Properties

Label 9702.2.a.dv.1.1
Level $9702$
Weight $2$
Character 9702.1
Self dual yes
Analytic conductor $77.471$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9702.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(77.4708600410\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.2700.1
Defining polynomial: \(x^{3} - 15 x - 20\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.41883\) of defining polynomial
Character \(\chi\) \(=\) 9702.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -4.41883 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -4.41883 q^{5} -1.00000 q^{8} +4.41883 q^{10} +1.00000 q^{11} +1.00000 q^{16} -2.37683 q^{17} -3.68842 q^{19} -4.41883 q^{20} -1.00000 q^{22} -4.73042 q^{23} +14.5261 q^{25} +6.52608 q^{29} -3.37683 q^{31} -1.00000 q^{32} +2.37683 q^{34} +7.68842 q^{37} +3.68842 q^{38} +4.41883 q^{40} -12.1492 q^{41} +3.06525 q^{43} +1.00000 q^{44} +4.73042 q^{46} +4.10725 q^{47} -14.5261 q^{50} -8.00000 q^{53} -4.41883 q^{55} -6.52608 q^{58} +12.5261 q^{59} +3.79567 q^{61} +3.37683 q^{62} +1.00000 q^{64} +10.1492 q^{67} -2.37683 q^{68} -0.934749 q^{71} -7.46083 q^{73} -7.68842 q^{74} -3.68842 q^{76} -0.418833 q^{79} -4.41883 q^{80} +12.1492 q^{82} +2.14925 q^{83} +10.5028 q^{85} -3.06525 q^{86} -1.00000 q^{88} +12.8377 q^{89} -4.73042 q^{92} -4.10725 q^{94} +16.2985 q^{95} +7.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{8} + O(q^{10}) \) \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{8} + 3 q^{11} + 3 q^{16} - 3 q^{17} - 9 q^{19} - 3 q^{22} - 3 q^{23} + 15 q^{25} - 9 q^{29} - 6 q^{31} - 3 q^{32} + 3 q^{34} + 21 q^{37} + 9 q^{38} - 12 q^{41} + 3 q^{43} + 3 q^{44} + 3 q^{46} - 3 q^{47} - 15 q^{50} - 24 q^{53} + 9 q^{58} + 9 q^{59} - 6 q^{61} + 6 q^{62} + 3 q^{64} + 6 q^{67} - 3 q^{68} - 9 q^{71} - 21 q^{74} - 9 q^{76} + 12 q^{79} + 12 q^{82} - 18 q^{83} - 3 q^{86} - 3 q^{88} + 12 q^{89} - 3 q^{92} + 3 q^{94} + 21 q^{97} + O(q^{100}) \)

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
\(5\) −4.41883 −1.97616 −0.988081 0.153935i \(-0.950805\pi\)
−0.988081 + 0.153935i \(0.950805\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 4.41883 1.39736
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.37683 −0.576467 −0.288233 0.957560i \(-0.593068\pi\)
−0.288233 + 0.957560i \(0.593068\pi\)
\(18\) 0 0
\(19\) −3.68842 −0.846181 −0.423090 0.906087i \(-0.639055\pi\)
−0.423090 + 0.906087i \(0.639055\pi\)
\(20\) −4.41883 −0.988081
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −4.73042 −0.986360 −0.493180 0.869927i \(-0.664166\pi\)
−0.493180 + 0.869927i \(0.664166\pi\)
\(24\) 0 0
\(25\) 14.5261 2.90522
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.52608 1.21186 0.605932 0.795517i \(-0.292801\pi\)
0.605932 + 0.795517i \(0.292801\pi\)
\(30\) 0 0
\(31\) −3.37683 −0.606497 −0.303249 0.952911i \(-0.598071\pi\)
−0.303249 + 0.952911i \(0.598071\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.37683 0.407624
\(35\) 0 0
\(36\) 0 0
\(37\) 7.68842 1.26397 0.631984 0.774981i \(-0.282241\pi\)
0.631984 + 0.774981i \(0.282241\pi\)
\(38\) 3.68842 0.598340
\(39\) 0 0
\(40\) 4.41883 0.698679
\(41\) −12.1492 −1.89739 −0.948697 0.316187i \(-0.897597\pi\)
−0.948697 + 0.316187i \(0.897597\pi\)
\(42\) 0 0
\(43\) 3.06525 0.467446 0.233723 0.972303i \(-0.424909\pi\)
0.233723 + 0.972303i \(0.424909\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) 4.73042 0.697462
\(47\) 4.10725 0.599104 0.299552 0.954080i \(-0.403163\pi\)
0.299552 + 0.954080i \(0.403163\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −14.5261 −2.05430
\(51\) 0 0
\(52\) 0 0
\(53\) −8.00000 −1.09888 −0.549442 0.835532i \(-0.685160\pi\)
−0.549442 + 0.835532i \(0.685160\pi\)
\(54\) 0 0
\(55\) −4.41883 −0.595835
\(56\) 0 0
\(57\) 0 0
\(58\) −6.52608 −0.856917
\(59\) 12.5261 1.63076 0.815379 0.578928i \(-0.196529\pi\)
0.815379 + 0.578928i \(0.196529\pi\)
\(60\) 0 0
\(61\) 3.79567 0.485985 0.242993 0.970028i \(-0.421871\pi\)
0.242993 + 0.970028i \(0.421871\pi\)
\(62\) 3.37683 0.428858
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 10.1492 1.23993 0.619964 0.784630i \(-0.287147\pi\)
0.619964 + 0.784630i \(0.287147\pi\)
\(68\) −2.37683 −0.288233
\(69\) 0 0
\(70\) 0 0
\(71\) −0.934749 −0.110934 −0.0554672 0.998461i \(-0.517665\pi\)
−0.0554672 + 0.998461i \(0.517665\pi\)
