
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 7.00000 0.759257
\(86\) −16.0000 −1.72532
\(87\) −2.00000 −0.214423
\(88\) 0 0
\(89\) −11.0000 −1.16600 −0.582999 0.812473i \(-0.698121\pi\)
−0.582999 + 0.812473i \(0.698121\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 2.00000 0.207390
\(94\) −20.0000 −2.06284
\(95\) 6.00000 0.615587
\(96\) 8.00000 0.816497
\(97\) 11.0000 1.11688 0.558440 0.829545i \(-0.311400\pi\)
0.558440 + 0.829545i \(0.311400\pi\)
\(98\) 0 0
\(99\) 5.00000 0.502519
\(100\) 2.00000 0.200000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −14.0000 −1.38621
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) −17.0000 −1.64345 −0.821726 0.569883i \(-0.806989\pi\)
−0.821726 + 0.569883i \(0.806989\pi\)
\(108\) −2.00000 −0.192450
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 10.0000 0.953463
\(111\) −7.00000 −0.664411
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) −12.0000 −1.12390
\(115\) 3.00000 0.279751
\(116\) 4.00000 0.371391
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) −10.0000 −0.905357
\(123\) 9.00000 0.811503
\(124\) −4.00000 −0.359211
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 0 0
\(129\) 8.00000 0.704361
\(130\) 2.00000 0.175412
\(131\) 22.0000 1.92215 0.961074 0.276289i \(-0.0891049\pi\)
0.961074 + 0.276289i \(0.0891049\pi\)
\(132\) −10.0000 −0.870388
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −14.0000 −1.19610 −0.598050 0.801459i \(-0.704058\pi\)
−0.598050 + 0.801459i \(0.704058\pi\)
\(138\) −6.00000 −0.510754
\(139\) −15.0000 −1.27228 −0.636142 0.771572i \(-0.719471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(140\) 0 0
\(141\) 10.0000 0.842152
\(142\) 18.0000 1.51053
\(143\) 5.00000 0.418121
\(144\) −4.00000 −0.333333
\(145\) 2.00000 0.166091
\(146\) 12.0000 0.993127
\(147\) 0 0
\(148\) 14.0000 1.15079
\(149\) 15.0000 1.22885 0.614424 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) −2.00000 −0.163299
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 7.00000 0.565916
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) −2.00000 −0.160128
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) −6.00000 −0.477334
\(159\) −5.00000 −0.396526
\(160\) −8.00000 −0.632456
\(161\) 0 0
\(162\) 2.00000 0.157135
\(163\) 15.0000 1.17489 0.587445 0.809264i \(-0.300134\pi\)
0.587445 + 0.809264i \(0.300134\pi\)
\(164\) −18.0000 −1.40556
\(165\) −5.00000 −0.389249
\(166\) 8.00000 0.620920
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 14.0000 1.07375
\(171\) 6.00000 0.458831
\(172\) −16.0000 −1.21999
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) −4.00000 −0.303239
\(175\) 0 0
\(176\) −20.0000 −1.50756
\(177\) 0 0
\(178\) −22.0000 −1.64897
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 2.00000 0.149071
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) 5.00000 0.369611
\(184\) 0 0
\(185\) 7.00000 0.514650
\(186\) 4.00000 0.293294
\(187\) 35.0000 2.55945
\(188\) −20.0000 −1.45865
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 8.00000 0.577350
\(193\) −17.0000 −1.22369 −0.611843 0.790979i \(-0.709572\pi\)
−0.611843 + 0.790979i \(0.709572\pi\)
\(194\) 22.0000 1.57951
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) 24.0000 1.70993 0.854965 0.518686i \(-0.173579\pi\)
0.854965 + 0.518686i \(0.173579\pi\)
\(198\) 10.0000 0.710669
\(199\) 28.0000 1.98487 0.992434 0.122782i \(-0.0391815\pi\)
0.992434 + 0.122782i \(0.0391815\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 0 0
