Properties

Label 3150.2.a.u.1.1
Level 3150
Weight 2
Character 3150.1
Self dual yes
Analytic conductor 25.153
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 3150.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} -1.00000 q^{8} +4.00000 q^{11} +3.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +7.00000 q^{17} -6.00000 q^{19} -4.00000 q^{22} +9.00000 q^{23} -3.00000 q^{26} +1.00000 q^{28} +3.00000 q^{29} -7.00000 q^{31} -1.00000 q^{32} -7.00000 q^{34} +10.0000 q^{37} +6.00000 q^{38} -1.00000 q^{41} -13.0000 q^{43} +4.00000 q^{44} -9.00000 q^{46} -2.00000 q^{47} +1.00000 q^{49} +3.00000 q^{52} -1.00000 q^{53} -1.00000 q^{56} -3.00000 q^{58} -11.0000 q^{59} +13.0000 q^{61} +7.00000 q^{62} +1.00000 q^{64} +7.00000 q^{68} +8.00000 q^{71} -8.00000 q^{73} -10.0000 q^{74} -6.00000 q^{76} +4.00000 q^{77} +4.00000 q^{79} +1.00000 q^{82} +7.00000 q^{83} +13.0000 q^{86} -4.00000 q^{88} -14.0000 q^{89} +3.00000 q^{91} +9.00000 q^{92} +2.00000 q^{94} -8.00000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 9.00000 1.87663 0.938315 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −0.156174 −0.0780869 0.996947i \(-0.524881\pi\)
−0.0780869 + 0.996947i \(0.524881\pi\)
\(42\) 0 0
\(43\) −13.0000 −1.98248 −0.991241 0.132068i \(-0.957838\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) −9.00000 −1.32698
\(47\) −2.00000 −0.291730 −0.145865 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 3.00000 0.416025
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −3.00000 −0.393919
\(59\) −11.0000 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(60\) 0 0
\(61\) 13.0000 1.66448 0.832240 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 7.00000 0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 7.00000 0.848875
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) −8.00000 −0.936329 −0.468165 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) −10.0000 −1.16248
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 1.00000 0.110432
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 13.0000 1.40183
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) −14.0000 −1.48400 −0.741999 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 3.00000 0.314485
\(92\) 9.00000 0.938315
\(93\) 0 0
\(94\) 2.00000 0.206284
\(95\) 0 0
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) 11.0000 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) −3.00000 −0.294174
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) 11.0000 1.01263
\(119\) 7.00000 0.641689
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) −13.0000 −1.17696
\(123\) 0 0
\(124\) −7.00000 −0.628619
\(125\) 0 0
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 20.0000 1.74741 0.873704 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 0 0
\(135\) 0 0
\(136\) −7.00000 −0.600245
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) 0 0
\(146\) 8.00000 0.662085
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −9.00000 −0.737309 −0.368654 0.929567i \(-0.620181\pi\)
−0.368654 + 0.929567i \(0.620181\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 6.00000 0.486664
\(153\) 0 0
\(154\) −4.00000 −0.322329