\(72\) 0 0
\(73\) −7.46083 −0.873224 −0.436612 0.899650i \(-0.643822\pi\)
−0.436612 + 0.899650i \(0.643822\pi\)
\(74\) −7.68842 −0.893760
\(75\) 0 0
\(76\) −3.68842 −0.423090
\(77\) 0 0
\(78\) 0 0
\(79\) −0.418833 −0.0471224 −0.0235612 0.999722i \(-0.507500\pi\)
−0.0235612 + 0.999722i \(0.507500\pi\)
\(80\) −4.41883 −0.494041
\(81\) 0 0
\(82\) 12.1492 1.34166
\(83\) 2.14925 0.235911 0.117955 0.993019i \(-0.462366\pi\)
0.117955 + 0.993019i \(0.462366\pi\)
\(84\) 0 0
\(85\) 10.5028 1.13919
\(86\) −3.06525 −0.330534
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) 12.8377 1.36079 0.680395 0.732846i \(-0.261808\pi\)
0.680395 + 0.732846i \(0.261808\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −4.73042 −0.493180
\(93\) 0 0
\(94\) −4.10725 −0.423630
\(95\) 16.2985 1.67219
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 14.5261 1.45261
\(101\) 15.3637 1.52875 0.764375 0.644772i \(-0.223048\pi\)
0.764375 + 0.644772i \(0.223048\pi\)
\(102\) 0 0
\(103\) −2.62317 −0.258468 −0.129234 0.991614i \(-0.541252\pi\)
−0.129234 + 0.991614i \(0.541252\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) −10.9029 −1.05402 −0.527012 0.849858i \(-0.676688\pi\)
−0.527012 + 0.849858i \(0.676688\pi\)
\(108\) 0 0
\(109\) −11.7957 −1.12982 −0.564910 0.825153i \(-0.691089\pi\)
−0.564910 + 0.825153i \(0.691089\pi\)
\(110\) 4.41883 0.421319
\(111\) 0 0
\(112\) 0 0
\(113\) −5.37683 −0.505810 −0.252905 0.967491i \(-0.581386\pi\)
−0.252905 + 0.967491i \(0.581386\pi\)
\(114\) 0 0
\(115\) 20.9029 1.94921
\(116\) 6.52608 0.605932
\(117\) 0 0
\(118\) −12.5261 −1.15312
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −3.79567 −0.343643
\(123\) 0 0
\(124\) −3.37683 −0.303249
\(125\) −42.0942 −3.76502
\(126\) 0 0
\(127\) 0.730416 0.0648139 0.0324070 0.999475i \(-0.489683\pi\)
0.0324070 + 0.999475i \(0.489683\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −7.37683 −0.644517 −0.322258 0.946652i \(-0.604442\pi\)
−0.322258 + 0.946652i \(0.604442\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −10.1492 −0.876762
\(135\) 0 0
\(136\) 2.37683 0.203812
\(137\) 8.83767 0.755053 0.377526 0.925999i \(-0.376775\pi\)
0.377526 + 0.925999i \(0.376775\pi\)
\(138\) 0 0
\(139\) 1.47392 0.125016 0.0625080 0.998044i \(-0.480090\pi\)
0.0625080 + 0.998044i \(0.480090\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.934749 0.0784424
\(143\) 0 0
\(144\) 0 0
\(145\) −28.8377 −2.39484
\(146\) 7.46083 0.617463
\(147\) 0 0
\(148\) 7.68842 0.631984
\(149\) 9.36375 0.767108 0.383554 0.923518i \(-0.374700\pi\)
0.383554 + 0.923518i \(0.374700\pi\)
\(150\) 0 0
\(151\) −13.5681 −1.10415 −0.552077 0.833793i \(-0.686165\pi\)
−0.552077 + 0.833793i \(0.686165\pi\)
\(152\) 3.68842 0.299170
\(153\) 0 0
\(154\) 0 0
\(155\) 14.9217 1.19854
\(156\) 0 0
\(157\) −18.7406 −1.49566 −0.747831 0.663890i \(-0.768904\pi\)
−0.747831 + 0.663890i \(0.768904\pi\)
\(158\) 0.418833 0.0333205
\(159\) 0 0
\(160\) 4.41883 0.349339
\(161\) 0 0
\(162\) 0 0
\(163\) 18.7724 1.47037 0.735185 0.677867i \(-0.237096\pi\)
0.735185 + 0.677867i \(0.237096\pi\)
\(164\) −12.1492 −0.948697
\(165\) 0 0
\(166\) −2.14925 −0.166814
\(167\) 23.8898 1.84865 0.924325 0.381606i \(-0.124629\pi\)
0.924325 + 0.381606i \(0.124629\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −10.5028 −0.805530
\(171\) 0 0
\(172\) 3.06525 0.233723
\(173\) −11.3768 −0.864965 −0.432482 0.901642i \(-0.642362\pi\)
−0.432482 + 0.901642i \(0.642362\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −12.8377 −0.962224
\(179\) −24.6101 −1.83944 −0.919722 0.392571i \(-0.871586\pi\)
−0.919722 + 0.392571i \(0.871586\pi\)
\(180\) 0 0
\(181\) 17.4608 1.29785 0.648927 0.760851i \(-0.275218\pi\)
0.648927 + 0.760851i \(0.275218\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.73042 0.348731
\(185\) −33.9738 −2.49781
\(186\) 0 0
\(187\) −2.37683 −0.173811
\(188\) 4.10725 0.299552
\(189\) 0 0
\(190\) −16.2985 −1.18242
\(191\) 16.8377 1.21833 0.609165 0.793043i \(-0.291505\pi\)
0.609165 + 0.793043i \(0.291505\pi\)
\(192\) 0 0
\(193\) 5.46083 0.393079 0.196540 0.980496i \(-0.437030\pi\)
0.196540 + 0.980496i \(0.437030\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) 0 0
\(197\) 9.68842 0.690271 0.345136 0.938553i \(-0.387833\pi\)
0.345136 + 0.938553i \(0.387833\pi\)