\(203\) 0 0
\(204\) −14.0000 −0.980196
\(205\) −9.00000 −0.628587
\(206\) 8.00000 0.557386
\(207\) 3.00000 0.208514
\(208\) −4.00000 −0.277350
\(209\) 30.0000 2.07514
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 10.0000 0.686803
\(213\) −9.00000 −0.616670
\(214\) −34.0000 −2.32419
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 0 0
\(218\) 8.00000 0.541828
\(219\) −6.00000 −0.405442
\(220\) 10.0000 0.674200
\(221\) 7.00000 0.470871
\(222\) −14.0000 −0.939618
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 20.0000 1.33038
\(227\) 2.00000 0.132745 0.0663723 0.997795i \(-0.478857\pi\)
0.0663723 + 0.997795i \(0.478857\pi\)
\(228\) −12.0000 −0.794719
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 0 0
\(233\) 19.0000 1.24473 0.622366 0.782727i \(-0.286172\pi\)
0.622366 + 0.782727i \(0.286172\pi\)
\(234\) 2.00000 0.130744
\(235\) −10.0000 −0.652328
\(236\) 0 0
\(237\) 3.00000 0.194871
\(238\) 0 0
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) 4.00000 0.258199
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 28.0000 1.79991
\(243\) −1.00000 −0.0641500
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 18.0000 1.14764
\(247\) 6.00000 0.381771
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 2.00000 0.126491
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 15.0000 0.943042
\(254\) −4.00000 −0.250982
\(255\) −7.00000 −0.438357
\(256\) 16.0000 1.00000
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 16.0000 0.996116
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 2.00000 0.123797
\(262\) 44.0000 2.71833
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 5.00000 0.307148
\(266\) 0 0
\(267\) 11.0000 0.673189
\(268\) −8.00000 −0.488678
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) −2.00000 −0.121716
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) −28.0000 −1.69775
\(273\) 0 0
\(274\) −28.0000 −1.69154
\(275\) 5.00000 0.301511
\(276\) −6.00000 −0.361158
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −30.0000 −1.79928
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 20.0000 1.19098
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 18.0000 1.06810
\(285\) −6.00000 −0.355409
\(286\) 10.0000 0.591312
\(287\) 0 0
\(288\) −8.00000 −0.471405
\(289\) 32.0000 1.88235
\(290\) 4.00000 0.234888
\(291\) −11.0000 −0.644831
\(292\) 12.0000 0.702247
\(293\) −4.00000 −0.233682 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.00000 −0.290129
\(298\) 30.0000 1.73785
\(299\) 3.00000 0.173494
\(300\) −2.00000 −0.115470
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) 0 0
\(304\) −24.0000 −1.37649
\(305\) −5.00000 −0.286299
\(306\) 14.0000 0.800327
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) −4.00000 −0.227185
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −36.0000 −2.03160
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) −24.0000 −1.34797 −0.673987 0.738743i \(-0.735420\pi\)
−0.673987 + 0.738743i \(0.735420\pi\)
\(318\) −10.0000 −0.560772
\(319\) 10.0000 0.559893
\(320\) −8.00000 −0.447214
\(321\) 17.0000 0.948847
\(322\) 0 0
\(323\) 42.0000 2.33694
\(324\) 2.00000 0.111111
\(325\) 1.00000 0.0554700
\(326\) 30.0000 1.66155
\(327\) −4.00000 −0.221201
\(328\) 0 0
\(329\) 0 0
\(330\) −10.0000 −0.550482
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 8.00000 0.439057
\(333\) 7.00000 0.383598
\(334\) 48.0000 2.62644
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 2.00000 0.108786
\(339\) −10.0000 −0.543125