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −4.00000 −0.318223
\(159\) 0 0
\(160\) 0 0
\(161\) 9.00000 0.709299
\(162\) 0 0
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0 0
\(166\) −7.00000 −0.543305
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) −13.0000 −0.991241
\(173\) 10.0000 0.760286 0.380143 0.924928i \(-0.375875\pi\)
0.380143 + 0.924928i \(0.375875\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 14.0000 1.04934
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) −9.00000 −0.663489
\(185\) 0 0
\(186\) 0 0
\(187\) 28.0000 2.04756
\(188\) −2.00000 −0.145865
\(189\) 0 0
\(190\) 0 0
\(191\) −21.0000 −1.51951 −0.759753 0.650211i \(-0.774680\pi\)
−0.759753 + 0.650211i \(0.774680\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 8.00000 0.574367
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −5.00000 −0.356235 −0.178118 0.984009i \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) 3.00000 0.210559
\(204\) 0 0
\(205\) 0 0
\(206\) −11.0000 −0.766406
\(207\) 0 0
\(208\) 3.00000 0.208013
\(209\) −24.0000 −1.66011
\(210\) 0 0
\(211\) 13.0000 0.894957 0.447478 0.894295i \(-0.352322\pi\)
0.447478 + 0.894295i \(0.352322\pi\)
\(212\) −1.00000 −0.0686803
\(213\) 0 0
\(214\) 6.00000 0.410152
\(215\) 0 0
\(216\) 0 0
\(217\) −7.00000 −0.475191
\(218\) 6.00000 0.406371
\(219\) 0 0
\(220\) 0 0
\(221\) 21.0000 1.41261
\(222\) 0 0
\(223\) −13.0000 −0.870544 −0.435272 0.900299i \(-0.643348\pi\)
−0.435272 + 0.900299i \(0.643348\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −16.0000 −1.06430
\(227\) −11.0000 −0.730096 −0.365048 0.930989i \(-0.618947\pi\)
−0.365048 + 0.930989i \(0.618947\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 −0.196960
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −11.0000 −0.716039
\(237\) 0 0
\(238\) −7.00000 −0.453743
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) 0 0
\(247\) −18.0000 −1.14531
\(248\) 7.00000 0.444500
\(249\) 0 0
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) 36.0000 2.26330
\(254\) −14.0000 −0.878438
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −17.0000 −1.06043 −0.530215 0.847863i \(-0.677889\pi\)
−0.530215 + 0.847863i \(0.677889\pi\)
\(258\) 0 0
\(259\) 10.0000 0.621370
\(260\) 0 0
\(261\) 0 0
\(262\) −20.0000 −1.23560
\(263\) 13.0000 0.801614 0.400807 0.916162i \(-0.368730\pi\)
0.400807 + 0.916162i \(0.368730\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6.00000 0.367884
\(267\) 0 0
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 7.00000 0.424437
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 0 0
\(277\) −12.0000 −0.721010 −0.360505 0.932757i \(-0.617396\pi\)
−0.360505 + 0.932757i \(0.617396\pi\)
\(278\) 8.00000 0.479808
\(279\) 0 0
\(280\) 0 0
\(281\) 32.0000 1.90896 0.954480 0.298275i \(-0.0964112\pi\)
0.954480 + 0.298275i \(0.0964112\pi\)
\(282\) 0 0
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 8.00000 0.474713
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) −1.00000 −0.0590281
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 0 0
\(292\) −8.00000 −0.468165
\(293\) −28.0000 −1.63578 −0.817889 0.575376i \(-0.804856\pi\)
−0.817889 + 0.575376i \(0.804856\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 9.00000 0.521356