\(198\) 0 0
\(199\) 20.2985 1.43892 0.719461 0.694533i \(-0.244389\pi\)
0.719461 + 0.694533i \(0.244389\pi\)
\(200\) −14.5261 −1.02715
\(201\) 0 0
\(202\) −15.3637 −1.08099
\(203\) 0 0
\(204\) 0 0
\(205\) 53.6855 3.74956
\(206\) 2.62317 0.182765
\(207\) 0 0
\(208\) 0 0
\(209\) −3.68842 −0.255133
\(210\) 0 0
\(211\) 22.5130 1.54986 0.774929 0.632048i \(-0.217785\pi\)
0.774929 + 0.632048i \(0.217785\pi\)
\(212\) −8.00000 −0.549442
\(213\) 0 0
\(214\) 10.9029 0.745308
\(215\) −13.5448 −0.923750
\(216\) 0 0
\(217\) 0 0
\(218\) 11.7957 0.798903
\(219\) 0 0
\(220\) −4.41883 −0.297918
\(221\) 0 0
\(222\) 0 0
\(223\) −7.46083 −0.499614 −0.249807 0.968296i \(-0.580367\pi\)
−0.249807 + 0.968296i \(0.580367\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 5.37683 0.357662
\(227\) 2.77241 0.184012 0.0920058 0.995758i \(-0.470672\pi\)
0.0920058 + 0.995758i \(0.470672\pi\)
\(228\) 0 0
\(229\) −2.53917 −0.167793 −0.0838965 0.996474i \(-0.526737\pi\)
−0.0838965 + 0.996474i \(0.526737\pi\)
\(230\) −20.9029 −1.37830
\(231\) 0 0
\(232\) −6.52608 −0.428458
\(233\) 24.0522 1.57571 0.787855 0.615861i \(-0.211192\pi\)
0.787855 + 0.615861i \(0.211192\pi\)
\(234\) 0 0
\(235\) −18.1492 −1.18393
\(236\) 12.5261 0.815379
\(237\) 0 0
\(238\) 0 0
\(239\) −7.59133 −0.491042 −0.245521 0.969391i \(-0.578959\pi\)
−0.245521 + 0.969391i \(0.578959\pi\)
\(240\) 0 0
\(241\) 16.2985 1.04988 0.524939 0.851140i \(-0.324088\pi\)
0.524939 + 0.851140i \(0.324088\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 0 0
\(244\) 3.79567 0.242993
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 3.37683 0.214429
\(249\) 0 0
\(250\) 42.0942 2.66227
\(251\) 8.61008 0.543463 0.271732 0.962373i \(-0.412404\pi\)
0.271732 + 0.962373i \(0.412404\pi\)
\(252\) 0 0
\(253\) −4.73042 −0.297399
\(254\) −0.730416 −0.0458304
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −0.837665 −0.0522521 −0.0261261 0.999659i \(-0.508317\pi\)
−0.0261261 + 0.999659i \(0.508317\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 7.37683 0.455742
\(263\) −10.8377 −0.668279 −0.334140 0.942524i \(-0.608446\pi\)
−0.334140 + 0.942524i \(0.608446\pi\)
\(264\) 0 0
\(265\) 35.3507 2.17157
\(266\) 0 0
\(267\) 0 0
\(268\) 10.1492 0.619964
\(269\) −17.8797 −1.09014 −0.545071 0.838390i \(-0.683497\pi\)
−0.545071 + 0.838390i \(0.683497\pi\)
\(270\) 0 0
\(271\) −8.83767 −0.536850 −0.268425 0.963301i \(-0.586503\pi\)
−0.268425 + 0.963301i \(0.586503\pi\)
\(272\) −2.37683 −0.144117
\(273\) 0 0
\(274\) −8.83767 −0.533903
\(275\) 14.5261 0.875956
\(276\) 0 0
\(277\) −16.0000 −0.961347 −0.480673 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) −1.47392 −0.0883997
\(279\) 0 0
\(280\) 0 0
\(281\) 15.9217 0.949807 0.474903 0.880038i \(-0.342483\pi\)
0.474903 + 0.880038i \(0.342483\pi\)
\(282\) 0 0
\(283\) −18.0840 −1.07498 −0.537491 0.843269i \(-0.680628\pi\)
−0.537491 + 0.843269i \(0.680628\pi\)
\(284\) −0.934749 −0.0554672
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −11.3507 −0.667686
\(290\) 28.8377 1.69341
\(291\) 0 0
\(292\) −7.46083 −0.436612
\(293\) −25.1492 −1.46923 −0.734617 0.678482i \(-0.762638\pi\)
−0.734617 + 0.678482i \(0.762638\pi\)
\(294\) 0 0
\(295\) −55.3507 −3.22264
\(296\) −7.68842 −0.446880
\(297\) 0 0
\(298\) −9.36375 −0.542427
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 13.5681 0.780755
\(303\) 0 0
\(304\) −3.68842 −0.211545
\(305\) −16.7724 −0.960386
\(306\) 0 0
\(307\) −3.86950 −0.220844 −0.110422 0.993885i \(-0.535220\pi\)
−0.110422 + 0.993885i \(0.535220\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −14.9217 −0.847494
\(311\) 13.5681 0.769375 0.384688 0.923047i \(-0.374309\pi\)
0.384688 + 0.923047i \(0.374309\pi\)
\(312\) 0 0
\(313\) 2.52608 0.142783 0.0713913 0.997448i \(-0.477256\pi\)
0.0713913 + 0.997448i \(0.477256\pi\)
\(314\) 18.7406 1.05759
\(315\) 0 0
\(316\) −0.418833 −0.0235612
\(317\) 20.0102 1.12388 0.561941 0.827177i \(-0.310055\pi\)
0.561941 + 0.827177i \(0.310055\pi\)
\(318\) 0 0
\(319\) 6.52608 0.365390
\(320\) −4.41883 −0.247020
\(321\) 0 0
\(322\) 0 0
\(323\) 8.76675 0.487795
\(324\) 0 0
\(325\) 0 0
\(326\) −18.7724 −1.03971
\(327\) 0 0
\(328\) 12.1492 0.670830
\(329\) 0 0
\(330\) 0 0
\(331\) −16.1492 −0.887643 −0.443821 0.896115i \(-0.646378\pi\)
−0.443821 + 0.896115i \(0.646378\pi\)