\(340\) 14.0000 0.759257
\(341\) −10.0000 −0.541530
\(342\) 12.0000 0.648886
\(343\) 0 0
\(344\) 0 0
\(345\) −3.00000 −0.161515
\(346\) 36.0000 1.93537
\(347\) 11.0000 0.590511 0.295255 0.955418i \(-0.404595\pi\)
0.295255 + 0.955418i \(0.404595\pi\)
\(348\) −4.00000 −0.214423
\(349\) −24.0000 −1.28469 −0.642345 0.766415i \(-0.722038\pi\)
−0.642345 + 0.766415i \(0.722038\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) −40.0000 −2.13201
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 9.00000 0.477670
\(356\) −22.0000 −1.16600
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 14.0000 0.735824
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 10.0000 0.522708
\(367\) −4.00000 −0.208798 −0.104399 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) −12.0000 −0.625543
\(369\) −9.00000 −0.468521
\(370\) 14.0000 0.727825
\(371\) 0 0
\(372\) 4.00000 0.207390
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) 70.0000 3.61961
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 12.0000 0.615587
\(381\) 2.00000 0.102463
\(382\) −24.0000 −1.22795
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −34.0000 −1.73055
\(387\) −8.00000 −0.406663
\(388\) 22.0000 1.11688
\(389\) −4.00000 −0.202808 −0.101404 0.994845i \(-0.532333\pi\)
−0.101404 + 0.994845i \(0.532333\pi\)
\(390\) −2.00000 −0.101274
\(391\) 21.0000 1.06202
\(392\) 0 0
\(393\) −22.0000 −1.10975
\(394\) 48.0000 2.41821
\(395\) −3.00000 −0.150946
\(396\) 10.0000 0.502519
\(397\) −15.0000 −0.752828 −0.376414 0.926451i \(-0.622843\pi\)
−0.376414 + 0.926451i \(0.622843\pi\)
\(398\) 56.0000 2.80703
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 8.00000 0.399004
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 35.0000 1.73489
\(408\) 0 0
\(409\) −30.0000 −1.48340 −0.741702 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) −18.0000 −0.888957
\(411\) 14.0000 0.690569
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) 6.00000 0.294884
\(415\) 4.00000 0.196352
\(416\) −8.00000 −0.392232
\(417\) 15.0000 0.734553
\(418\) 60.0000 2.93470
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −24.0000 −1.16830
\(423\) −10.0000 −0.486217
\(424\) 0 0
\(425\) 7.00000 0.339550
\(426\) −18.0000 −0.872103
\(427\) 0 0
\(428\) −34.0000 −1.64345
\(429\) −5.00000 −0.241402
\(430\) −16.0000 −0.771589
\(431\) −40.0000 −1.92673 −0.963366 0.268190i \(-0.913575\pi\)
−0.963366 + 0.268190i \(0.913575\pi\)
\(432\) 4.00000 0.192450
\(433\) 20.0000 0.961139 0.480569 0.876957i \(-0.340430\pi\)
0.480569 + 0.876957i \(0.340430\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) 8.00000 0.383131
\(437\) 18.0000 0.861057
\(438\) −12.0000 −0.573382
\(439\) −15.0000 −0.715911 −0.357955 0.933739i \(-0.616526\pi\)
−0.357955 + 0.933739i \(0.616526\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 14.0000 0.665912
\(443\) −1.00000 −0.0475114 −0.0237557 0.999718i \(-0.507562\pi\)
−0.0237557 + 0.999718i \(0.507562\pi\)
\(444\) −14.0000 −0.664411
\(445\) −11.0000 −0.521450
\(446\) 16.0000 0.757622
\(447\) −15.0000 −0.709476
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 2.00000 0.0942809
\(451\) −45.0000 −2.11897
\(452\) 20.0000 0.940721
\(453\) 8.00000 0.375873
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 0 0
\(457\) −7.00000 −0.327446 −0.163723 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(458\) −28.0000 −1.30835
\(459\) −7.00000 −0.326732
\(460\) 6.00000 0.279751
\(461\) −37.0000 −1.72326 −0.861631 0.507535i \(-0.830557\pi\)