\(299\) 27.0000 1.56145
\(300\) 0 0
\(301\) −13.0000 −0.749308
\(302\) −2.00000 −0.115087
\(303\) 0 0
\(304\) −6.00000 −0.344124
\(305\) 0 0
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 4.00000 0.227921
\(309\) 0 0
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 0 0
\(313\) 16.0000 0.904373 0.452187 0.891923i \(-0.350644\pi\)
0.452187 + 0.891923i \(0.350644\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 11.0000 0.617822 0.308911 0.951091i \(-0.400036\pi\)
0.308911 + 0.951091i \(0.400036\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 0 0
\(322\) −9.00000 −0.501550
\(323\) −42.0000 −2.33694
\(324\) 0 0
\(325\) 0 0
\(326\) 11.0000 0.609234
\(327\) 0 0
\(328\) 1.00000 0.0552158
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) −5.00000 −0.274825 −0.137412 0.990514i \(-0.543879\pi\)
−0.137412 + 0.990514i \(0.543879\pi\)
\(332\) 7.00000 0.384175
\(333\) 0 0
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) 4.00000 0.217571
\(339\) 0 0
\(340\) 0 0
\(341\) −28.0000 −1.51629
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 13.0000 0.700913
\(345\) 0 0
\(346\) −10.0000 −0.537603
\(347\) 32.0000 1.71785 0.858925 0.512101i \(-0.171133\pi\)
0.858925 + 0.512101i \(0.171133\pi\)
\(348\) 0 0
\(349\) 19.0000 1.01705 0.508523 0.861048i \(-0.330192\pi\)
0.508523 + 0.861048i \(0.330192\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 6.00000 0.317110
\(359\) 11.0000 0.580558 0.290279 0.956942i \(-0.406252\pi\)
0.290279 + 0.956942i \(0.406252\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 2.00000 0.105118
\(363\) 0 0
\(364\) 3.00000 0.157243
\(365\) 0 0
\(366\) 0 0
\(367\) 17.0000 0.887393 0.443696 0.896177i \(-0.353667\pi\)
0.443696 + 0.896177i \(0.353667\pi\)
\(368\) 9.00000 0.469157
\(369\) 0 0
\(370\) 0 0
\(371\) −1.00000 −0.0519174
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) −28.0000 −1.44785
\(375\) 0 0
\(376\) 2.00000 0.103142
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) −15.0000 −0.770498 −0.385249 0.922813i \(-0.625884\pi\)
−0.385249 + 0.922813i \(0.625884\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 21.0000 1.07445
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) −8.00000 −0.406138
\(389\) 26.0000 1.31825 0.659126 0.752032i \(-0.270926\pi\)
0.659126 + 0.752032i \(0.270926\pi\)
\(390\) 0 0
\(391\) 63.0000 3.18605
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 5.00000 0.251896
\(395\) 0 0
\(396\) 0 0
\(397\) −19.0000 −0.953583 −0.476791 0.879017i \(-0.658200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) 0 0
\(401\) 4.00000 0.199750 0.0998752 0.995000i \(-0.468156\pi\)
0.0998752 + 0.995000i \(0.468156\pi\)
\(402\) 0 0
\(403\) −21.0000 −1.04608
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) −3.00000 −0.148888
\(407\) 40.0000 1.98273
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 11.0000 0.541931
\(413\) −11.0000 −0.541275
\(414\) 0 0
\(415\) 0 0
\(416\) −3.00000 −0.147087
\(417\) 0 0
\(418\) 24.0000 1.17388
\(419\) −9.00000 −0.439679 −0.219839 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −13.0000 −0.632830
\(423\) 0 0
\(424\) 1.00000 0.0485643
\(425\) 0 0
\(426\) 0 0