\(332\) 2.14925 0.117955
\(333\) 0 0
\(334\) −23.8898 −1.30719
\(335\) −44.8478 −2.45030
\(336\) 0 0
\(337\) 23.1362 1.26031 0.630154 0.776471i \(-0.282992\pi\)
0.630154 + 0.776471i \(0.282992\pi\)
\(338\) 13.0000 0.707107
\(339\) 0 0
\(340\) 10.5028 0.569596
\(341\) −3.37683 −0.182866
\(342\) 0 0
\(343\) 0 0
\(344\) −3.06525 −0.165267
\(345\) 0 0
\(346\) 11.3768 0.611622
\(347\) −15.6566 −0.840489 −0.420245 0.907411i \(-0.638056\pi\)
−0.420245 + 0.907411i \(0.638056\pi\)
\(348\) 0 0
\(349\) −20.0102 −1.07112 −0.535560 0.844497i \(-0.679899\pi\)
−0.535560 + 0.844497i \(0.679899\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) −7.46083 −0.397100 −0.198550 0.980091i \(-0.563623\pi\)
−0.198550 + 0.980091i \(0.563623\pi\)
\(354\) 0 0
\(355\) 4.13050 0.219224
\(356\) 12.8377 0.680395
\(357\) 0 0
\(358\) 24.6101 1.30068
\(359\) 11.2463 0.593559 0.296779 0.954946i \(-0.404087\pi\)
0.296779 + 0.954946i \(0.404087\pi\)
\(360\) 0 0
\(361\) −5.39558 −0.283978
\(362\) −17.4608 −0.917721
\(363\) 0 0
\(364\) 0 0
\(365\) 32.9682 1.72563
\(366\) 0 0
\(367\) −5.91600 −0.308813 −0.154406 0.988007i \(-0.549347\pi\)
−0.154406 + 0.988007i \(0.549347\pi\)
\(368\) −4.73042 −0.246590
\(369\) 0 0
\(370\) 33.9738 1.76622
\(371\) 0 0
\(372\) 0 0
\(373\) −23.1260 −1.19742 −0.598709 0.800966i \(-0.704320\pi\)
−0.598709 + 0.800966i \(0.704320\pi\)
\(374\) 2.37683 0.122903
\(375\) 0 0
\(376\) −4.10725 −0.211815
\(377\) 0 0
\(378\) 0 0
\(379\) −6.77241 −0.347876 −0.173938 0.984757i \(-0.555649\pi\)
−0.173938 + 0.984757i \(0.555649\pi\)
\(380\) 16.2985 0.836095
\(381\) 0 0
\(382\) −16.8377 −0.861490
\(383\) −25.3637 −1.29603 −0.648013 0.761629i \(-0.724400\pi\)
−0.648013 + 0.761629i \(0.724400\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5.46083 −0.277949
\(387\) 0 0
\(388\) 7.00000 0.355371
\(389\) −25.2565 −1.28056 −0.640278 0.768144i \(-0.721181\pi\)
−0.640278 + 0.768144i \(0.721181\pi\)
\(390\) 0 0
\(391\) 11.2434 0.568604
\(392\) 0 0
\(393\) 0 0
\(394\) −9.68842 −0.488095
\(395\) 1.85075 0.0931214
\(396\) 0 0
\(397\) −13.4739 −0.676237 −0.338118 0.941104i \(-0.609790\pi\)
−0.338118 + 0.941104i \(0.609790\pi\)
\(398\) −20.2985 −1.01747
\(399\) 0 0
\(400\) 14.5261 0.726304
\(401\) −33.8898 −1.69238 −0.846189 0.532883i \(-0.821108\pi\)
−0.846189 + 0.532883i \(0.821108\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 15.3637 0.764375
\(405\) 0 0
\(406\) 0 0
\(407\) 7.68842 0.381101
\(408\) 0 0
\(409\) −4.21450 −0.208394 −0.104197 0.994557i \(-0.533227\pi\)
−0.104197 + 0.994557i \(0.533227\pi\)
\(410\) −53.6855 −2.65134
\(411\) 0 0
\(412\) −2.62317 −0.129234
\(413\) 0 0
\(414\) 0 0
\(415\) −9.49717 −0.466198
\(416\) 0 0
\(417\) 0 0
\(418\) 3.68842 0.180406
\(419\) 22.3116 1.08999 0.544996 0.838439i \(-0.316531\pi\)
0.544996 + 0.838439i \(0.316531\pi\)
\(420\) 0 0
\(421\) 18.3116 0.892452 0.446226 0.894920i \(-0.352768\pi\)
0.446226 + 0.894920i \(0.352768\pi\)
\(422\) −22.5130 −1.09592
\(423\) 0 0
\(424\) 8.00000 0.388514
\(425\) −34.5261 −1.67476
\(426\) 0 0
\(427\) 0 0
\(428\) −10.9029 −0.527012
\(429\) 0 0
\(430\) 13.5448 0.653190
\(431\) 28.8377 1.38906 0.694531 0.719463i \(-0.255612\pi\)
0.694531 + 0.719463i \(0.255612\pi\)
\(432\) 0 0
\(433\) 7.62317 0.366346 0.183173 0.983081i \(-0.441363\pi\)
0.183173 + 0.983081i \(0.441363\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −11.7957 −0.564910
\(437\) 17.4477 0.834639
\(438\) 0 0
\(439\) −33.3739 −1.59285 −0.796425 0.604737i \(-0.793278\pi\)
−0.796425 + 0.604737i \(0.793278\pi\)
\(440\) 4.41883 0.210660
\(441\) 0 0
\(442\) 0 0
\(443\) 4.85075 0.230466 0.115233 0.993338i \(-0.463239\pi\)
0.115233 + 0.993338i \(0.463239\pi\)
\(444\) 0 0
\(445\) −56.7275 −2.68914
\(446\) 7.46083 0.353281
\(447\) 0 0
\(448\) 0 0
\(449\) −14.3450 −0.676982 −0.338491 0.940970i \(-0.609917\pi\)
−0.338491 + 0.940970i \(0.609917\pi\)
\(450\) 0 0
\(451\) −12.1492 −0.572086
\(452\) −5.37683 −0.252905
\(453\) 0 0
\(454\) −2.77241 −0.130116
\(455\) 0 0
\(456\) 0 0
\(457\) −25.1827 −1.17800 −0.588998 0.808135i \(-0.700477\pi\)
−0.588998 + 0.808135i \(0.700477\pi\)
\(458\) 2.53917 0.118648
\(459\) 0 0
\(460\) 20.9029 0.974603
\(461\) −13.0187 −0.606344 −0.303172 0.952936i \(-0.598046\pi\)
−0.303172 + 0.952936i \(0.598046\pi\)
\(462\) 0 0
\(463\) −14.2145 −0.660604 −0.330302 0.943875i \(-0.607151\pi\)