−0.861631 + 0.507535i \(0.830557\pi\)
\(462\) 0 0
\(463\) 15.0000 0.697109 0.348555 0.937288i \(-0.386673\pi\)
0.348555 + 0.937288i \(0.386673\pi\)
\(464\) −8.00000 −0.371391
\(465\) 2.00000 0.0927478
\(466\) 38.0000 1.76032
\(467\) 1.00000 0.0462745 0.0231372 0.999732i \(-0.492635\pi\)
0.0231372 + 0.999732i \(0.492635\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) −20.0000 −0.922531
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) −40.0000 −1.83920
\(474\) 6.00000 0.275589
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) 5.00000 0.228934
\(478\) 18.0000 0.823301
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) 8.00000 0.365148
\(481\) 7.00000 0.319173
\(482\) −44.0000 −2.00415
\(483\) 0 0
\(484\) 28.0000 1.27273
\(485\) 11.0000 0.499484
\(486\) −2.00000 −0.0907218
\(487\) 5.00000 0.226572 0.113286 0.993562i \(-0.463862\pi\)
0.113286 + 0.993562i \(0.463862\pi\)
\(488\) 0 0
\(489\) −15.0000 −0.678323
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 18.0000 0.811503
\(493\) 14.0000 0.630528
\(494\) 12.0000 0.539906
\(495\) 5.00000 0.224733
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) −8.00000 −0.358489
\(499\) −14.0000 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) 2.00000 0.0894427
\(501\) −24.0000 −1.07224
\(502\) 0 0
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 30.0000 1.33366
\(507\) −1.00000 −0.0444116
\(508\) −4.00000 −0.177471
\(509\) −27.0000 −1.19675 −0.598377 0.801215i \(-0.704187\pi\)
−0.598377 + 0.801215i \(0.704187\pi\)
\(510\) −14.0000 −0.619930
\(511\) 0 0
\(512\) 32.0000 1.41421
\(513\) −6.00000 −0.264906
\(514\) −4.00000 −0.176432
\(515\) 4.00000 0.176261
\(516\) 16.0000 0.704361
\(517\) −50.0000 −2.19900
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 4.00000 0.175075
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 44.0000 1.92215
\(525\) 0 0
\(526\) −32.0000 −1.39527
\(527\) −14.0000 −0.609850
\(528\) 20.0000 0.870388
\(529\) −14.0000 −0.608696
\(530\) 10.0000 0.434372
\(531\) 0 0
\(532\) 0 0
\(533\) −9.00000 −0.389833
\(534\) 22.0000 0.952033
\(535\) −17.0000 −0.734974
\(536\) 0 0
\(537\) −6.00000 −0.258919
\(538\) 48.0000 2.06943
\(539\) 0 0
\(540\) −2.00000 −0.0860663
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 44.0000 1.88996
\(543\) −7.00000 −0.300399
\(544\) −56.0000 −2.40098
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) −28.0000 −1.19610
\(549\) −5.00000 −0.213395
\(550\) 10.0000 0.426401
\(551\) 12.0000 0.511217
\(552\) 0 0
\(553\) 0 0
\(554\) −4.00000 −0.169944
\(555\) −7.00000 −0.297133
\(556\) −30.0000 −1.27228
\(557\) −2.00000 −0.0847427 −0.0423714 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) −4.00000 −0.169334
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −35.0000 −1.47770
\(562\) 36.0000 1.51857
\(563\) −11.0000 −0.463595 −0.231797 0.972764i \(-0.574461\pi\)
−0.231797 + 0.972764i \(0.574461\pi\)
\(564\) 20.0000 0.842152
\(565\) 10.0000 0.420703
\(566\) −40.0000 −1.68133
\(567\) 0 0
\(568\) 0 0
\(569\) −20.0000 −0.838444 −0.419222 0.907884i \(-0.637697\pi\)
−0.419222 + 0.907884i \(0.637697\pi\)
\(570\) −12.0000 −0.502625
\(571\) −39.0000 −1.63210 −0.816050 0.577982i \(-0.803840\pi\)
−0.816050 + 0.577982i \(0.803840\pi\)
\(572\) 10.0000 0.418121
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) 3.00000 0.125109
\(576\) −8.00000 −0.333333
\(577\) 7.00000 0.291414 0.145707 0.989328i \(-0.453454\pi\)
0.145707 + 0.989328i \(0.453454\pi\)
\(578\) 64.0000 2.66205
\(579\) 17.0000 0.706496