\(427\) 13.0000 0.629114
\(428\) −6.00000 −0.290021
\(429\) 0 0
\(430\) 0 0
\(431\) −21.0000 −1.01153 −0.505767 0.862670i \(-0.668791\pi\)
−0.505767 + 0.862670i \(0.668791\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 7.00000 0.336011
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) −54.0000 −2.58317
\(438\) 0 0
\(439\) −35.0000 −1.67046 −0.835229 0.549902i \(-0.814665\pi\)
−0.835229 + 0.549902i \(0.814665\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −21.0000 −0.998868
\(443\) 2.00000 0.0950229 0.0475114 0.998871i \(-0.484871\pi\)
0.0475114 + 0.998871i \(0.484871\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 13.0000 0.615568
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) −4.00000 −0.188353
\(452\) 16.0000 0.752577
\(453\) 0 0
\(454\) 11.0000 0.516256
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −22.0000 −1.02799
\(459\) 0 0
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 3.00000 0.139272
\(465\) 0 0
\(466\) −18.0000 −0.833834
\(467\) −5.00000 −0.231372 −0.115686 0.993286i \(-0.536907\pi\)
−0.115686 + 0.993286i \(0.536907\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 11.0000 0.506316
\(473\) −52.0000 −2.39096
\(474\) 0 0
\(475\) 0 0
\(476\) 7.00000 0.320844
\(477\) 0 0
\(478\) 8.00000 0.365911
\(479\) −30.0000 −1.37073 −0.685367 0.728197i \(-0.740358\pi\)
−0.685367 + 0.728197i \(0.740358\pi\)
\(480\) 0 0
\(481\) 30.0000 1.36788
\(482\) −22.0000 −1.00207
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 0 0
\(487\) 4.00000 0.181257 0.0906287 0.995885i \(-0.471112\pi\)
0.0906287 + 0.995885i \(0.471112\pi\)
\(488\) −13.0000 −0.588482
\(489\) 0 0
\(490\) 0 0
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) 0 0
\(493\) 21.0000 0.945792
\(494\) 18.0000 0.809858
\(495\) 0 0
\(496\) −7.00000 −0.314309
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) −21.0000 −0.940089 −0.470045 0.882643i \(-0.655762\pi\)
−0.470045 + 0.882643i \(0.655762\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −21.0000 −0.937276
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −36.0000 −1.60040
\(507\) 0 0
\(508\) 14.0000 0.621150
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 17.0000 0.749838
\(515\) 0 0
\(516\) 0 0
\(517\) −8.00000 −0.351840
\(518\) −10.0000 −0.439375
\(519\) 0 0
\(520\) 0 0
\(521\) −43.0000 −1.88386 −0.941932 0.335803i \(-0.890992\pi\)
−0.941932 + 0.335803i \(0.890992\pi\)
\(522\) 0 0
\(523\) 14.0000 0.612177 0.306089 0.952003i \(-0.400980\pi\)
0.306089 + 0.952003i \(0.400980\pi\)
\(524\) 20.0000 0.873704
\(525\) 0 0
\(526\) −13.0000 −0.566827
\(527\) −49.0000 −2.13447
\(528\) 0 0
\(529\) 58.0000 2.52174
\(530\) 0 0
\(531\) 0 0
\(532\) −6.00000 −0.260133
\(533\) −3.00000 −0.129944
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −6.00000 −0.258678
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −42.0000 −1.80572 −0.902861 0.429934i \(-0.858537\pi\)
−0.902861 + 0.429934i \(0.858537\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −7.00000 −0.300123
\(545\) 0 0
\(546\) 0 0
\(547\) 9.00000 0.384812 0.192406 0.981315i \(-0.438371\pi\)
0.192406 + 0.981315i \(0.438371\pi\)
\(548\) 12.0000 0.512615
\(549\) 0 0
\(550\) 0 0
\(551\) −18.0000 −0.766826
