Properties

Label 8016.2.a.be.1.6
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.0427374\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +0.957263 q^{5} +0.898491 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +0.957263 q^{5} +0.898491 q^{7} +1.00000 q^{9} +0.936680 q^{11} +1.86614 q^{13} +0.957263 q^{15} +6.88802 q^{17} -0.644628 q^{19} +0.898491 q^{21} +1.95775 q^{23} -4.08365 q^{25} +1.00000 q^{27} -0.602379 q^{29} -3.41687 q^{31} +0.936680 q^{33} +0.860092 q^{35} +11.6974 q^{37} +1.86614 q^{39} +0.378801 q^{41} +8.52617 q^{43} +0.957263 q^{45} +1.26703 q^{47} -6.19271 q^{49} +6.88802 q^{51} -9.54479 q^{53} +0.896648 q^{55} -0.644628 q^{57} +1.15472 q^{59} +12.4961 q^{61} +0.898491 q^{63} +1.78639 q^{65} -7.35619 q^{67} +1.95775 q^{69} -12.2991 q^{71} +0.169007 q^{73} -4.08365 q^{75} +0.841599 q^{77} +3.88101 q^{79} +1.00000 q^{81} +3.18308 q^{83} +6.59364 q^{85} -0.602379 q^{87} +6.13364 q^{89} +1.67671 q^{91} -3.41687 q^{93} -0.617078 q^{95} +6.69554 q^{97} +0.936680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + O(q^{10}) \) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + q^{11} + 10q^{13} + 10q^{15} + 17q^{17} - 2q^{19} + q^{21} + 3q^{23} + 21q^{25} + 11q^{27} + 17q^{29} + 15q^{31} + q^{33} - 11q^{35} + 4q^{37} + 10q^{39} + 16q^{41} - 10q^{43} + 10q^{45} + 16q^{47} + 22q^{49} + 17q^{51} + 42q^{53} + 5q^{55} - 2q^{57} + 2q^{59} + 12q^{61} + q^{63} + 10q^{65} + q^{67} + 3q^{69} + 9q^{71} + 24q^{73} + 21q^{75} + 22q^{77} + 30q^{79} + 11q^{81} - 16q^{83} + 25q^{85} + 17q^{87} + 37q^{89} - q^{91} + 15q^{93} - 5q^{95} + 4q^{97} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0.957263 0.428101 0.214050 0.976823i \(-0.431334\pi\)
0.214050 + 0.976823i \(0.431334\pi\)
\(6\) 0 0
\(7\) 0.898491 0.339598 0.169799 0.985479i \(-0.445688\pi\)
0.169799 + 0.985479i \(0.445688\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.936680 0.282420 0.141210 0.989980i \(-0.454901\pi\)
0.141210 + 0.989980i \(0.454901\pi\)
\(12\) 0 0
\(13\) 1.86614 0.517575 0.258788 0.965934i \(-0.416677\pi\)
0.258788 + 0.965934i \(0.416677\pi\)
\(14\) 0 0
\(15\) 0.957263 0.247164
\(16\) 0 0
\(17\) 6.88802 1.67059 0.835295 0.549802i \(-0.185297\pi\)
0.835295 + 0.549802i \(0.185297\pi\)
\(18\) 0 0
\(19\) −0.644628 −0.147888 −0.0739439 0.997262i \(-0.523559\pi\)
−0.0739439 + 0.997262i \(0.523559\pi\)
\(20\) 0 0
\(21\) 0.898491 0.196067
\(22\) 0 0
\(23\) 1.95775 0.408219 0.204110 0.978948i \(-0.434570\pi\)
0.204110 + 0.978948i \(0.434570\pi\)
\(24\) 0 0
\(25\) −4.08365 −0.816730
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.602379 −0.111859 −0.0559295 0.998435i \(-0.517812\pi\)
−0.0559295 + 0.998435i \(0.517812\pi\)
\(30\) 0 0
\(31\) −3.41687 −0.613687 −0.306844 0.951760i \(-0.599273\pi\)
−0.306844 + 0.951760i \(0.599273\pi\)
\(32\) 0 0
\(33\) 0.936680 0.163055
\(34\) 0 0
\(35\) 0.860092 0.145382
\(36\) 0 0
\(37\) 11.6974 1.92304 0.961521 0.274731i \(-0.0885890\pi\)
0.961521 + 0.274731i \(0.0885890\pi\)
\(38\) 0 0
\(39\) 1.86614 0.298822
\(40\) 0 0
\(41\) 0.378801 0.0591588 0.0295794 0.999562i \(-0.490583\pi\)
0.0295794 + 0.999562i \(0.490583\pi\)
\(42\) 0 0
\(43\) 8.52617 1.30023 0.650114 0.759836i \(-0.274721\pi\)
0.650114 + 0.759836i \(0.274721\pi\)
\(44\) 0 0
\(45\) 0.957263 0.142700
\(46\) 0 0
\(47\) 1.26703 0.184815 0.0924075 0.995721i \(-0.470544\pi\)
0.0924075 + 0.995721i \(0.470544\pi\)
\(48\) 0 0
\(49\) −6.19271 −0.884673
\(50\) 0 0
\(51\) 6.88802 0.964516
\(52\) 0 0
\(53\) −9.54479 −1.31108 −0.655539 0.755161i \(-0.727559\pi\)
−0.655539 + 0.755161i \(0.727559\pi\)
\(54\) 0 0
\(55\) 0.896648 0.120904
\(56\) 0 0
\(57\) −0.644628 −0.0853830
\(58\) 0 0
\(59\) 1.15472 0.150331 0.0751657 0.997171i \(-0.476051\pi\)
0.0751657 + 0.997171i \(0.476051\pi\)
\(60\) 0 0
\(61\) 12.4961 1.59997 0.799984 0.600021i \(-0.204841\pi\)
0.799984 + 0.600021i \(0.204841\pi\)
\(62\) 0 0
\(63\) 0.898491 0.113199
\(64\) 0 0
\(65\) 1.78639 0.221574
\(66\) 0 0
\(67\) −7.35619 −0.898702 −0.449351 0.893355i \(-0.648345\pi\)
−0.449351 + 0.893355i \(0.648345\pi\)
\(68\) 0 0
\(69\) 1.95775 0.235686
\(70\) 0 0
\(71\) −12.2991 −1.45964 −0.729819 0.683640i \(-0.760396\pi\)