\(580\) 4.00000 0.166091
\(581\) 0 0
\(582\) −22.0000 −0.911929
\(583\) 25.0000 1.03539
\(584\) 0 0
\(585\) 1.00000 0.0413449
\(586\) −8.00000 −0.330477
\(587\) 2.00000 0.0825488 0.0412744 0.999148i \(-0.486858\pi\)
0.0412744 + 0.999148i \(0.486858\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) −24.0000 −0.987228
\(592\) −28.0000 −1.15079
\(593\) 16.0000 0.657041 0.328521 0.944497i \(-0.393450\pi\)
0.328521 + 0.944497i \(0.393450\pi\)
\(594\) −10.0000 −0.410305
\(595\) 0 0
\(596\) 30.0000 1.22885
\(597\) −28.0000 −1.14596
\(598\) 6.00000 0.245358
\(599\) 20.0000 0.817178 0.408589 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) 0 0
\(601\) 5.00000 0.203954 0.101977 0.994787i \(-0.467483\pi\)
0.101977 + 0.994787i \(0.467483\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) −16.0000 −0.651031
\(605\) 14.0000 0.569181
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −48.0000 −1.94666
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) −10.0000 −0.404557
\(612\) 14.0000 0.565916
\(613\) 9.00000 0.363507 0.181753 0.983344i \(-0.441823\pi\)
0.181753 + 0.983344i \(0.441823\pi\)
\(614\) −46.0000 −1.85641
\(615\) 9.00000 0.362915
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −8.00000 −0.321807
\(619\) 38.0000 1.52735 0.763674 0.645601i \(-0.223393\pi\)
0.763674 + 0.645601i \(0.223393\pi\)
\(620\) −4.00000 −0.160644
\(621\) −3.00000 −0.120386
\(622\) −40.0000 −1.60385
\(623\) 0 0
\(624\) 4.00000 0.160128
\(625\) 1.00000 0.0400000
\(626\) 44.0000 1.75859
\(627\) −30.0000 −1.19808
\(628\) −36.0000 −1.43656
\(629\) 49.0000 1.95376
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) 12.0000 0.476957
\(634\) −48.0000 −1.90632
\(635\) −2.00000 −0.0793676
\(636\) −10.0000 −0.396526
\(637\) 0 0
\(638\) 20.0000 0.791808
\(639\) 9.00000 0.356034
\(640\) 0 0
\(641\) 20.0000 0.789953 0.394976 0.918691i \(-0.370753\pi\)
0.394976 + 0.918691i \(0.370753\pi\)
\(642\) 34.0000 1.34187
\(643\) 37.0000 1.45914 0.729569 0.683907i \(-0.239721\pi\)
0.729569 + 0.683907i \(0.239721\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 84.0000 3.30494
\(647\) −17.0000 −0.668339 −0.334169 0.942513i \(-0.608456\pi\)
−0.334169 + 0.942513i \(0.608456\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 30.0000 1.17489
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) −8.00000 −0.312825
\(655\) 22.0000 0.859611
\(656\) 36.0000 1.40556
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) −10.0000 −0.389249
\(661\) 40.0000 1.55582 0.777910 0.628376i \(-0.216280\pi\)
0.777910 + 0.628376i \(0.216280\pi\)
\(662\) 0 0
\(663\) −7.00000 −0.271857
\(664\) 0 0
\(665\) 0 0
\(666\) 14.0000 0.542489
\(667\) 6.00000 0.232321
\(668\) 48.0000 1.85718
\(669\) −8.00000 −0.309298
\(670\) −8.00000 −0.309067
\(671\) −25.0000 −0.965114
\(672\) 0 0
\(673\) 42.0000 1.61898 0.809491 0.587133i \(-0.199743\pi\)
0.809491 + 0.587133i \(0.199743\pi\)
\(674\) 16.0000 0.616297
\(675\) −1.00000 −0.0384900
\(676\) 2.00000 0.0769231
\(677\) −21.0000 −0.807096 −0.403548 0.914959i \(-0.632223\pi\)
−0.403548 + 0.914959i \(0.632223\pi\)
\(678\) −20.0000 −0.768095
\(679\) 0 0
\(680\) 0 0
\(681\) −2.00000 −0.0766402
\(682\) −20.0000 −0.765840
\(683\) 16.0000 0.612223 0.306111 0.951996i \(-0.400972\pi\)
0.306111 + 0.951996i \(0.400972\pi\)
\(684\) 12.0000 0.458831
\(685\) −14.0000 −0.534913
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) 32.0000 1.21999
\(689\) 5.00000 0.190485
\(690\) −6.00000 −0.228416