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) 12.0000 0.509831
\(555\) 0 0
\(556\) −8.00000 −0.339276
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 0 0
\(559\) −39.0000 −1.64952
\(560\) 0 0
\(561\) 0 0
\(562\) −32.0000 −1.34984
\(563\) 19.0000 0.800755 0.400377 0.916350i \(-0.368879\pi\)
0.400377 + 0.916350i \(0.368879\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −39.0000 −1.63210 −0.816050 0.577982i \(-0.803840\pi\)
−0.816050 + 0.577982i \(0.803840\pi\)
\(572\) 12.0000 0.501745
\(573\) 0 0
\(574\) 1.00000 0.0417392
\(575\) 0 0
\(576\) 0 0
\(577\) −46.0000 −1.91501 −0.957503 0.288425i \(-0.906868\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) −32.0000 −1.33102
\(579\) 0 0
\(580\) 0 0
\(581\) 7.00000 0.290409
\(582\) 0 0
\(583\) −4.00000 −0.165663
\(584\) 8.00000 0.331042
\(585\) 0 0
\(586\) 28.0000 1.15667
\(587\) 7.00000 0.288921 0.144460 0.989511i \(-0.453855\pi\)
0.144460 + 0.989511i \(0.453855\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) 0 0
\(591\) 0 0
\(592\) 10.0000 0.410997
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.00000 −0.368654
\(597\) 0 0
\(598\) −27.0000 −1.10411
\(599\) −21.0000 −0.858037 −0.429018 0.903296i \(-0.641140\pi\)
−0.429018 + 0.903296i \(0.641140\pi\)
\(600\) 0 0
\(601\) 30.0000 1.22373 0.611863 0.790964i \(-0.290420\pi\)
0.611863 + 0.790964i \(0.290420\pi\)
\(602\) 13.0000 0.529840
\(603\) 0 0
\(604\) 2.00000 0.0813788
\(605\) 0 0
\(606\) 0 0
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 −0.242734
\(612\) 0 0
\(613\) −42.0000 −1.69636 −0.848182 0.529705i \(-0.822303\pi\)
−0.848182 + 0.529705i \(0.822303\pi\)
\(614\) −2.00000 −0.0807134
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) −26.0000 −1.04672 −0.523360 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 0 0
\(619\) 14.0000 0.562708 0.281354 0.959604i \(-0.409217\pi\)
0.281354 + 0.959604i \(0.409217\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 30.0000 1.20289
\(623\) −14.0000 −0.560898
\(624\) 0 0
\(625\) 0 0
\(626\) −16.0000 −0.639489
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) 70.0000 2.79108
\(630\) 0 0
\(631\) −22.0000 −0.875806 −0.437903 0.899022i \(-0.644279\pi\)
−0.437903 + 0.899022i \(0.644279\pi\)
\(632\) −4.00000 −0.159111
\(633\) 0 0
\(634\) −11.0000 −0.436866
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 0.118864
\(638\) −12.0000 −0.475085
\(639\) 0 0
\(640\) 0 0
\(641\) 14.0000 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(642\) 0 0
\(643\) 8.00000 0.315489 0.157745 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) 9.00000 0.354650
\(645\) 0 0
\(646\) 42.0000 1.65247
\(647\) −28.0000 −1.10079 −0.550397 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 0 0
\(649\) −44.0000 −1.72715
\(650\) 0 0
\(651\) 0 0
\(652\) −11.0000 −0.430793
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 −0.0390434
\(657\) 0 0
\(658\) 2.00000 0.0779681
\(659\) 16.0000 0.623272 0.311636 0.950202i \(-0.399123\pi\)
0.311636 + 0.950202i \(0.399123\pi\)
\(660\) 0 0
\(661\) −2.00000 −0.0777910 −0.0388955 0.999243i \(-0.512384\pi\)
−0.0388955 + 0.999243i \(0.512384\pi\)
\(662\) 5.00000 0.194331
\(663\) 0 0
\(664\) −7.00000 −0.271653