−0.729819 + 0.683640i \(0.760396\pi\)
\(72\) 0 0
\(73\) 0.169007 0.0197808 0.00989041 0.999951i \(-0.496852\pi\)
0.00989041 + 0.999951i \(0.496852\pi\)
\(74\) 0 0
\(75\) −4.08365 −0.471539
\(76\) 0 0
\(77\) 0.841599 0.0959091
\(78\) 0 0
\(79\) 3.88101 0.436648 0.218324 0.975876i \(-0.429941\pi\)
0.218324 + 0.975876i \(0.429941\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.18308 0.349388 0.174694 0.984623i \(-0.444106\pi\)
0.174694 + 0.984623i \(0.444106\pi\)
\(84\) 0 0
\(85\) 6.59364 0.715181
\(86\) 0 0
\(87\) −0.602379 −0.0645818
\(88\) 0 0
\(89\) 6.13364 0.650165 0.325082 0.945686i \(-0.394608\pi\)
0.325082 + 0.945686i \(0.394608\pi\)
\(90\) 0 0
\(91\) 1.67671 0.175767
\(92\) 0 0
\(93\) −3.41687 −0.354313
\(94\) 0 0
\(95\) −0.617078 −0.0633109
\(96\) 0 0
\(97\) 6.69554 0.679829 0.339914 0.940456i \(-0.389602\pi\)
0.339914 + 0.940456i \(0.389602\pi\)
\(98\) 0 0
\(99\) 0.936680 0.0941398
\(100\) 0 0
\(101\) −1.63976 −0.163162 −0.0815812 0.996667i \(-0.525997\pi\)
−0.0815812 + 0.996667i \(0.525997\pi\)
\(102\) 0 0
\(103\) 15.3568 1.51315 0.756575 0.653907i \(-0.226871\pi\)
0.756575 + 0.653907i \(0.226871\pi\)
\(104\) 0 0
\(105\) 0.860092 0.0839364
\(106\) 0 0
\(107\) −17.5800 −1.69952 −0.849762 0.527167i \(-0.823254\pi\)
−0.849762 + 0.527167i \(0.823254\pi\)
\(108\) 0 0
\(109\) 4.23275 0.405424 0.202712 0.979238i \(-0.435025\pi\)
0.202712 + 0.979238i \(0.435025\pi\)
\(110\) 0 0
\(111\) 11.6974 1.11027
\(112\) 0 0
\(113\) 9.07442 0.853649 0.426825 0.904334i \(-0.359632\pi\)
0.426825 + 0.904334i \(0.359632\pi\)
\(114\) 0 0
\(115\) 1.87408 0.174759
\(116\) 0 0
\(117\) 1.86614 0.172525
\(118\) 0 0
\(119\) 6.18883 0.567329
\(120\) 0 0
\(121\) −10.1226 −0.920239
\(122\) 0 0
\(123\) 0.378801 0.0341553
\(124\) 0 0
\(125\) −8.69544 −0.777743
\(126\) 0 0
\(127\) 2.02939 0.180079 0.0900397 0.995938i \(-0.471301\pi\)
0.0900397 + 0.995938i \(0.471301\pi\)
\(128\) 0 0
\(129\) 8.52617 0.750687
\(130\) 0 0
\(131\) 2.24829 0.196434 0.0982169 0.995165i \(-0.468686\pi\)
0.0982169 + 0.995165i \(0.468686\pi\)
\(132\) 0 0
\(133\) −0.579192 −0.0502224
\(134\) 0 0
\(135\) 0.957263 0.0823880
\(136\) 0 0
\(137\) 17.5077 1.49578 0.747892 0.663821i \(-0.231066\pi\)
0.747892 + 0.663821i \(0.231066\pi\)
\(138\) 0 0
\(139\) −10.4488 −0.886254 −0.443127 0.896459i \(-0.646131\pi\)
−0.443127 + 0.896459i \(0.646131\pi\)
\(140\) 0 0
\(141\) 1.26703 0.106703
\(142\) 0 0
\(143\) 1.74798 0.146173
\(144\) 0 0
\(145\) −0.576635 −0.0478869
\(146\) 0 0
\(147\) −6.19271 −0.510766
\(148\) 0 0
\(149\) 14.6570 1.20074 0.600372 0.799721i \(-0.295019\pi\)
0.600372 + 0.799721i \(0.295019\pi\)
\(150\) 0 0
\(151\) −14.9495 −1.21658 −0.608288 0.793716i \(-0.708144\pi\)
−0.608288 + 0.793716i \(0.708144\pi\)
\(152\) 0 0
\(153\) 6.88802 0.556863
\(154\) 0 0
\(155\) −3.27084 −0.262720
\(156\) 0 0
\(157\) −19.1037 −1.52464 −0.762320 0.647201i \(-0.775939\pi\)
−0.762320 + 0.647201i \(0.775939\pi\)
\(158\) 0 0
\(159\) −9.54479 −0.756951
\(160\) 0 0
\(161\) 1.75902 0.138630
\(162\) 0 0
\(163\) −22.8963 −1.79338 −0.896689 0.442661i \(-0.854035\pi\)
−0.896689 + 0.442661i \(0.854035\pi\)
\(164\) 0 0
\(165\) 0.896648 0.0698040
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −9.51751 −0.732116
\(170\) 0 0
\(171\) −0.644628 −0.0492959
\(172\) 0 0
\(173\) −6.22466 −0.473252 −0.236626 0.971601i \(-0.576042\pi\)
−0.236626 + 0.971601i \(0.576042\pi\)
\(174\) 0 0
\(175\) −3.66912 −0.277360
\(176\) 0 0
\(177\) 1.15472 0.0867939
\(178\) 0 0
\(179\) −5.88741 −0.440045 −0.220023 0.975495i \(-0.570613\pi\)
−0.220023 + 0.975495i \(0.570613\pi\)
\(180\) 0 0
\(181\) 16.5734 1.23189 0.615945 0.787789i \(-0.288774\pi\)
0.615945 + 0.787789i \(0.288774\pi\)
\(182\) 0 0
\(183\) 12.4961 0.923742
\(184\) 0 0
\(185\) 11.1975 0.823256
\(186\) 0 0
\(187\) 6.45187 0.471807
\(188\) 0 0
\(189\) 0.898491 0.0653556
\(190\) 0 0
\(191\) −9.02118 −0.652749 −0.326375 0.945240i \(-0.605827\pi\)
−0.326375 + 0.945240i \(0.605827\pi\)
\(192\) 0 0
\(193\) 22.2488 1.60150 0.800751 0.598997i \(-0.204434\pi\)
0.800751 + 0.598997i \(0.204434\pi\)
\(194\) 0 0
\(195\) 1.78639 0.127926
\(196\) 0 0