−0.330302 + 0.943875i \(0.607151\pi\)
\(464\) 6.52608 0.302966
\(465\) 0 0
\(466\) −24.0522 −1.11420
\(467\) 2.39558 0.110854 0.0554271 0.998463i \(-0.482348\pi\)
0.0554271 + 0.998463i \(0.482348\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 18.1492 0.837162
\(471\) 0 0
\(472\) −12.5261 −0.576560
\(473\) 3.06525 0.140940
\(474\) 0 0
\(475\) −53.5782 −2.45834
\(476\) 0 0
\(477\) 0 0
\(478\) 7.59133 0.347219
\(479\) −10.8377 −0.495186 −0.247593 0.968864i \(-0.579640\pi\)
−0.247593 + 0.968864i \(0.579640\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −16.2985 −0.742376
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −30.9318 −1.40454
\(486\) 0 0
\(487\) −34.6435 −1.56985 −0.784923 0.619593i \(-0.787298\pi\)
−0.784923 + 0.619593i \(0.787298\pi\)
\(488\) −3.79567 −0.171822
\(489\) 0 0
\(490\) 0 0
\(491\) −38.1492 −1.72165 −0.860826 0.508900i \(-0.830052\pi\)
−0.860826 + 0.508900i \(0.830052\pi\)
\(492\) 0 0
\(493\) −15.5114 −0.698599
\(494\) 0 0
\(495\) 0 0
\(496\) −3.37683 −0.151624
\(497\) 0 0
\(498\) 0 0
\(499\) −0.623166 −0.0278968 −0.0139484 0.999903i \(-0.504440\pi\)
−0.0139484 + 0.999903i \(0.504440\pi\)
\(500\) −42.0942 −1.88251
\(501\) 0 0
\(502\) −8.61008 −0.384287
\(503\) −31.1362 −1.38829 −0.694146 0.719834i \(-0.744218\pi\)
−0.694146 + 0.719834i \(0.744218\pi\)
\(504\) 0 0
\(505\) −67.8898 −3.02106
\(506\) 4.73042 0.210293
\(507\) 0 0
\(508\) 0.730416 0.0324070
\(509\) 42.1043 1.86624 0.933121 0.359563i \(-0.117074\pi\)
0.933121 + 0.359563i \(0.117074\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 0.837665 0.0369478
\(515\) 11.5913 0.510775
\(516\) 0 0
\(517\) 4.10725 0.180637
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −25.2667 −1.10483 −0.552417 0.833568i \(-0.686294\pi\)
−0.552417 + 0.833568i \(0.686294\pi\)
\(524\) −7.37683 −0.322258
\(525\) 0 0
\(526\) 10.8377 0.472545
\(527\) 8.02617 0.349626
\(528\) 0 0
\(529\) −0.623166 −0.0270942
\(530\) −35.3507 −1.53553
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 48.1782 2.08292
\(536\) −10.1492 −0.438381
\(537\) 0 0
\(538\) 17.8797 0.770847
\(539\) 0 0
\(540\) 0 0
\(541\) −4.41883 −0.189980 −0.0949902 0.995478i \(-0.530282\pi\)
−0.0949902 + 0.995478i \(0.530282\pi\)
\(542\) 8.83767 0.379610
\(543\) 0 0
\(544\) 2.37683 0.101906
\(545\) 52.1231 2.23271
\(546\) 0 0
\(547\) −27.6622 −1.18275 −0.591376 0.806396i \(-0.701415\pi\)
−0.591376 + 0.806396i \(0.701415\pi\)
\(548\) 8.83767 0.377526
\(549\) 0 0
\(550\) −14.5261 −0.619394
\(551\) −24.0709 −1.02546
\(552\) 0 0
\(553\) 0 0
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) 1.47392 0.0625080
\(557\) 7.98691 0.338416 0.169208 0.985580i \(-0.445879\pi\)
0.169208 + 0.985580i \(0.445879\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −15.9217 −0.671615
\(563\) 27.3507 1.15269 0.576346 0.817205i \(-0.304478\pi\)
0.576346 + 0.817205i \(0.304478\pi\)
\(564\) 0 0
\(565\) 23.7593 0.999562
\(566\) 18.0840 0.760127
\(567\) 0 0
\(568\) 0.934749 0.0392212
\(569\) 29.4477 1.23451 0.617257 0.786762i \(-0.288244\pi\)
0.617257 + 0.786762i \(0.288244\pi\)
\(570\) 0 0
\(571\) −14.5261 −0.607898 −0.303949 0.952688i \(-0.598305\pi\)
−0.303949 + 0.952688i \(0.598305\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −68.7144 −2.86559
\(576\) 0 0
\(577\) 13.3956 0.557665 0.278833 0.960340i \(-0.410053\pi\)
0.278833 + 0.960340i \(0.410053\pi\)
\(578\) 11.3507 0.472125
\(579\) 0 0
\(580\) −28.8377 −1.19742
\(581\) 0 0
\(582\) 0 0
\(583\) −8.00000 −0.331326
\(584\) 7.46083 0.308731
\(585\) 0 0
\(586\) 25.1492 1.03891
\(587\) 11.2928 0.466105 0.233053 0.972464i \(-0.425129\pi\)
0.233053 + 0.972464i \(0.425129\pi\)
\(588\) 0 0
\(589\) 12.4552 0.513206
\(590\) 55.3507 2.27875
\(591\) 0 0
\(592\) 7.68842 0.315992
\(593\) 19.5782 0.803982 0.401991 0.915644i \(-0.368318\pi\)
0.401991 + 0.915644i \(0.368318\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.36375 0.383554
\(597\) 0 0
\(598\) 0 0
\(599\) −10.9318 −0.446662 −0.223331 0.974743i \(-0.571693\pi\)
−0.223331 + 0.974743i \(0.571693\pi\)
\(600\) 0 0
\(601\) −41.2202 −1.68141 −0.840703 0.541497i \(-0.817858\pi\)
−0.840703 + 0.541497i \(0.817858\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −13.5681 −0.552077
\(605\) −4.41883 −0.179651
\(606\) 0 0