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 36.0000 1.36851
\(693\) 0 0
\(694\) 22.0000 0.835109
\(695\) −15.0000 −0.568982
\(696\) 0 0
\(697\) −63.0000 −2.38630
\(698\) −48.0000 −1.81683
\(699\) −19.0000 −0.718646
\(700\) 0 0
\(701\) 28.0000 1.05755 0.528773 0.848763i \(-0.322652\pi\)
0.528773 + 0.848763i \(0.322652\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 42.0000 1.58406
\(704\) −40.0000 −1.50756
\(705\) 10.0000 0.376622
\(706\) 12.0000 0.451626
\(707\) 0 0
\(708\) 0 0
\(709\) −44.0000 −1.65245 −0.826227 0.563337i \(-0.809517\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(710\) 18.0000 0.675528
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) 5.00000 0.186989
\(716\) 12.0000 0.448461
\(717\) −9.00000 −0.336111
\(718\) −32.0000 −1.19423
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) −4.00000 −0.149071
\(721\) 0 0
\(722\) 34.0000 1.26535
\(723\) 22.0000 0.818189
\(724\) 14.0000 0.520306
\(725\) 2.00000 0.0742781
\(726\) −28.0000 −1.03918
\(727\) 18.0000 0.667583 0.333792 0.942647i \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 12.0000 0.444140
\(731\) −56.0000 −2.07123
\(732\) 10.0000 0.369611
\(733\) −43.0000 −1.58824 −0.794121 0.607760i \(-0.792068\pi\)
−0.794121 + 0.607760i \(0.792068\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) −24.0000 −0.884652
\(737\) −20.0000 −0.736709
\(738\) −18.0000 −0.662589
\(739\) −6.00000 −0.220714 −0.110357 0.993892i \(-0.535199\pi\)
−0.110357 + 0.993892i \(0.535199\pi\)
\(740\) 14.0000 0.514650
\(741\) −6.00000 −0.220416
\(742\) 0 0
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 0 0
\(745\) 15.0000 0.549557
\(746\) −64.0000 −2.34321
\(747\) 4.00000 0.146352
\(748\) 70.0000 2.55945
\(749\) 0 0
\(750\) −2.00000 −0.0730297
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 40.0000 1.45865
\(753\) 0 0
\(754\) 4.00000 0.145671
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) 20.0000 0.726912 0.363456 0.931611i \(-0.381597\pi\)
0.363456 + 0.931611i \(0.381597\pi\)
\(758\) 20.0000 0.726433
\(759\) −15.0000 −0.544466
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 4.00000 0.144905
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 7.00000 0.253086
\(766\) 12.0000 0.433578
\(767\) 0 0
\(768\) −16.0000 −0.577350
\(769\) 28.0000 1.00971 0.504853 0.863205i \(-0.331547\pi\)
0.504853 + 0.863205i \(0.331547\pi\)
\(770\) 0 0
\(771\) 2.00000 0.0720282
\(772\) −34.0000 −1.22369
\(773\) 20.0000 0.719350 0.359675 0.933078i \(-0.382888\pi\)
0.359675 + 0.933078i \(0.382888\pi\)
\(774\) −16.0000 −0.575108
\(775\) −2.00000 −0.0718421
\(776\) 0 0
\(777\) 0 0
\(778\) −8.00000 −0.286814
\(779\) −54.0000 −1.93475
\(780\) −2.00000 −0.0716115
\(781\) 45.0000 1.61023
\(782\) 42.0000 1.50192
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) −18.0000 −0.642448
\(786\) −44.0000 −1.56943
\(787\) −44.0000 −1.56843 −0.784215 0.620489i \(-0.786934\pi\)
−0.784215 + 0.620489i \(0.786934\pi\)
\(788\) 48.0000 1.70993
\(789\) 16.0000 0.569615
\(790\) −6.00000 −0.213470
\(791\) 0 0
\(792\) 0 0
\(793\) −5.00000 −0.177555
\(794\) −30.0000 −1.06466
\(795\) −5.00000 −0.177332
\(796\) 56.0000 1.98487
\(797\) −39.0000 −1.38145 −0.690725 0.723117i \(-0.742709\pi\)
−0.690725 + 0.723117i \(0.742709\pi\)
\(798\) 0 0
\(799\) −70.0000 −2.47642
\(800\) −8.00000 −0.282843
\(801\) −11.0000 −0.388666
\(802\) −28.0000 −0.988714
\(803\) 30.0000 1.05868
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) −24.0000 −0.844840
\(808\) 0 0
\(809\) −50.0000 −1.75791 −0.878953 0.476908i \(-0.841757\pi\)