\(197\) 16.2786 1.15980 0.579901 0.814687i \(-0.303091\pi\)
0.579901 + 0.814687i \(0.303091\pi\)
\(198\) 0 0
\(199\) −6.40270 −0.453875 −0.226938 0.973909i \(-0.572871\pi\)
−0.226938 + 0.973909i \(0.572871\pi\)
\(200\) 0 0
\(201\) −7.35619 −0.518866
\(202\) 0 0
\(203\) −0.541232 −0.0379870
\(204\) 0 0
\(205\) 0.362612 0.0253259
\(206\) 0 0
\(207\) 1.95775 0.136073
\(208\) 0 0
\(209\) −0.603810 −0.0417664
\(210\) 0 0
\(211\) 24.7500 1.70386 0.851930 0.523656i \(-0.175432\pi\)
0.851930 + 0.523656i \(0.175432\pi\)
\(212\) 0 0
\(213\) −12.2991 −0.842723
\(214\) 0 0
\(215\) 8.16178 0.556629
\(216\) 0 0
\(217\) −3.07002 −0.208407
\(218\) 0 0
\(219\) 0.169007 0.0114205
\(220\) 0 0
\(221\) 12.8540 0.864656
\(222\) 0 0
\(223\) 9.03276 0.604879 0.302439 0.953169i \(-0.402199\pi\)
0.302439 + 0.953169i \(0.402199\pi\)
\(224\) 0 0
\(225\) −4.08365 −0.272243
\(226\) 0 0
\(227\) −2.59080 −0.171958 −0.0859788 0.996297i \(-0.527402\pi\)
−0.0859788 + 0.996297i \(0.527402\pi\)
\(228\) 0 0
\(229\) −16.1034 −1.06415 −0.532073 0.846699i \(-0.678587\pi\)
−0.532073 + 0.846699i \(0.678587\pi\)
\(230\) 0 0
\(231\) 0.841599 0.0553731
\(232\) 0 0
\(233\) 4.40995 0.288905 0.144453 0.989512i \(-0.453858\pi\)
0.144453 + 0.989512i \(0.453858\pi\)
\(234\) 0 0
\(235\) 1.21288 0.0791195
\(236\) 0 0
\(237\) 3.88101 0.252099
\(238\) 0 0
\(239\) 21.3757 1.38268 0.691341 0.722529i \(-0.257020\pi\)
0.691341 + 0.722529i \(0.257020\pi\)
\(240\) 0 0
\(241\) −19.1359 −1.23265 −0.616326 0.787491i \(-0.711380\pi\)
−0.616326 + 0.787491i \(0.711380\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −5.92805 −0.378729
\(246\) 0 0
\(247\) −1.20297 −0.0765430
\(248\) 0 0
\(249\) 3.18308 0.201719
\(250\) 0 0
\(251\) −11.2928 −0.712794 −0.356397 0.934335i \(-0.615995\pi\)
−0.356397 + 0.934335i \(0.615995\pi\)
\(252\) 0 0
\(253\) 1.83379 0.115289
\(254\) 0 0
\(255\) 6.59364 0.412910
\(256\) 0 0
\(257\) −12.4069 −0.773922 −0.386961 0.922096i \(-0.626475\pi\)
−0.386961 + 0.922096i \(0.626475\pi\)
\(258\) 0 0
\(259\) 10.5100 0.653061
\(260\) 0 0
\(261\) −0.602379 −0.0372863
\(262\) 0 0
\(263\) 21.5868 1.33110 0.665550 0.746353i \(-0.268197\pi\)
0.665550 + 0.746353i \(0.268197\pi\)
\(264\) 0 0
\(265\) −9.13687 −0.561274
\(266\) 0 0
\(267\) 6.13364 0.375373
\(268\) 0 0
\(269\) 21.8764 1.33383 0.666913 0.745135i \(-0.267615\pi\)
0.666913 + 0.745135i \(0.267615\pi\)
\(270\) 0 0
\(271\) −18.0512 −1.09653 −0.548265 0.836304i \(-0.684712\pi\)
−0.548265 + 0.836304i \(0.684712\pi\)
\(272\) 0 0
\(273\) 1.67671 0.101479
\(274\) 0 0
\(275\) −3.82507 −0.230660
\(276\) 0 0
\(277\) 30.0096 1.80310 0.901552 0.432670i \(-0.142429\pi\)
0.901552 + 0.432670i \(0.142429\pi\)
\(278\) 0 0
\(279\) −3.41687 −0.204562
\(280\) 0 0
\(281\) 12.5473 0.748508 0.374254 0.927326i \(-0.377899\pi\)
0.374254 + 0.927326i \(0.377899\pi\)
\(282\) 0 0
\(283\) −4.41753 −0.262595 −0.131297 0.991343i \(-0.541914\pi\)
−0.131297 + 0.991343i \(0.541914\pi\)
\(284\) 0 0
\(285\) −0.617078 −0.0365525
\(286\) 0 0
\(287\) 0.340349 0.0200902
\(288\) 0 0
\(289\) 30.4448 1.79087
\(290\) 0 0
\(291\) 6.69554 0.392499
\(292\) 0 0
\(293\) 28.2336 1.64942 0.824712 0.565553i \(-0.191337\pi\)
0.824712 + 0.565553i \(0.191337\pi\)
\(294\) 0 0
\(295\) 1.10537 0.0643570
\(296\) 0 0
\(297\) 0.936680 0.0543517
\(298\) 0 0
\(299\) 3.65344 0.211284
\(300\) 0 0
\(301\) 7.66069 0.441555
\(302\) 0 0
\(303\) −1.63976 −0.0942018
\(304\) 0 0
\(305\) 11.9621 0.684948
\(306\) 0 0
\(307\) 12.9138 0.737028 0.368514 0.929622i \(-0.379867\pi\)
0.368514 + 0.929622i \(0.379867\pi\)
\(308\) 0 0
\(309\) 15.3568 0.873617
\(310\) 0 0
\(311\) −22.6980 −1.28708 −0.643542 0.765411i \(-0.722536\pi\)
−0.643542 + 0.765411i \(0.722536\pi\)
\(312\) 0 0
\(313\) −9.71914 −0.549358 −0.274679 0.961536i \(-0.588572\pi\)
−0.274679 + 0.961536i \(0.588572\pi\)
\(314\) 0 0
\(315\) 0.860092 0.0484607
\(316\) 0 0
\(317\) 20.4152 1.14663 0.573315 0.819335i \(-0.305657\pi\)
0.573315 + 0.819335i \(0.305657\pi\)
\(318\) 0 0
\(319\) −0.564236 −0.0315911
\(320\) 0 0
\(321\) −17.5800 −0.981220
\(322\) 0 0
\(323\) −4.44021 −0.247060
\(324\) 0 0
\(325\) −7.62067 −0.422719
\(326\) 0 0
\(327\) 4.23275 0.234071
\(328\) 0 0
