Properties

Label 9200.2.a.cz.1.5
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 24 x^{4} + x^{3} - 35 x^{2} + 17 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.189375\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.189375 q^{3} +1.65661 q^{7} -2.96414 q^{9} +O(q^{10})\) \(q-0.189375 q^{3} +1.65661 q^{7} -2.96414 q^{9} -0.0759321 q^{11} -1.24146 q^{13} +5.17593 q^{17} -0.792262 q^{19} -0.313721 q^{21} +1.00000 q^{23} +1.12946 q^{27} -2.85401 q^{29} -8.90112 q^{31} +0.0143797 q^{33} +6.92065 q^{37} +0.235102 q^{39} +4.64279 q^{41} +1.75255 q^{43} -10.0033 q^{47} -4.25565 q^{49} -0.980193 q^{51} -11.1284 q^{53} +0.150035 q^{57} +12.4581 q^{59} -12.0098 q^{61} -4.91041 q^{63} +6.96067 q^{67} -0.189375 q^{69} +7.71650 q^{71} -7.49476 q^{73} -0.125790 q^{77} +15.6615 q^{79} +8.67852 q^{81} -6.68518 q^{83} +0.540478 q^{87} -3.03333 q^{89} -2.05661 q^{91} +1.68565 q^{93} -3.21747 q^{97} +0.225073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + 7q^{11} - 7q^{13} + 7q^{19} - 6q^{21} + 7q^{23} - 11q^{29} + 10q^{31} - 19q^{33} - 19q^{37} + 24q^{39} - 16q^{41} - 6q^{43} - 6q^{47} - 17q^{49} + 7q^{51} - 15q^{53} - 8q^{57} + 11q^{59} + 5q^{61} - 13q^{63} - 9q^{67} - 3q^{69} + 14q^{71} - 10q^{73} - 6q^{77} + 32q^{79} - 5q^{81} - q^{83} - 10q^{87} - 24q^{89} + 7q^{91} - 26q^{93} + 7q^{97} + 61q^{99} + O(q^{100}) \)

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
\(3\) −0.189375 −0.109336 −0.0546680 0.998505i \(-0.517410\pi\)
−0.0546680 + 0.998505i \(0.517410\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.65661 0.626139 0.313070 0.949730i \(-0.398643\pi\)
0.313070 + 0.949730i \(0.398643\pi\)
\(8\) 0 0
\(9\) −2.96414 −0.988046
\(10\) 0 0
\(11\) −0.0759321 −0.0228944 −0.0114472 0.999934i \(-0.503644\pi\)
−0.0114472 + 0.999934i \(0.503644\pi\)
\(12\) 0 0
\(13\) −1.24146 −0.344319 −0.172159 0.985069i \(-0.555074\pi\)
−0.172159 + 0.985069i \(0.555074\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.17593 1.25535 0.627673 0.778477i \(-0.284007\pi\)
0.627673 + 0.778477i \(0.284007\pi\)
\(18\) 0 0
\(19\) −0.792262 −0.181757 −0.0908787 0.995862i \(-0.528968\pi\)
−0.0908787 + 0.995862i \(0.528968\pi\)
\(20\) 0 0
\(21\) −0.313721 −0.0684595
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.12946 0.217365
\(28\) 0 0
\(29\) −2.85401 −0.529976 −0.264988 0.964252i \(-0.585368\pi\)
−0.264988 + 0.964252i \(0.585368\pi\)
\(30\) 0 0
\(31\) −8.90112 −1.59869 −0.799345 0.600873i \(-0.794820\pi\)
−0.799345 + 0.600873i \(0.794820\pi\)
\(32\) 0 0
\(33\) 0.0143797 0.00250318
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.92065 1.13775 0.568874 0.822425i \(-0.307379\pi\)
0.568874 + 0.822425i \(0.307379\pi\)
\(38\) 0 0
\(39\) 0.235102 0.0376464
\(40\) 0 0
\(41\) 4.64279 0.725082 0.362541 0.931968i \(-0.381909\pi\)
0.362541 + 0.931968i \(0.381909\pi\)
\(42\) 0 0
\(43\) 1.75255 0.267262 0.133631 0.991031i \(-0.457336\pi\)
0.133631 + 0.991031i \(0.457336\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.0033 −1.45913 −0.729563 0.683914i \(-0.760276\pi\)
−0.729563 + 0.683914i \(0.760276\pi\)
\(48\) 0 0
\(49\) −4.25565 −0.607950