\(665\) 0 0
\(666\) 0 0
\(667\) 27.0000 1.04544
\(668\) 12.0000 0.464294
\(669\) 0 0
\(670\) 0 0
\(671\) 52.0000 2.00744
\(672\) 0 0
\(673\) −31.0000 −1.19496 −0.597481 0.801883i \(-0.703832\pi\)
−0.597481 + 0.801883i \(0.703832\pi\)
\(674\) −5.00000 −0.192593
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 0 0
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) 0 0
\(682\) 28.0000 1.07218
\(683\) −38.0000 −1.45403 −0.727015 0.686622i \(-0.759093\pi\)
−0.727015 + 0.686622i \(0.759093\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) −13.0000 −0.495620
\(689\) −3.00000 −0.114291
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 10.0000 0.380143
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) 0 0
\(696\) 0 0
\(697\) −7.00000 −0.265144
\(698\) −19.0000 −0.719161
\(699\) 0 0
\(700\) 0 0
\(701\) 7.00000 0.264386 0.132193 0.991224i \(-0.457798\pi\)
0.132193 + 0.991224i \(0.457798\pi\)
\(702\) 0 0
\(703\) −60.0000 −2.26294
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) −6.00000 −0.225653
\(708\) 0 0
\(709\) 28.0000 1.05156 0.525781 0.850620i \(-0.323773\pi\)
0.525781 + 0.850620i \(0.323773\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 14.0000 0.524672
\(713\) −63.0000 −2.35937
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 −0.224231
\(717\) 0 0
\(718\) −11.0000 −0.410516
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 11.0000 0.409661
\(722\) −17.0000 −0.632674
\(723\) 0 0
\(724\) −2.00000 −0.0743294
\(725\) 0 0
\(726\) 0 0
\(727\) 3.00000 0.111264 0.0556319 0.998451i \(-0.482283\pi\)
0.0556319 + 0.998451i \(0.482283\pi\)
\(728\) −3.00000 −0.111187
\(729\) 0 0
\(730\) 0 0
\(731\) −91.0000 −3.36576
\(732\) 0 0
\(733\) 41.0000 1.51437 0.757185 0.653201i \(-0.226574\pi\)
0.757185 + 0.653201i \(0.226574\pi\)
\(734\) −17.0000 −0.627481
\(735\) 0 0
\(736\) −9.00000 −0.331744
\(737\) 0 0
\(738\) 0 0
\(739\) −47.0000 −1.72892 −0.864461 0.502699i \(-0.832340\pi\)
−0.864461 + 0.502699i \(0.832340\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.00000 0.0367112
\(743\) −45.0000 −1.65089 −0.825445 0.564483i \(-0.809076\pi\)
−0.825445 + 0.564483i \(0.809076\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 14.0000 0.512576
\(747\) 0 0
\(748\) 28.0000 1.02378
\(749\) −6.00000 −0.219235
\(750\) 0 0
\(751\) −10.0000 −0.364905 −0.182453 0.983215i \(-0.558404\pi\)
−0.182453 + 0.983215i \(0.558404\pi\)
\(752\) −2.00000 −0.0729325
\(753\) 0 0
\(754\) −9.00000 −0.327761
\(755\) 0 0
\(756\) 0 0
\(757\) 20.0000 0.726912 0.363456 0.931611i \(-0.381597\pi\)
0.363456 + 0.931611i \(0.381597\pi\)
\(758\) 15.0000 0.544825
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) −6.00000 −0.217215
\(764\) −21.0000 −0.759753
\(765\) 0 0
\(766\) 0 0
\(767\) −33.0000 −1.19156
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14.0000 −0.503871
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) −26.0000 −0.932145
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) 32.0000 1.14505
\(782\) −63.0000 −2.25288
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) −22.0000 −0.784215 −0.392108 0.919919i \(-0.628254\pi\)
−0.392108 + 0.919919i \(0.628254\pi\)
\(788\) −5.00000 −0.178118
\(789\) 0 0