\(329\) 1.13841 0.0627628
\(330\) 0 0
\(331\) −34.7167 −1.90820 −0.954102 0.299481i \(-0.903186\pi\)
−0.954102 + 0.299481i \(0.903186\pi\)
\(332\) 0 0
\(333\) 11.6974 0.641014
\(334\) 0 0
\(335\) −7.04181 −0.384735
\(336\) 0 0
\(337\) 15.0198 0.818179 0.409090 0.912494i \(-0.365846\pi\)
0.409090 + 0.912494i \(0.365846\pi\)
\(338\) 0 0
\(339\) 9.07442 0.492855
\(340\) 0 0
\(341\) −3.20051 −0.173317
\(342\) 0 0
\(343\) −11.8535 −0.640031
\(344\) 0 0
\(345\) 1.87408 0.100897
\(346\) 0 0
\(347\) 34.1773 1.83473 0.917367 0.398041i \(-0.130310\pi\)
0.917367 + 0.398041i \(0.130310\pi\)
\(348\) 0 0
\(349\) −22.2400 −1.19048 −0.595240 0.803548i \(-0.702943\pi\)
−0.595240 + 0.803548i \(0.702943\pi\)
\(350\) 0 0
\(351\) 1.86614 0.0996074
\(352\) 0 0
\(353\) 20.8093 1.10757 0.553783 0.832661i \(-0.313184\pi\)
0.553783 + 0.832661i \(0.313184\pi\)
\(354\) 0 0
\(355\) −11.7735 −0.624873
\(356\) 0 0
\(357\) 6.18883 0.327547
\(358\) 0 0
\(359\) 2.72748 0.143951 0.0719755 0.997406i \(-0.477070\pi\)
0.0719755 + 0.997406i \(0.477070\pi\)
\(360\) 0 0
\(361\) −18.5845 −0.978129
\(362\) 0 0
\(363\) −10.1226 −0.531300
\(364\) 0 0
\(365\) 0.161784 0.00846818
\(366\) 0 0
\(367\) 8.20332 0.428210 0.214105 0.976811i \(-0.431317\pi\)
0.214105 + 0.976811i \(0.431317\pi\)
\(368\) 0 0
\(369\) 0.378801 0.0197196
\(370\) 0 0
\(371\) −8.57591 −0.445239
\(372\) 0 0
\(373\) −3.50902 −0.181690 −0.0908451 0.995865i \(-0.528957\pi\)
−0.0908451 + 0.995865i \(0.528957\pi\)
\(374\) 0 0
\(375\) −8.69544 −0.449030
\(376\) 0 0
\(377\) −1.12413 −0.0578954
\(378\) 0 0
\(379\) −33.9160 −1.74215 −0.871075 0.491151i \(-0.836576\pi\)
−0.871075 + 0.491151i \(0.836576\pi\)
\(380\) 0 0
\(381\) 2.02939 0.103969
\(382\) 0 0
\(383\) −22.6926 −1.15954 −0.579768 0.814782i \(-0.696857\pi\)
−0.579768 + 0.814782i \(0.696857\pi\)
\(384\) 0 0
\(385\) 0.805631 0.0410587
\(386\) 0 0
\(387\) 8.52617 0.433409
\(388\) 0 0
\(389\) 1.72176 0.0872967 0.0436483 0.999047i \(-0.486102\pi\)
0.0436483 + 0.999047i \(0.486102\pi\)
\(390\) 0 0
\(391\) 13.4850 0.681967
\(392\) 0 0
\(393\) 2.24829 0.113411
\(394\) 0 0
\(395\) 3.71514 0.186929
\(396\) 0 0
\(397\) −8.23927 −0.413517 −0.206759 0.978392i \(-0.566291\pi\)
−0.206759 + 0.978392i \(0.566291\pi\)
\(398\) 0 0
\(399\) −0.579192 −0.0289959
\(400\) 0 0
\(401\) 16.2106 0.809517 0.404759 0.914424i \(-0.367356\pi\)
0.404759 + 0.914424i \(0.367356\pi\)
\(402\) 0 0
\(403\) −6.37636 −0.317629
\(404\) 0 0
\(405\) 0.957263 0.0475668
\(406\) 0 0
\(407\) 10.9567 0.543105
\(408\) 0 0
\(409\) −5.21408 −0.257819 −0.128910 0.991656i \(-0.541148\pi\)
−0.128910 + 0.991656i \(0.541148\pi\)
\(410\) 0 0
\(411\) 17.5077 0.863591
\(412\) 0 0
\(413\) 1.03750 0.0510522
\(414\) 0 0
\(415\) 3.04704 0.149573
\(416\) 0 0
\(417\) −10.4488 −0.511679
\(418\) 0 0
\(419\) 29.4092 1.43673 0.718367 0.695664i \(-0.244890\pi\)
0.718367 + 0.695664i \(0.244890\pi\)
\(420\) 0 0
\(421\) −6.96349 −0.339380 −0.169690 0.985497i \(-0.554277\pi\)
−0.169690 + 0.985497i \(0.554277\pi\)
\(422\) 0 0
\(423\) 1.26703 0.0616050
\(424\) 0 0
\(425\) −28.1282 −1.36442
\(426\) 0 0
\(427\) 11.2277 0.543346
\(428\) 0 0
\(429\) 1.74798 0.0843932
\(430\) 0 0
\(431\) −15.9755 −0.769513 −0.384756 0.923018i \(-0.625715\pi\)
−0.384756 + 0.923018i \(0.625715\pi\)
\(432\) 0 0
\(433\) 17.0269 0.818260 0.409130 0.912476i \(-0.365832\pi\)
0.409130 + 0.912476i \(0.365832\pi\)
\(434\) 0 0
\(435\) −0.576635 −0.0276475
\(436\) 0 0
\(437\) −1.26202 −0.0603706
\(438\) 0 0
\(439\) 4.69318 0.223993 0.111997 0.993709i \(-0.464275\pi\)
0.111997 + 0.993709i \(0.464275\pi\)
\(440\) 0 0
\(441\) −6.19271 −0.294891
\(442\) 0 0
\(443\) −16.9535 −0.805485 −0.402742 0.915313i \(-0.631943\pi\)
−0.402742 + 0.915313i \(0.631943\pi\)
\(444\) 0 0
\(445\) 5.87151 0.278336
\(446\) 0 0
\(447\) 14.6570 0.693250
\(448\) 0 0
\(449\) −2.99166 −0.141185 −0.0705926 0.997505i \(-0.522489\pi\)
−0.0705926 + 0.997505i \(0.522489\pi\)
\(450\) 0 0
\(451\) 0.354815 0.0167076
\(452\) 0 0
\(453\) −14.9495 −0.702391
\(454\) 0 0
\(455\) 1.60506 0.0752461
\(456\) 0 0
\(457\) −17.8935 −0.837023 −0.418512 0.908211i \(-0.637448\pi\)
−0.418512 + 0.908211i \(0.637448\pi\)