−0.878953 + 0.476908i \(0.841757\pi\)
\(810\) 2.00000 0.0702728
\(811\) −24.0000 −0.842754 −0.421377 0.906886i \(-0.638453\pi\)
−0.421377 + 0.906886i \(0.638453\pi\)
\(812\) 0 0
\(813\) −22.0000 −0.771574
\(814\) 70.0000 2.45350
\(815\) 15.0000 0.525427
\(816\) 28.0000 0.980196
\(817\) −48.0000 −1.67931
\(818\) −60.0000 −2.09785
\(819\) 0 0
\(820\) −18.0000 −0.628587
\(821\) 17.0000 0.593304 0.296652 0.954986i \(-0.404130\pi\)
0.296652 + 0.954986i \(0.404130\pi\)
\(822\) 28.0000 0.976612
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 0 0
\(825\) −5.00000 −0.174078
\(826\) 0 0
\(827\) −26.0000 −0.904109 −0.452054 0.891990i \(-0.649309\pi\)
−0.452054 + 0.891990i \(0.649309\pi\)
\(828\) 6.00000 0.208514
\(829\) 2.00000 0.0694629 0.0347314 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 8.00000 0.277684
\(831\) 2.00000 0.0693792
\(832\) −8.00000 −0.277350
\(833\) 0 0
\(834\) 30.0000 1.03882
\(835\) 24.0000 0.830554
\(836\) 60.0000 2.07514
\(837\) 2.00000 0.0691301
\(838\) −52.0000 −1.79631
\(839\) −17.0000 −0.586905 −0.293453 0.955974i \(-0.594804\pi\)
−0.293453 + 0.955974i \(0.594804\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −40.0000 −1.37849
\(843\) −18.0000 −0.619953
\(844\) −24.0000 −0.826114
\(845\) 1.00000 0.0344010
\(846\) −20.0000 −0.687614
\(847\) 0 0
\(848\) −20.0000 −0.686803
\(849\) 20.0000 0.686398
\(850\) 14.0000 0.480196
\(851\) 21.0000 0.719871
\(852\) −18.0000 −0.616670
\(853\) 39.0000 1.33533 0.667667 0.744460i \(-0.267293\pi\)
0.667667 + 0.744460i \(0.267293\pi\)
\(854\) 0 0
\(855\) 6.00000 0.205196
\(856\) 0 0
\(857\) 45.0000 1.53717 0.768585 0.639747i \(-0.220961\pi\)
0.768585 + 0.639747i \(0.220961\pi\)
\(858\) −10.0000 −0.341394
\(859\) −19.0000 −0.648272 −0.324136 0.946011i \(-0.605073\pi\)
−0.324136 + 0.946011i \(0.605073\pi\)
\(860\) −16.0000 −0.545595
\(861\) 0 0
\(862\) −80.0000 −2.72481
\(863\) 6.00000 0.204242 0.102121 0.994772i \(-0.467437\pi\)
0.102121 + 0.994772i \(0.467437\pi\)
\(864\) 8.00000 0.272166
\(865\) 18.0000 0.612018
\(866\) 40.0000 1.35926
\(867\) −32.0000 −1.08678
\(868\) 0 0
\(869\) −15.0000 −0.508840
\(870\) −4.00000 −0.135613
\(871\) −4.00000 −0.135535
\(872\) 0 0
\(873\) 11.0000 0.372294
\(874\) 36.0000 1.21772
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) −30.0000 −1.01245
\(879\) 4.00000 0.134917
\(880\) −20.0000 −0.674200
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) 0 0
\(883\) 44.0000 1.48072 0.740359 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) 14.0000 0.470871
\(885\) 0 0
\(886\) −2.00000 −0.0671913
\(887\) −13.0000 −0.436497 −0.218249 0.975893i \(-0.570034\pi\)
−0.218249 + 0.975893i \(0.570034\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −22.0000 −0.737442
\(891\) 5.00000 0.167506
\(892\) 16.0000 0.535720
\(893\) −60.0000 −2.00782
\(894\) −30.0000 −1.00335
\(895\) 6.00000 0.200558
\(896\) 0 0
\(897\) −3.00000 −0.100167
\(898\) 18.0000 0.600668
\(899\) −4.00000 −0.133407
\(900\) 2.00000 0.0666667
\(901\) 35.0000 1.16602
\(902\) −90.0000 −2.99667
\(903\) 0 0
\(904\) 0 0
\(905\) 7.00000 0.232688
\(906\) 16.0000 0.531564
\(907\) 38.0000 1.26177 0.630885 0.775877i \(-0.282692\pi\)
0.630885 + 0.775877i \(0.282692\pi\)
\(908\) 4.00000 0.132745
\(909\) 0 0
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 24.0000 0.794719
\(913\) 20.0000 0.661903
\(914\) −14.0000 −0.463079
\(915\) 5.00000 0.165295
\(916\) −28.0000 −0.925146
\(917\) 0 0
\(918\) −14.0000 −0.462069