\(790\) 0 0
\(791\) 16.0000 0.568895
\(792\) 0 0
\(793\) 39.0000 1.38493
\(794\) 19.0000 0.674285
\(795\) 0 0
\(796\) 8.00000 0.283552
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) −14.0000 −0.495284
\(800\) 0 0
\(801\) 0 0
\(802\) −4.00000 −0.141245
\(803\) −32.0000 −1.12926
\(804\) 0 0
\(805\) 0 0
\(806\) 21.0000 0.739693
\(807\) 0 0
\(808\) 6.00000 0.211079
\(809\) 18.0000 0.632846 0.316423 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 0 0
\(811\) −40.0000 −1.40459 −0.702295 0.711886i \(-0.747841\pi\)
−0.702295 + 0.711886i \(0.747841\pi\)
\(812\) 3.00000 0.105279
\(813\) 0 0
\(814\) −40.0000 −1.40200
\(815\) 0 0
\(816\) 0 0
\(817\) 78.0000 2.72887
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) −11.0000 −0.383203
\(825\) 0 0
\(826\) 11.0000 0.382739
\(827\) 34.0000 1.18230 0.591148 0.806563i \(-0.298675\pi\)
0.591148 + 0.806563i \(0.298675\pi\)
\(828\) 0 0
\(829\) −25.0000 −0.868286 −0.434143 0.900844i \(-0.642949\pi\)
−0.434143 + 0.900844i \(0.642949\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 3.00000 0.104006
\(833\) 7.00000 0.242536
\(834\) 0 0
\(835\) 0 0
\(836\) −24.0000 −0.830057
\(837\) 0 0
\(838\) 9.00000 0.310900
\(839\) 32.0000 1.10476 0.552381 0.833592i \(-0.313719\pi\)
0.552381 + 0.833592i \(0.313719\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) −8.00000 −0.275698
\(843\) 0 0
\(844\) 13.0000 0.447478
\(845\) 0 0
\(846\) 0 0
\(847\) 5.00000 0.171802
\(848\) −1.00000 −0.0343401
\(849\) 0 0
\(850\) 0 0
\(851\) 90.0000 3.08516
\(852\) 0 0
\(853\) 13.0000 0.445112 0.222556 0.974920i \(-0.428560\pi\)
0.222556 + 0.974920i \(0.428560\pi\)
\(854\) −13.0000 −0.444851
\(855\) 0 0
\(856\) 6.00000 0.205076
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 0 0
\(859\) 36.0000 1.22830 0.614152 0.789188i \(-0.289498\pi\)
0.614152 + 0.789188i \(0.289498\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 21.0000 0.715263
\(863\) −28.0000 −0.953131 −0.476566 0.879139i \(-0.658119\pi\)
−0.476566 + 0.879139i \(0.658119\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 2.00000 0.0679628
\(867\) 0 0
\(868\) −7.00000 −0.237595
\(869\) 16.0000 0.542763
\(870\) 0 0
\(871\) 0 0
\(872\) 6.00000 0.203186
\(873\) 0 0
\(874\) 54.0000 1.82658
\(875\) 0 0
\(876\) 0 0
\(877\) −8.00000 −0.270141 −0.135070 0.990836i \(-0.543126\pi\)
−0.135070 + 0.990836i \(0.543126\pi\)
\(878\) 35.0000 1.18119
\(879\) 0 0
\(880\) 0 0
\(881\) −13.0000 −0.437981 −0.218991 0.975727i \(-0.570276\pi\)
−0.218991 + 0.975727i \(0.570276\pi\)
\(882\) 0 0
\(883\) 21.0000 0.706706 0.353353 0.935490i \(-0.385041\pi\)
0.353353 + 0.935490i \(0.385041\pi\)
\(884\) 21.0000 0.706306
\(885\) 0 0
\(886\) −2.00000 −0.0671913
\(887\) −38.0000 −1.27592 −0.637958 0.770072i \(-0.720220\pi\)
−0.637958 + 0.770072i \(0.720220\pi\)
\(888\) 0 0
\(889\) 14.0000 0.469545
\(890\) 0 0
\(891\) 0 0
\(892\) −13.0000 −0.435272
\(893\) 12.0000 0.401565
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −30.0000 −1.00111
\(899\) −21.0000 −0.700389
\(900\) 0 0
\(901\) −7.00000 −0.233204
\(902\) 4.00000 0.133185
\(903\) 0 0
\(904\) −16.0000 −0.532152
\(905\) 0 0
\(906\) 0 0
\(907\) −47.0000 −1.56061 −0.780305 0.625400i \(-0.784936\pi\)