\(607\) −31.3405 −1.27207 −0.636036 0.771660i \(-0.719427\pi\)
−0.636036 + 0.771660i \(0.719427\pi\)
\(608\) 3.68842 0.149585
\(609\) 0 0
\(610\) 16.7724 0.679095
\(611\) 0 0
\(612\) 0 0
\(613\) 17.0885 0.690198 0.345099 0.938566i \(-0.387845\pi\)
0.345099 + 0.938566i \(0.387845\pi\)
\(614\) 3.86950 0.156160
\(615\) 0 0
\(616\) 0 0
\(617\) 6.96817 0.280528 0.140264 0.990114i \(-0.455205\pi\)
0.140264 + 0.990114i \(0.455205\pi\)
\(618\) 0 0
\(619\) −0.0187473 −0.000753517 0 −0.000376759 1.00000i \(-0.500120\pi\)
−0.000376759 1.00000i \(0.500120\pi\)
\(620\) 14.9217 0.599268
\(621\) 0 0
\(622\) −13.5681 −0.544030
\(623\) 0 0
\(624\) 0 0
\(625\) 113.377 4.53507
\(626\) −2.52608 −0.100963
\(627\) 0 0
\(628\) −18.7406 −0.747831
\(629\) −18.2741 −0.728636
\(630\) 0 0
\(631\) −5.78550 −0.230317 −0.115159 0.993347i \(-0.536738\pi\)
−0.115159 + 0.993347i \(0.536738\pi\)
\(632\) 0.418833 0.0166603
\(633\) 0 0
\(634\) −20.0102 −0.794705
\(635\) −3.22759 −0.128083
\(636\) 0 0
\(637\) 0 0
\(638\) −6.52608 −0.258370
\(639\) 0 0
\(640\) 4.41883 0.174670
\(641\) −15.3768 −0.607348 −0.303674 0.952776i \(-0.598213\pi\)
−0.303674 + 0.952776i \(0.598213\pi\)
\(642\) 0 0
\(643\) −35.8058 −1.41204 −0.706022 0.708190i \(-0.749512\pi\)
−0.706022 + 0.708190i \(0.749512\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8.76675 −0.344923
\(647\) −9.25650 −0.363910 −0.181955 0.983307i \(-0.558243\pi\)
−0.181955 + 0.983307i \(0.558243\pi\)
\(648\) 0 0
\(649\) 12.5261 0.491692
\(650\) 0 0
\(651\) 0 0
\(652\) 18.7724 0.735185
\(653\) −24.8478 −0.972371 −0.486185 0.873856i \(-0.661612\pi\)
−0.486185 + 0.873856i \(0.661612\pi\)
\(654\) 0 0
\(655\) 32.5970 1.27367
\(656\) −12.1492 −0.474348
\(657\) 0 0
\(658\) 0 0
\(659\) 6.60442 0.257272 0.128636 0.991692i \(-0.458940\pi\)
0.128636 + 0.991692i \(0.458940\pi\)
\(660\) 0 0
\(661\) −13.2332 −0.514714 −0.257357 0.966316i \(-0.582852\pi\)
−0.257357 + 0.966316i \(0.582852\pi\)
\(662\) 16.1492 0.627658
\(663\) 0 0
\(664\) −2.14925 −0.0834070
\(665\) 0 0
\(666\) 0 0
\(667\) −30.8711 −1.19533
\(668\) 23.8898 0.924325
\(669\) 0 0
\(670\) 44.8478 1.73262
\(671\) 3.79567 0.146530
\(672\) 0 0
\(673\) 0.130501 0.00503045 0.00251523 0.999997i \(-0.499199\pi\)
0.00251523 + 0.999997i \(0.499199\pi\)
\(674\) −23.1362 −0.891172
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −28.1174 −1.08064 −0.540320 0.841460i \(-0.681697\pi\)
−0.540320 + 0.841460i \(0.681697\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −10.5028 −0.402765
\(681\) 0 0
\(682\) 3.37683 0.129306
\(683\) −15.9029 −0.608508 −0.304254 0.952591i \(-0.598407\pi\)
−0.304254 + 0.952591i \(0.598407\pi\)
\(684\) 0 0
\(685\) −39.0522 −1.49211
\(686\) 0 0
\(687\) 0 0
\(688\) 3.06525 0.116862
\(689\) 0 0
\(690\) 0 0
\(691\) −15.9813 −0.607956 −0.303978 0.952679i \(-0.598315\pi\)
−0.303978 + 0.952679i \(0.598315\pi\)
\(692\) −11.3768 −0.432482
\(693\) 0 0
\(694\) 15.6566 0.594316
\(695\) −6.51300 −0.247052
\(696\) 0 0
\(697\) 28.8767 1.09378
\(698\) 20.0102 0.757396
\(699\) 0 0
\(700\) 0 0
\(701\) −13.9869 −0.528278 −0.264139 0.964485i \(-0.585088\pi\)
−0.264139 + 0.964485i \(0.585088\pi\)
\(702\) 0 0
\(703\) −28.3581 −1.06955
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 7.46083 0.280792
\(707\) 0 0
\(708\) 0 0
\(709\) 7.64191 0.286998 0.143499 0.989650i \(-0.454165\pi\)
0.143499 + 0.989650i \(0.454165\pi\)
\(710\) −4.13050 −0.155015
\(711\) 0 0
\(712\) −12.8377 −0.481112
\(713\) 15.9738 0.598225
\(714\) 0 0
\(715\) 0 0
\(716\) −24.6101 −0.919722
\(717\) 0 0
\(718\) −11.2463 −0.419709
\(719\) 19.4376 0.724899 0.362450 0.932003i \(-0.381940\pi\)
0.362450 + 0.932003i \(0.381940\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 5.39558 0.200803
\(723\) 0 0
\(724\) 17.4608 0.648927
\(725\) 94.7984 3.52072
\(726\) 0 0
\(727\) −44.9217 −1.66605 −0.833026 0.553234i \(-0.813394\pi\)
−0.833026 + 0.553234i \(0.813394\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −32.9682 −1.22021
\(731\) −7.28559 −0.269467
\(732\) 0 0
\(733\) 25.0420 0.924947 0.462474 0.886633i \(-0.346962\pi\)
0.462474 + 0.886633i \(0.346962\pi\)
\(734\) 5.91600 0.218364
\(735\) 0 0
\(736\) 4.73042 0.174365
\(737\) 10.1492 0.373852
\(738\) 0 0
\(739\) −6.62317 −0.243637 −0.121819 0.992552i \(-0.538873\pi\)
−0.121819 + 0.992552i \(0.538873\pi\)