\(919\) −19.0000 −0.626752 −0.313376 0.949629i \(-0.601460\pi\)
−0.313376 + 0.949629i \(0.601460\pi\)
\(920\) 0 0
\(921\) 23.0000 0.757876
\(922\) −74.0000 −2.43706
\(923\) 9.00000 0.296239
\(924\) 0 0
\(925\) 7.00000 0.230159
\(926\) 30.0000 0.985861
\(927\) 4.00000 0.131377
\(928\) −16.0000 −0.525226
\(929\) 29.0000 0.951459 0.475730 0.879592i \(-0.342184\pi\)
0.475730 + 0.879592i \(0.342184\pi\)
\(930\) 4.00000 0.131165
\(931\) 0 0
\(932\) 38.0000 1.24473
\(933\) 20.0000 0.654771
\(934\) 2.00000 0.0654420
\(935\) 35.0000 1.14462
\(936\) 0 0
\(937\) 6.00000 0.196011 0.0980057 0.995186i \(-0.468754\pi\)
0.0980057 + 0.995186i \(0.468754\pi\)
\(938\) 0 0
\(939\) −22.0000 −0.717943
\(940\) −20.0000 −0.652328
\(941\) −15.0000 −0.488986 −0.244493 0.969651i \(-0.578622\pi\)
−0.244493 + 0.969651i \(0.578622\pi\)
\(942\) 36.0000 1.17294
\(943\) −27.0000 −0.879241
\(944\) 0 0
\(945\) 0 0
\(946\) −80.0000 −2.60102
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 6.00000 0.194871
\(949\) 6.00000 0.194768
\(950\) 12.0000 0.389331
\(951\) 24.0000 0.778253
\(952\) 0 0
\(953\) −15.0000 −0.485898 −0.242949 0.970039i \(-0.578115\pi\)
−0.242949 + 0.970039i \(0.578115\pi\)
\(954\) 10.0000 0.323762
\(955\) −12.0000 −0.388311
\(956\) 18.0000 0.582162
\(957\) −10.0000 −0.323254
\(958\) −6.00000 −0.193851
\(959\) 0 0
\(960\) 8.00000 0.258199
\(961\) −27.0000 −0.870968
\(962\) 14.0000 0.451378
\(963\) −17.0000 −0.547817
\(964\) −44.0000 −1.41714
\(965\) −17.0000 −0.547249
\(966\) 0 0
\(967\) −8.00000 −0.257263 −0.128631 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) 0 0
\(969\) −42.0000 −1.34923
\(970\) 22.0000 0.706377
\(971\) 28.0000 0.898563 0.449281 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 0 0
\(974\) 10.0000 0.320421
\(975\) −1.00000 −0.0320256
\(976\) 20.0000 0.640184
\(977\) −12.0000 −0.383914 −0.191957 0.981403i \(-0.561483\pi\)
−0.191957 + 0.981403i \(0.561483\pi\)
\(978\) −30.0000 −0.959294
\(979\) −55.0000 −1.75781
\(980\) 0 0
\(981\) 4.00000 0.127710
\(982\) 0 0
\(983\) 4.00000 0.127580 0.0637901 0.997963i \(-0.479681\pi\)
0.0637901 + 0.997963i \(0.479681\pi\)
\(984\) 0 0
\(985\) 24.0000 0.764704
\(986\) 28.0000 0.891702
\(987\) 0 0
\(988\) 12.0000 0.381771
\(989\) −24.0000 −0.763156
\(990\) 10.0000 0.317821
\(991\) −57.0000 −1.81066 −0.905332 0.424704i \(-0.860378\pi\)
−0.905332 + 0.424704i \(0.860378\pi\)
\(992\) 16.0000 0.508001
\(993\) 0 0
\(994\) 0 0
\(995\) 28.0000 0.887660
\(996\) −8.00000 −0.253490
\(997\) −8.00000 −0.253363 −0.126681 0.991943i \(-0.540433\pi\)
−0.126681 + 0.991943i \(0.540433\pi\)
\(998\) −28.0000 −0.886325
\(999\) −7.00000 −0.221470
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 9555.2.a.u.1.1 1
7.6 odd 2 195.2.a.c.1.1 1
21.20 even 2 585.2.a.c.1.1 1
28.27 even 2 3120.2.a.d.1.1 1
35.13 even 4 975.2.c.c.274.1 2
35.27 even 4 975.2.c.c.274.2 2
35.34 odd 2 975.2.a.a.1.1 1
84.83 odd 2 9360.2.a.bv.1.1 1
91.90 odd 2 2535.2.a.d.1.1 1
105.62 odd 4 2925.2.c.a.2224.1 2
105.83 odd 4 2925.2.c.a.2224.2 2
105.104 even 2 2925.2.a.s.1.1 1
273.272 even 2 7605.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.c.1.1 1 7.6 odd 2
585.2.a.c.1.1 1 21.20 even 2
975.2.a.a.1.1 1 35.34 odd 2
975.2.c.c.274.1 2 35.13 even 4
975.2.c.c.274.2 2 35.27 even 4
2535.2.a.d.1.1 1 91.90 odd 2
2925.2.a.s.1.1 1 105.104 even 2
2925.2.c.a.2224.1 2 105.62 odd 4
2925.2.c.a.2224.2 2 105.83 odd 4
3120.2.a.d.1.1 1 28.27 even 2
7605.2.a.t.1.1 1 273.272 even 2
9360.2.a.bv.1.1 1 84.83 odd 2
9555.2.a.u.1.1 1 1.1 even 1 trivial