\(458\) 0 0
\(459\) 6.88802 0.321505
\(460\) 0 0
\(461\) 11.1815 0.520775 0.260388 0.965504i \(-0.416150\pi\)
0.260388 + 0.965504i \(0.416150\pi\)
\(462\) 0 0
\(463\) 21.5593 1.00195 0.500974 0.865463i \(-0.332975\pi\)
0.500974 + 0.865463i \(0.332975\pi\)
\(464\) 0 0
\(465\) −3.27084 −0.151681
\(466\) 0 0
\(467\) −40.8278 −1.88929 −0.944643 0.328099i \(-0.893592\pi\)
−0.944643 + 0.328099i \(0.893592\pi\)
\(468\) 0 0
\(469\) −6.60948 −0.305197
\(470\) 0 0
\(471\) −19.1037 −0.880251
\(472\) 0 0
\(473\) 7.98629 0.367210
\(474\) 0 0
\(475\) 2.63243 0.120784
\(476\) 0 0
\(477\) −9.54479 −0.437026
\(478\) 0 0
\(479\) −32.5220 −1.48597 −0.742984 0.669309i \(-0.766590\pi\)
−0.742984 + 0.669309i \(0.766590\pi\)
\(480\) 0 0
\(481\) 21.8290 0.995318
\(482\) 0 0
\(483\) 1.75902 0.0800383
\(484\) 0 0
\(485\) 6.40939 0.291035
\(486\) 0 0
\(487\) 25.6360 1.16168 0.580839 0.814019i \(-0.302725\pi\)
0.580839 + 0.814019i \(0.302725\pi\)
\(488\) 0 0
\(489\) −22.8963 −1.03541
\(490\) 0 0
\(491\) −26.7553 −1.20745 −0.603724 0.797193i \(-0.706317\pi\)
−0.603724 + 0.797193i \(0.706317\pi\)
\(492\) 0 0
\(493\) −4.14920 −0.186870
\(494\) 0 0
\(495\) 0.896648 0.0403013
\(496\) 0 0
\(497\) −11.0507 −0.495690
\(498\) 0 0
\(499\) 24.6712 1.10444 0.552218 0.833700i \(-0.313782\pi\)
0.552218 + 0.833700i \(0.313782\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 22.6975 1.01203 0.506017 0.862524i \(-0.331117\pi\)
0.506017 + 0.862524i \(0.331117\pi\)
\(504\) 0 0
\(505\) −1.56968 −0.0698500
\(506\) 0 0
\(507\) −9.51751 −0.422687
\(508\) 0 0
\(509\) −12.3937 −0.549341 −0.274670 0.961538i \(-0.588569\pi\)
−0.274670 + 0.961538i \(0.588569\pi\)
\(510\) 0 0
\(511\) 0.151852 0.00671752
\(512\) 0 0
\(513\) −0.644628 −0.0284610
\(514\) 0 0
\(515\) 14.7005 0.647781
\(516\) 0 0
\(517\) 1.18680 0.0521954
\(518\) 0 0
\(519\) −6.22466 −0.273232
\(520\) 0 0
\(521\) −17.6134 −0.771657 −0.385828 0.922571i \(-0.626084\pi\)
−0.385828 + 0.922571i \(0.626084\pi\)
\(522\) 0 0
\(523\) 40.4400 1.76832 0.884159 0.467186i \(-0.154732\pi\)
0.884159 + 0.467186i \(0.154732\pi\)
\(524\) 0 0
\(525\) −3.66912 −0.160134
\(526\) 0 0
\(527\) −23.5354 −1.02522
\(528\) 0 0
\(529\) −19.1672 −0.833357
\(530\) 0 0
\(531\) 1.15472 0.0501105
\(532\) 0 0
\(533\) 0.706897 0.0306191
\(534\) 0 0
\(535\) −16.8287 −0.727567
\(536\) 0 0
\(537\) −5.88741 −0.254060
\(538\) 0 0
\(539\) −5.80059 −0.249849
\(540\) 0 0
\(541\) −23.1829 −0.996712 −0.498356 0.866973i \(-0.666063\pi\)
−0.498356 + 0.866973i \(0.666063\pi\)
\(542\) 0 0
\(543\) 16.5734 0.711232
\(544\) 0 0
\(545\) 4.05185 0.173562
\(546\) 0 0
\(547\) −38.5664 −1.64898 −0.824490 0.565876i \(-0.808538\pi\)
−0.824490 + 0.565876i \(0.808538\pi\)
\(548\) 0 0
\(549\) 12.4961 0.533323
\(550\) 0 0
\(551\) 0.388310 0.0165426
\(552\) 0 0
\(553\) 3.48705 0.148285
\(554\) 0 0
\(555\) 11.1975 0.475307
\(556\) 0 0
\(557\) 39.5743 1.67682 0.838408 0.545042i \(-0.183486\pi\)
0.838408 + 0.545042i \(0.183486\pi\)
\(558\) 0 0
\(559\) 15.9111 0.672966
\(560\) 0 0
\(561\) 6.45187 0.272398
\(562\) 0 0
\(563\) 6.35440 0.267806 0.133903 0.990994i \(-0.457249\pi\)
0.133903 + 0.990994i \(0.457249\pi\)
\(564\) 0 0
\(565\) 8.68660 0.365448
\(566\) 0 0
\(567\) 0.898491 0.0377331
\(568\) 0 0
\(569\) −25.9936 −1.08971 −0.544854 0.838531i \(-0.683415\pi\)
−0.544854 + 0.838531i \(0.683415\pi\)
\(570\) 0 0
\(571\) 23.3120 0.975577 0.487788 0.872962i \(-0.337804\pi\)
0.487788 + 0.872962i \(0.337804\pi\)
\(572\) 0 0
\(573\) −9.02118 −0.376865
\(574\) 0 0
\(575\) −7.99477 −0.333405
\(576\) 0 0
\(577\) −13.5360 −0.563513 −0.281756 0.959486i \(-0.590917\pi\)
−0.281756 + 0.959486i \(0.590917\pi\)
\(578\) 0 0
\(579\) 22.2488 0.924628
\(580\) 0 0
\(581\) 2.85997 0.118651
\(582\) 0 0
\(583\) −8.94041 −0.370274
\(584\) 0 0
\(585\) 1.78639 0.0738581
\(586\) 0 0
\(587\) −0.367276 −0.0151591 −0.00757955 0.999971i \(-0.502413\pi\)
−0.00757955 + 0.999971i \(0.502413\pi\)
\(588\) 0 0
\(589\) 2.20261 0.0907568
\(590\) 0 0
\(591\) 16.2786 0.669612
\(592\) 0 0
\(593\) 39.9010 1.63854 0.819270 0.573409i \(-0.194379\pi\)
0.819270 + 0.573409i \(0.194379\pi\)
\(594\) 0 0
\(595\) 5.92433 0.242874
\(596\) 0 0