\(740\) −33.9738 −1.24890
\(741\) 0 0
\(742\) 0 0
\(743\) 39.3972 1.44534 0.722671 0.691192i \(-0.242914\pi\)
0.722671 + 0.691192i \(0.242914\pi\)
\(744\) 0 0
\(745\) −41.3768 −1.51593
\(746\) 23.1260 0.846703
\(747\) 0 0
\(748\) −2.37683 −0.0869056
\(749\) 0 0
\(750\) 0 0
\(751\) −10.7072 −0.390710 −0.195355 0.980733i \(-0.562586\pi\)
−0.195355 + 0.980733i \(0.562586\pi\)
\(752\) 4.10725 0.149776
\(753\) 0 0
\(754\) 0 0
\(755\) 59.9551 2.18199
\(756\) 0 0
\(757\) −17.2797 −0.628043 −0.314022 0.949416i \(-0.601676\pi\)
−0.314022 + 0.949416i \(0.601676\pi\)
\(758\) 6.77241 0.245985
\(759\) 0 0
\(760\) −16.2985 −0.591209
\(761\) 32.7087 1.18569 0.592846 0.805316i \(-0.298004\pi\)
0.592846 + 0.805316i \(0.298004\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 16.8377 0.609165
\(765\) 0 0
\(766\) 25.3637 0.916429
\(767\) 0 0
\(768\) 0 0
\(769\) 12.2145 0.440466 0.220233 0.975447i \(-0.429318\pi\)
0.220233 + 0.975447i \(0.429318\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.46083 0.196540
\(773\) −0.204334 −0.00734937 −0.00367468 0.999993i \(-0.501170\pi\)
−0.00367468 + 0.999993i \(0.501170\pi\)
\(774\) 0 0
\(775\) −49.0522 −1.76201
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 25.2565 0.905489
\(779\) 44.8115 1.60554
\(780\) 0 0
\(781\) −0.934749 −0.0334480
\(782\) −11.2434 −0.402064
\(783\) 0 0
\(784\) 0 0
\(785\) 82.8115 2.95567
\(786\) 0 0
\(787\) 25.5579 0.911041 0.455521 0.890225i \(-0.349453\pi\)
0.455521 + 0.890225i \(0.349453\pi\)
\(788\) 9.68842 0.345136
\(789\) 0 0
\(790\) −1.85075 −0.0658468
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 13.4739 0.478171
\(795\) 0 0
\(796\) 20.2985 0.719461
\(797\) −30.0477 −1.06434 −0.532171 0.846637i \(-0.678624\pi\)
−0.532171 + 0.846637i \(0.678624\pi\)
\(798\) 0 0
\(799\) −9.76225 −0.345364
\(800\) −14.5261 −0.513575
\(801\) 0 0
\(802\) 33.8898 1.19669
\(803\) −7.46083 −0.263287
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −15.3637 −0.540495
\(809\) −2.34342 −0.0823901 −0.0411951 0.999151i \(-0.513117\pi\)
−0.0411951 + 0.999151i \(0.513117\pi\)
\(810\) 0 0
\(811\) −11.8695 −0.416794 −0.208397 0.978044i \(-0.566825\pi\)
−0.208397 + 0.978044i \(0.566825\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −7.68842 −0.269479
\(815\) −82.9522 −2.90569
\(816\) 0 0
\(817\) −11.3059 −0.395544
\(818\) 4.21450 0.147357
\(819\) 0 0
\(820\) 53.6855 1.87478
\(821\) 37.4812 1.30810 0.654051 0.756451i \(-0.273068\pi\)
0.654051 + 0.756451i \(0.273068\pi\)
\(822\) 0 0
\(823\) 1.29284 0.0450654 0.0225327 0.999746i \(-0.492827\pi\)
0.0225327 + 0.999746i \(0.492827\pi\)
\(824\) 2.62317 0.0913823
\(825\) 0 0
\(826\) 0 0
\(827\) −43.3319 −1.50680 −0.753399 0.657563i \(-0.771587\pi\)
−0.753399 + 0.657563i \(0.771587\pi\)
\(828\) 0 0
\(829\) 40.1174 1.39334 0.696668 0.717394i \(-0.254665\pi\)
0.696668 + 0.717394i \(0.254665\pi\)
\(830\) 9.49717 0.329652
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −105.565 −3.65323
\(836\) −3.68842 −0.127567
\(837\) 0 0
\(838\) −22.3116 −0.770741
\(839\) −54.6912 −1.88815 −0.944074 0.329733i \(-0.893041\pi\)
−0.944074 + 0.329733i \(0.893041\pi\)
\(840\) 0 0
\(841\) 13.5897 0.468612
\(842\) −18.3116 −0.631059
\(843\) 0 0
\(844\) 22.5130 0.774929
\(845\) 57.4448 1.97616
\(846\) 0 0
\(847\) 0 0
\(848\) −8.00000 −0.274721
\(849\) 0 0
\(850\) 34.5261 1.18423
\(851\) −36.3694 −1.24673
\(852\) 0 0
\(853\) −20.8275 −0.713120 −0.356560 0.934272i \(-0.616050\pi\)
−0.356560 + 0.934272i \(0.616050\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 10.9029 0.372654
\(857\) 36.8433 1.25854 0.629272 0.777185i \(-0.283353\pi\)
0.629272 + 0.777185i \(0.283353\pi\)
\(858\) 0 0
\(859\) 38.5782 1.31627 0.658136 0.752899i \(-0.271345\pi\)
0.658136 + 0.752899i \(0.271345\pi\)
\(860\) −13.5448 −0.461875
\(861\) 0 0
\(862\) −28.8377 −0.982215
\(863\) 17.2565 0.587418 0.293709 0.955895i \(-0.405110\pi\)
0.293709 + 0.955895i \(0.405110\pi\)
\(864\) 0 0
\(865\) 50.2723 1.70931
\(866\) −7.62317 −0.259046
\(867\) 0 0
\(868\) 0 0
\(869\) −0.418833 −0.0142079
\(870\) 0 0
\(871\) 0 0
\(872\) 11.7957 0.399452
\(873\) 0 0
\(874\) −17.4477 −0.590179
\(875\) 0 0
\(876\) 0 0
\(877\) 0.250837 0.00847016 0.00423508 0.999991i \(-0.498652\pi\)
0.00423508 + 0.999991i \(0.498652\pi\)
\(878\) 33.3739 1.12632
\(879\) 0 0