−0.780305 + 0.625400i \(0.784936\pi\)
\(908\) −11.0000 −0.365048
\(909\) 0 0
\(910\) 0 0
\(911\) 21.0000 0.695761 0.347881 0.937539i \(-0.386901\pi\)
0.347881 + 0.937539i \(0.386901\pi\)
\(912\) 0 0
\(913\) 28.0000 0.926665
\(914\) −17.0000 −0.562310
\(915\) 0 0
\(916\) 22.0000 0.726900
\(917\) 20.0000 0.660458
\(918\) 0 0
\(919\) −10.0000 −0.329870 −0.164935 0.986304i \(-0.552741\pi\)
−0.164935 + 0.986304i \(0.552741\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 14.0000 0.461065
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) 0 0
\(926\) −16.0000 −0.525793
\(927\) 0 0
\(928\) −3.00000 −0.0984798
\(929\) 31.0000 1.01708 0.508539 0.861039i \(-0.330186\pi\)
0.508539 + 0.861039i \(0.330186\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 18.0000 0.589610
\(933\) 0 0
\(934\) 5.00000 0.163605
\(935\) 0 0
\(936\) 0 0
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −40.0000 −1.30396 −0.651981 0.758235i \(-0.726062\pi\)
−0.651981 + 0.758235i \(0.726062\pi\)
\(942\) 0 0
\(943\) −9.00000 −0.293080
\(944\) −11.0000 −0.358020
\(945\) 0 0
\(946\) 52.0000 1.69067
\(947\) −2.00000 −0.0649913 −0.0324956 0.999472i \(-0.510346\pi\)
−0.0324956 + 0.999472i \(0.510346\pi\)
\(948\) 0 0
\(949\) −24.0000 −0.779073
\(950\) 0 0
\(951\) 0 0
\(952\) −7.00000 −0.226871
\(953\) −12.0000 −0.388718 −0.194359 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −8.00000 −0.258738
\(957\) 0 0
\(958\) 30.0000 0.969256
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) −30.0000 −0.967239
\(963\) 0 0
\(964\) 22.0000 0.708572
\(965\) 0 0
\(966\) 0 0
\(967\) 26.0000 0.836104 0.418052 0.908423i \(-0.362713\pi\)
0.418052 + 0.908423i \(0.362713\pi\)
\(968\) −5.00000 −0.160706
\(969\) 0 0
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) −8.00000 −0.256468
\(974\) −4.00000 −0.128168
\(975\) 0 0
\(976\) 13.0000 0.416120
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) −56.0000 −1.78977
\(980\) 0 0
\(981\) 0 0
\(982\) −6.00000 −0.191468
\(983\) 4.00000 0.127580 0.0637901 0.997963i \(-0.479681\pi\)
0.0637901 + 0.997963i \(0.479681\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −21.0000 −0.668776
\(987\) 0 0
\(988\) −18.0000 −0.572656
\(989\) −117.000 −3.72038
\(990\) 0 0
\(991\) −26.0000 −0.825917 −0.412959 0.910750i \(-0.635505\pi\)
−0.412959 + 0.910750i \(0.635505\pi\)
\(992\) 7.00000 0.222250
\(993\) 0 0
\(994\) −8.00000 −0.253745
\(995\) 0 0
\(996\) 0 0
\(997\) −14.0000 −0.443384 −0.221692 0.975117i \(-0.571158\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(998\) 21.0000 0.664743
\(999\) 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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3150.2.a.u.1.1 yes 1
3.2 odd 2 3150.2.a.bi.1.1 yes 1
5.2 odd 4 3150.2.g.u.2899.1 2
5.3 odd 4 3150.2.g.u.2899.2 2
5.4 even 2 3150.2.a.bf.1.1 yes 1
15.2 even 4 3150.2.g.d.2899.2 2
15.8 even 4 3150.2.g.d.2899.1 2
15.14 odd 2 3150.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3150.2.a.b.1.1 1 15.14 odd 2
3150.2.a.u.1.1 yes 1 1.1 even 1 trivial
3150.2.a.bf.1.1 yes 1 5.4 even 2
3150.2.a.bi.1.1 yes 1 3.2 odd 2
3150.2.g.d.2899.1 2 15.8 even 4
3150.2.g.d.2899.2 2 15.2 even 4
3150.2.g.u.2899.1 2 5.2 odd 4
3150.2.g.u.2899.2 2 5.3 odd 4