\(597\) −6.40270 −0.262045
\(598\) 0 0
\(599\) 25.2610 1.03214 0.516068 0.856548i \(-0.327395\pi\)
0.516068 + 0.856548i \(0.327395\pi\)
\(600\) 0 0
\(601\) −4.06751 −0.165917 −0.0829586 0.996553i \(-0.526437\pi\)
−0.0829586 + 0.996553i \(0.526437\pi\)
\(602\) 0 0
\(603\) −7.35619 −0.299567
\(604\) 0 0
\(605\) −9.69002 −0.393955
\(606\) 0 0
\(607\) 21.4937 0.872403 0.436202 0.899849i \(-0.356323\pi\)
0.436202 + 0.899849i \(0.356323\pi\)
\(608\) 0 0
\(609\) −0.541232 −0.0219318
\(610\) 0 0
\(611\) 2.36446 0.0956557
\(612\) 0 0
\(613\) −26.4260 −1.06734 −0.533668 0.845694i \(-0.679187\pi\)
−0.533668 + 0.845694i \(0.679187\pi\)
\(614\) 0 0
\(615\) 0.362612 0.0146219
\(616\) 0 0
\(617\) 11.4704 0.461781 0.230890 0.972980i \(-0.425836\pi\)
0.230890 + 0.972980i \(0.425836\pi\)
\(618\) 0 0
\(619\) 1.13826 0.0457507 0.0228753 0.999738i \(-0.492718\pi\)
0.0228753 + 0.999738i \(0.492718\pi\)
\(620\) 0 0
\(621\) 1.95775 0.0785618
\(622\) 0 0
\(623\) 5.51103 0.220795
\(624\) 0 0
\(625\) 12.0944 0.483777
\(626\) 0 0
\(627\) −0.603810 −0.0241138
\(628\) 0 0
\(629\) 80.5720 3.21261
\(630\) 0 0
\(631\) 38.2823 1.52400 0.761998 0.647580i \(-0.224219\pi\)
0.761998 + 0.647580i \(0.224219\pi\)
\(632\) 0 0
\(633\) 24.7500 0.983723
\(634\) 0 0
\(635\) 1.94266 0.0770921
\(636\) 0 0
\(637\) −11.5565 −0.457885
\(638\) 0 0
\(639\) −12.2991 −0.486546
\(640\) 0 0
\(641\) 0.729527 0.0288146 0.0144073 0.999896i \(-0.495414\pi\)
0.0144073 + 0.999896i \(0.495414\pi\)
\(642\) 0 0
\(643\) 5.10557 0.201344 0.100672 0.994920i \(-0.467901\pi\)
0.100672 + 0.994920i \(0.467901\pi\)
\(644\) 0 0
\(645\) 8.16178 0.321370
\(646\) 0 0
\(647\) 4.04426 0.158996 0.0794981 0.996835i \(-0.474668\pi\)
0.0794981 + 0.996835i \(0.474668\pi\)
\(648\) 0 0
\(649\) 1.08160 0.0424565
\(650\) 0 0
\(651\) −3.07002 −0.120324
\(652\) 0 0
\(653\) 0.252341 0.00987485 0.00493743 0.999988i \(-0.498428\pi\)
0.00493743 + 0.999988i \(0.498428\pi\)
\(654\) 0 0
\(655\) 2.15220 0.0840935
\(656\) 0 0
\(657\) 0.169007 0.00659361
\(658\) 0 0
\(659\) −19.7130 −0.767908 −0.383954 0.923352i \(-0.625438\pi\)
−0.383954 + 0.923352i \(0.625438\pi\)
\(660\) 0 0
\(661\) −33.3046 −1.29540 −0.647699 0.761896i \(-0.724268\pi\)
−0.647699 + 0.761896i \(0.724268\pi\)
\(662\) 0 0
\(663\) 12.8540 0.499209
\(664\) 0 0
\(665\) −0.554439 −0.0215002
\(666\) 0 0
\(667\) −1.17931 −0.0456630
\(668\) 0 0
\(669\) 9.03276 0.349227
\(670\) 0 0
\(671\) 11.7049 0.451862
\(672\) 0 0
\(673\) −24.1873 −0.932353 −0.466176 0.884692i \(-0.654369\pi\)
−0.466176 + 0.884692i \(0.654369\pi\)
\(674\) 0 0
\(675\) −4.08365 −0.157180
\(676\) 0 0
\(677\) 10.2383 0.393489 0.196744 0.980455i \(-0.436963\pi\)
0.196744 + 0.980455i \(0.436963\pi\)
\(678\) 0 0
\(679\) 6.01588 0.230868
\(680\) 0 0
\(681\) −2.59080 −0.0992798
\(682\) 0 0
\(683\) 25.9050 0.991226 0.495613 0.868543i \(-0.334943\pi\)
0.495613 + 0.868543i \(0.334943\pi\)
\(684\) 0 0
\(685\) 16.7595 0.640346
\(686\) 0 0
\(687\) −16.1034 −0.614385
\(688\) 0 0
\(689\) −17.8120 −0.678581
\(690\) 0 0
\(691\) −28.3962 −1.08024 −0.540121 0.841588i \(-0.681621\pi\)
−0.540121 + 0.841588i \(0.681621\pi\)
\(692\) 0 0
\(693\) 0.841599 0.0319697
\(694\) 0 0
\(695\) −10.0022 −0.379406
\(696\) 0 0
\(697\) 2.60919 0.0988301
\(698\) 0 0
\(699\) 4.40995 0.166800
\(700\) 0 0
\(701\) −50.6482 −1.91295 −0.956477 0.291806i \(-0.905744\pi\)
−0.956477 + 0.291806i \(0.905744\pi\)
\(702\) 0 0
\(703\) −7.54047 −0.284394
\(704\) 0 0
\(705\) 1.21288 0.0456797
\(706\) 0 0
\(707\) −1.47331 −0.0554096
\(708\) 0 0
\(709\) −44.0789 −1.65542 −0.827710 0.561157i \(-0.810357\pi\)
−0.827710 + 0.561157i \(0.810357\pi\)
\(710\) 0 0
\(711\) 3.88101 0.145549
\(712\) 0 0
\(713\) −6.68937 −0.250519
\(714\) 0 0
\(715\) 1.67327 0.0625769
\(716\) 0 0
\(717\) 21.3757 0.798291
\(718\) 0 0
\(719\) 14.6295 0.545587 0.272793 0.962073i \(-0.412052\pi\)
0.272793 + 0.962073i \(0.412052\pi\)
\(720\) 0 0
\(721\) 13.7979 0.513862
\(722\) 0 0
\(723\) −19.1359 −0.711672
\(724\) 0 0
\(725\) 2.45990 0.0913585
\(726\) 0 0
\(727\) 52.4926 1.94684 0.973421 0.229023i \(-0.0735530\pi\)
0.973421 + 0.229023i \(0.0735530\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 58.7284 2.17215