\(880\) −4.41883 −0.148959
\(881\) −16.2985 −0.549110 −0.274555 0.961571i \(-0.588531\pi\)
−0.274555 + 0.961571i \(0.588531\pi\)
\(882\) 0 0
\(883\) −33.9551 −1.14268 −0.571340 0.820714i \(-0.693576\pi\)
−0.571340 + 0.820714i \(0.693576\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −4.85075 −0.162964
\(887\) −19.4608 −0.653431 −0.326715 0.945123i \(-0.605942\pi\)
−0.326715 + 0.945123i \(0.605942\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 56.7275 1.90151
\(891\) 0 0
\(892\) −7.46083 −0.249807
\(893\) −15.1492 −0.506950
\(894\) 0 0
\(895\) 108.748 3.63504
\(896\) 0 0
\(897\) 0 0
\(898\) 14.3450 0.478699
\(899\) −22.0375 −0.734992
\(900\) 0 0
\(901\) 19.0147 0.633470
\(902\) 12.1492 0.404526
\(903\) 0 0
\(904\) 5.37683 0.178831
\(905\) −77.1565 −2.56477
\(906\) 0 0
\(907\) 0.772415 0.0256476 0.0128238 0.999918i \(-0.495918\pi\)
0.0128238 + 0.999918i \(0.495918\pi\)
\(908\) 2.77241 0.0920058
\(909\) 0 0
\(910\) 0 0
\(911\) 8.94491 0.296358 0.148179 0.988961i \(-0.452659\pi\)
0.148179 + 0.988961i \(0.452659\pi\)
\(912\) 0 0
\(913\) 2.14925 0.0711297
\(914\) 25.1827 0.832969
\(915\) 0 0
\(916\) −2.53917 −0.0838965
\(917\) 0 0
\(918\) 0 0
\(919\) 58.8812 1.94231 0.971157 0.238443i \(-0.0766369\pi\)
0.971157 + 0.238443i \(0.0766369\pi\)
\(920\) −20.9029 −0.689149
\(921\) 0 0
\(922\) 13.0187 0.428750
\(923\) 0 0
\(924\) 0 0
\(925\) 111.683 3.67210
\(926\) 14.2145 0.467117
\(927\) 0 0
\(928\) −6.52608 −0.214229
\(929\) 22.5392 0.739486 0.369743 0.929134i \(-0.379446\pi\)
0.369743 + 0.929134i \(0.379446\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 24.0522 0.787855
\(933\) 0 0
\(934\) −2.39558 −0.0783858
\(935\) 10.5028 0.343479
\(936\) 0 0
\(937\) −12.9478 −0.422987 −0.211494 0.977379i \(-0.567833\pi\)
−0.211494 + 0.977379i \(0.567833\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −18.1492 −0.591963
\(941\) −48.8246 −1.59164 −0.795818 0.605536i \(-0.792959\pi\)
−0.795818 + 0.605536i \(0.792959\pi\)
\(942\) 0 0
\(943\) 57.4710 1.87151
\(944\) 12.5261 0.407689
\(945\) 0 0
\(946\) −3.06525 −0.0996599
\(947\) 31.1231 1.01136 0.505682 0.862720i \(-0.331241\pi\)
0.505682 + 0.862720i \(0.331241\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 53.5782 1.73831
\(951\) 0 0
\(952\) 0 0
\(953\) −16.2797 −0.527353 −0.263676 0.964611i \(-0.584935\pi\)
−0.263676 + 0.964611i \(0.584935\pi\)
\(954\) 0 0
\(955\) −74.4028 −2.40762
\(956\) −7.59133 −0.245521
\(957\) 0 0
\(958\) 10.8377 0.350149
\(959\) 0 0
\(960\) 0 0
\(961\) −19.5970 −0.632161
\(962\) 0 0
\(963\) 0 0
\(964\) 16.2985 0.524939
\(965\) −24.1305 −0.776788
\(966\) 0 0
\(967\) 3.91308 0.125836 0.0629181 0.998019i \(-0.479959\pi\)
0.0629181 + 0.998019i \(0.479959\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 0 0
\(970\) 30.9318 0.993161
\(971\) −39.3132 −1.26162 −0.630810 0.775938i \(-0.717277\pi\)
−0.630810 + 0.775938i \(0.717277\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 34.6435 1.11005
\(975\) 0 0
\(976\) 3.79567 0.121496
\(977\) 23.3507 0.747054 0.373527 0.927619i \(-0.378148\pi\)
0.373527 + 0.927619i \(0.378148\pi\)
\(978\) 0 0
\(979\) 12.8377 0.410294
\(980\) 0 0
\(981\) 0 0
\(982\) 38.1492 1.21739
\(983\) 4.51592 0.144035 0.0720177 0.997403i \(-0.477056\pi\)
0.0720177 + 0.997403i \(0.477056\pi\)
\(984\) 0 0
\(985\) −42.8115 −1.36409
\(986\) 15.5114 0.493984
\(987\) 0 0
\(988\) 0 0
\(989\) −14.4999 −0.461070
\(990\) 0 0
\(991\) 59.9273 1.90365 0.951827 0.306635i \(-0.0992032\pi\)
0.951827 + 0.306635i \(0.0992032\pi\)
\(992\) 3.37683 0.107215
\(993\) 0 0
\(994\) 0 0
\(995\) −89.6957 −2.84354
\(996\) 0 0
\(997\) −21.5073 −0.681144 −0.340572 0.940218i \(-0.610621\pi\)
−0.340572 + 0.940218i \(0.610621\pi\)
\(998\) 0.623166 0.0197260
\(999\) 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 9702.2.a.dv.1.1 3
3.2 odd 2 3234.2.a.bf.1.3 3
7.2 even 3 1386.2.k.v.991.3 6
7.4 even 3 1386.2.k.v.793.3 6
7.6 odd 2 9702.2.a.dw.1.3 3
21.2 odd 6 462.2.i.g.67.1 6
21.11 odd 6 462.2.i.g.331.1 yes 6
21.20 even 2 3234.2.a.bh.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.i.g.67.1 6 21.2 odd 6
462.2.i.g.331.1 yes 6 21.11 odd 6
1386.2.k.v.793.3 6 7.4 even 3
1386.2.k.v.991.3 6 7.2 even 3
3234.2.a.bf.1.3 3 3.2 odd 2
3234.2.a.bh.1.1 3 21.20 even 2
9702.2.a.dv.1.1 3 1.1 even 1 trivial
9702.2.a.dw.1.3 3 7.6 odd 2