\(732\) 0 0
\(733\) 12.5837 0.464791 0.232396 0.972621i \(-0.425344\pi\)
0.232396 + 0.972621i \(0.425344\pi\)
\(734\) 0 0
\(735\) −5.92805 −0.218660
\(736\) 0 0
\(737\) −6.89040 −0.253811
\(738\) 0 0
\(739\) 0.539612 0.0198500 0.00992498 0.999951i \(-0.496841\pi\)
0.00992498 + 0.999951i \(0.496841\pi\)
\(740\) 0 0
\(741\) −1.20297 −0.0441921
\(742\) 0 0
\(743\) 11.9778 0.439422 0.219711 0.975565i \(-0.429489\pi\)
0.219711 + 0.975565i \(0.429489\pi\)
\(744\) 0 0
\(745\) 14.0306 0.514040
\(746\) 0 0
\(747\) 3.18308 0.116463
\(748\) 0 0
\(749\) −15.7955 −0.577154
\(750\) 0 0
\(751\) 31.2764 1.14129 0.570647 0.821196i \(-0.306693\pi\)
0.570647 + 0.821196i \(0.306693\pi\)
\(752\) 0 0
\(753\) −11.2928 −0.411532
\(754\) 0 0
\(755\) −14.3106 −0.520818
\(756\) 0 0
\(757\) −13.8376 −0.502935 −0.251467 0.967866i \(-0.580913\pi\)
−0.251467 + 0.967866i \(0.580913\pi\)
\(758\) 0 0
\(759\) 1.83379 0.0665622
\(760\) 0 0
\(761\) −14.8220 −0.537297 −0.268649 0.963238i \(-0.586577\pi\)
−0.268649 + 0.963238i \(0.586577\pi\)
\(762\) 0 0
\(763\) 3.80309 0.137681
\(764\) 0 0
\(765\) 6.59364 0.238394
\(766\) 0 0
\(767\) 2.15487 0.0778078
\(768\) 0 0
\(769\) −30.8191 −1.11136 −0.555682 0.831395i \(-0.687543\pi\)
−0.555682 + 0.831395i \(0.687543\pi\)
\(770\) 0 0
\(771\) −12.4069 −0.446824
\(772\) 0 0
\(773\) 9.42958 0.339159 0.169579 0.985517i \(-0.445759\pi\)
0.169579 + 0.985517i \(0.445759\pi\)
\(774\) 0 0
\(775\) 13.9533 0.501217
\(776\) 0 0
\(777\) 10.5100 0.377045
\(778\) 0 0
\(779\) −0.244186 −0.00874886
\(780\) 0 0
\(781\) −11.5204 −0.412231
\(782\) 0 0
\(783\) −0.602379 −0.0215273
\(784\) 0 0
\(785\) −18.2872 −0.652699
\(786\) 0 0
\(787\) −24.6894 −0.880081 −0.440041 0.897978i \(-0.645036\pi\)
−0.440041 + 0.897978i \(0.645036\pi\)
\(788\) 0 0
\(789\) 21.5868 0.768511
\(790\) 0 0
\(791\) 8.15329 0.289897
\(792\) 0 0
\(793\) 23.3196 0.828103
\(794\) 0 0
\(795\) −9.13687 −0.324051
\(796\) 0 0
\(797\) −16.2017 −0.573893 −0.286947 0.957947i \(-0.592640\pi\)
−0.286947 + 0.957947i \(0.592640\pi\)
\(798\) 0 0
\(799\) 8.72731 0.308750
\(800\) 0 0
\(801\) 6.13364 0.216722
\(802\) 0 0
\(803\) 0.158306 0.00558649
\(804\) 0 0
\(805\) 1.68385 0.0593478
\(806\) 0 0
\(807\) 21.8764 0.770085
\(808\) 0 0
\(809\) −5.73547 −0.201648 −0.100824 0.994904i \(-0.532148\pi\)
−0.100824 + 0.994904i \(0.532148\pi\)
\(810\) 0 0
\(811\) −36.0299 −1.26518 −0.632590 0.774487i \(-0.718008\pi\)
−0.632590 + 0.774487i \(0.718008\pi\)
\(812\) 0 0
\(813\) −18.0512 −0.633082
\(814\) 0 0
\(815\) −21.9178 −0.767747
\(816\) 0 0
\(817\) −5.49620 −0.192288
\(818\) 0 0
\(819\) 1.67671 0.0585891
\(820\) 0 0
\(821\) −12.5282 −0.437238 −0.218619 0.975810i \(-0.570155\pi\)
−0.218619 + 0.975810i \(0.570155\pi\)
\(822\) 0 0
\(823\) −43.0141 −1.49938 −0.749689 0.661791i \(-0.769797\pi\)
−0.749689 + 0.661791i \(0.769797\pi\)
\(824\) 0 0
\(825\) −3.82507 −0.133172
\(826\) 0 0
\(827\) 20.6080 0.716612 0.358306 0.933604i \(-0.383355\pi\)
0.358306 + 0.933604i \(0.383355\pi\)
\(828\) 0 0
\(829\) −29.3130 −1.01808 −0.509040 0.860743i \(-0.670000\pi\)
−0.509040 + 0.860743i \(0.670000\pi\)
\(830\) 0 0
\(831\) 30.0096 1.04102
\(832\) 0 0
\(833\) −42.6555 −1.47793
\(834\) 0 0
\(835\) −0.957263 −0.0331274
\(836\) 0 0
\(837\) −3.41687 −0.118104
\(838\) 0 0
\(839\) −29.9614 −1.03438 −0.517191 0.855870i \(-0.673022\pi\)
−0.517191 + 0.855870i \(0.673022\pi\)
\(840\) 0 0
\(841\) −28.6371 −0.987488
\(842\) 0 0
\(843\) 12.5473 0.432151
\(844\) 0 0
\(845\) −9.11076 −0.313420
\(846\) 0 0
\(847\) −9.09510 −0.312511
\(848\) 0 0
\(849\) −4.41753 −0.151609
\(850\) 0 0
\(851\) 22.9006 0.785023
\(852\) 0 0
\(853\) 47.0657 1.61150 0.805750 0.592256i \(-0.201762\pi\)
0.805750 + 0.592256i \(0.201762\pi\)
\(854\) 0 0
\(855\) −0.617078 −0.0211036
\(856\) 0 0
\(857\) −14.7556 −0.504041 −0.252020 0.967722i \(-0.581095\pi\)
−0.252020 + 0.967722i \(0.581095\pi\)
\(858\) 0 0
\(859\) −25.5694 −0.872416 −0.436208 0.899846i \(-0.643679\pi\)
−0.436208 + 0.899846i \(0.643679\pi\)
\(860\) 0 0
\(861\) 0.340349 0.0115991
\(862\) 0 0
\(863\) 26.7717 0.911320 0.455660 0.890154i \(-0.349403\pi\)
0.455660 + 0.890154i \(0.349403\pi\)
\(864\) 0 0
\(865\) −5.95863 −0.202600
\(866\) 0 0
\(867\) 30.4448 1.03396
\(868\) 0 0
\(869\) 3.63526 0.123318
\(870\) 0 0
\(871\) −13.7277 −0.465146
\(872\) 0 0
\(873\) 6.69554 0.226610
\(874\) 0 0
\(875\) −7.81277 −0.264120
\(876\) 0 0
\(877\) −41.9329 −1.41597 −0.707986 0.706226i \(-0.750396\pi\)
−0.707986 + 0.706226i \(0.750396\pi\)
\(878\) 0 0
\(879\) 28.2336 0.952295
\(880\) 0 0
\(881\) −38.2857 −1.28988 −0.644939 0.764234i \(-0.723117\pi\)
−0.644939 + 0.764234i \(0.723117\pi\)
\(882\) 0 0
\(883\) −23.8441 −0.802417 −0.401209 0.915987i \(-0.631410\pi\)
−0.401209 + 0.915987i \(0.631410\pi\)
\(884\) 0 0
\(885\) 1.10537 0.0371565
\(886\) 0 0
\(887\) 4.51521 0.151606 0.0758030 0.997123i \(-0.475848\pi\)
0.0758030 + 0.997123i \(0.475848\pi\)
\(888\) 0 0
\(889\) 1.82339 0.0611546
\(890\) 0 0
\(891\) 0.936680 0.0313799
\(892\) 0 0
\(893\) −0.816762 −0.0273319
\(894\) 0 0
\(895\) −5.63579 −0.188384
\(896\) 0 0
\(897\) 3.65344 0.121985
\(898\) 0 0
\(899\) 2.05825 0.0686464
\(900\) 0 0
\(901\) −65.7447 −2.19027
\(902\) 0 0
\(903\) 7.66069 0.254932
\(904\) 0 0
\(905\) 15.8651 0.527373
\(906\) 0 0
\(907\) −23.7096 −0.787265 −0.393633 0.919268i \(-0.628782\pi\)
−0.393633 + 0.919268i \(0.628782\pi\)
\(908\) 0 0
\(909\) −1.63976 −0.0543875
\(910\) 0 0
\(911\) 26.7056 0.884797 0.442399 0.896819i \(-0.354128\pi\)
0.442399 + 0.896819i \(0.354128\pi\)
\(912\) 0 0
\(913\) 2.98152 0.0986741
\(914\) 0 0
\(915\) 11.9621 0.395455
\(916\) 0 0
\(917\) 2.02007 0.0667085
\(918\) 0 0
\(919\) 49.7330 1.64054 0.820271 0.571975i \(-0.193823\pi\)
0.820271 + 0.571975i \(0.193823\pi\)
\(920\) 0 0
\(921\) 12.9138 0.425524
\(922\) 0 0
\(923\) −22.9520 −0.755473
\(924\) 0 0
\(925\) −47.7681 −1.57061
\(926\) 0 0
\(927\) 15.3568 0.504383
\(928\) 0 0
\(929\) 50.3384 1.65155 0.825774 0.564001i \(-0.190739\pi\)
0.825774 + 0.564001i \(0.190739\pi\)
\(930\) 0 0
\(931\) 3.99199 0.130832
\(932\) 0 0
\(933\) −22.6980 −0.743099
\(934\) 0 0
\(935\) 6.17613 0.201981
\(936\) 0 0
\(937\) 44.8159 1.46407 0.732036 0.681266i \(-0.238570\pi\)
0.732036 + 0.681266i \(0.238570\pi\)
\(938\) 0 0
\(939\) −9.71914 −0.317172
\(940\) 0 0
\(941\) 4.20187 0.136977 0.0684885 0.997652i \(-0.478182\pi\)
0.0684885 + 0.997652i \(0.478182\pi\)
\(942\) 0 0
\(943\) 0.741598 0.0241498
\(944\) 0 0
\(945\) 0.860092 0.0279788
\(946\) 0 0
\(947\) −45.7156 −1.48556 −0.742778 0.669537i \(-0.766492\pi\)
−0.742778 + 0.669537i \(0.766492\pi\)
\(948\) 0 0
\(949\) 0.315392 0.0102381
\(950\) 0 0
\(951\) 20.4152 0.662008
\(952\) 0 0
\(953\) 29.7636 0.964138 0.482069 0.876133i \(-0.339885\pi\)
0.482069 + 0.876133i \(0.339885\pi\)
\(954\) 0 0
\(955\) −8.63564 −0.279443
\(956\) 0 0
\(957\) −0.564236 −0.0182392
\(958\) 0 0
\(959\) 15.7305 0.507965
\(960\) 0 0
\(961\) −19.3250 −0.623388
\(962\) 0 0
\(963\) −17.5800 −0.566508
\(964\) 0 0
\(965\) 21.2979 0.685604
\(966\) 0 0
\(967\) 24.3229 0.782170 0.391085 0.920355i \(-0.372100\pi\)
0.391085 + 0.920355i \(0.372100\pi\)
\(968\) 0 0
\(969\) −4.44021 −0.142640
\(970\) 0 0
\(971\) 44.8086 1.43798 0.718989 0.695022i \(-0.244605\pi\)
0.718989 + 0.695022i \(0.244605\pi\)
\(972\) 0 0
\(973\) −9.38814 −0.300970
\(974\) 0 0
\(975\) −7.62067 −0.244057
\(976\) 0 0
\(977\) 25.8444 0.826836 0.413418 0.910541i \(-0.364335\pi\)
0.413418 + 0.910541i \(0.364335\pi\)
\(978\) 0 0
\(979\) 5.74526 0.183619
\(980\) 0 0
\(981\) 4.23275 0.135141
\(982\) 0 0
\(983\) 11.9377 0.380754 0.190377 0.981711i \(-0.439029\pi\)
0.190377 + 0.981711i \(0.439029\pi\)
\(984\) 0 0
\(985\) 15.5829 0.496512
\(986\) 0 0
\(987\) 1.13841 0.0362361
\(988\) 0 0
\(989\) 16.6921 0.530778
\(990\) 0 0
\(991\) −12.7875 −0.406209 −0.203105 0.979157i \(-0.565103\pi\)
−0.203105 + 0.979157i \(0.565103\pi\)
\(992\) 0 0
\(993\) −34.7167 −1.10170
\(994\) 0 0
\(995\) −6.12906 −0.194304
\(996\) 0 0
\(997\) 52.0763 1.64927 0.824636 0.565664i \(-0.191380\pi\)
0.824636 + 0.565664i \(0.191380\pi\)
\(998\) 0 0
\(999\) 11.6974 0.370090
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 8016.2.a.be.1.6 11
4.3 odd 2 4008.2.a.k.1.6 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.k.1.6 11 4.3 odd 2
8016.2.a.be.1.6 11 1.1 even 1 trivial