\(50\) 0 0
\(51\) −0.980193 −0.137254
\(52\) 0 0
\(53\) −11.1284 −1.52860 −0.764301 0.644859i \(-0.776916\pi\)
−0.764301 + 0.644859i \(0.776916\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.150035 0.0198726
\(58\) 0 0
\(59\) 12.4581 1.62191 0.810955 0.585108i \(-0.198948\pi\)
0.810955 + 0.585108i \(0.198948\pi\)
\(60\) 0 0
\(61\) −12.0098 −1.53770 −0.768849 0.639430i \(-0.779170\pi\)
−0.768849 + 0.639430i \(0.779170\pi\)
\(62\) 0 0
\(63\) −4.91041 −0.618654
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.96067 0.850381 0.425191 0.905104i \(-0.360207\pi\)
0.425191 + 0.905104i \(0.360207\pi\)
\(68\) 0 0
\(69\) −0.189375 −0.0227981
\(70\) 0 0
\(71\) 7.71650 0.915779 0.457890 0.889009i \(-0.348605\pi\)
0.457890 + 0.889009i \(0.348605\pi\)
\(72\) 0 0
\(73\) −7.49476 −0.877196 −0.438598 0.898683i \(-0.644525\pi\)
−0.438598 + 0.898683i \(0.644525\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.125790 −0.0143351
\(78\) 0 0
\(79\) 15.6615 1.76206 0.881029 0.473063i \(-0.156852\pi\)
0.881029 + 0.473063i \(0.156852\pi\)
\(80\) 0 0
\(81\) 8.67852 0.964280
\(82\) 0 0
\(83\) −6.68518 −0.733793 −0.366897 0.930262i \(-0.619580\pi\)
−0.366897 + 0.930262i \(0.619580\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.540478 0.0579454
\(88\) 0 0
\(89\) −3.03333 −0.321532 −0.160766 0.986993i \(-0.551396\pi\)
−0.160766 + 0.986993i \(0.551396\pi\)
\(90\) 0 0
\(91\) −2.05661 −0.215592
\(92\) 0 0
\(93\) 1.68565 0.174794
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −3.21747 −0.326684 −0.163342 0.986569i \(-0.552227\pi\)
−0.163342 + 0.986569i \(0.552227\pi\)
\(98\) 0 0
\(99\) 0.225073 0.0226207
\(100\) 0 0
\(101\) −16.6059 −1.65235 −0.826173 0.563417i \(-0.809486\pi\)
−0.826173 + 0.563417i \(0.809486\pi\)
\(102\) 0 0
\(103\) −7.30241 −0.719528 −0.359764 0.933043i \(-0.617143\pi\)
−0.359764 + 0.933043i \(0.617143\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.356936 −0.0345063 −0.0172532 0.999851i \(-0.505492\pi\)
−0.0172532 + 0.999851i \(0.505492\pi\)
\(108\) 0 0
\(109\) 14.0359 1.34440 0.672198 0.740371i \(-0.265350\pi\)
0.672198 + 0.740371i \(0.265350\pi\)
\(110\) 0 0
\(111\) −1.31060 −0.124397
\(112\) 0 0
\(113\) 1.17924 0.110933 0.0554667 0.998461i \(-0.482335\pi\)
0.0554667 + 0.998461i \(0.482335\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.67986 0.340203
\(118\) 0 0
\(119\) 8.57448 0.786022
\(120\) 0 0
\(121\) −10.9942 −0.999476
\(122\) 0 0
\(123\) −0.879230 −0.0792775
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 19.0097 1.68684 0.843420 0.537255i \(-0.180539\pi\)
0.843420 + 0.537255i \(0.180539\pi\)
\(128\) 0 0
\(129\) −0.331890 −0.0292213
\(130\) 0 0
\(131\) −4.29043 −0.374857 −0.187428 0.982278i \(-0.560015\pi\)
−0.187428 + 0.982278i \(0.560015\pi\)
\(132\) 0 0
\(133\) −1.31247 −0.113805
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −12.2499 −1.04658 −0.523290 0.852155i \(-0.675296\pi\)
−0.523290 + 0.852155i \(0.675296\pi\)
\(138\) 0 0
\(139\) −2.61437 −0.221748 −0.110874 0.993834i \(-0.535365\pi\)
−0.110874 + 0.993834i \(0.535365\pi\)
\(140\) 0 0
\(141\) 1.89437 0.159535
\(142\) 0 0
\(143\) 0.0942666 0.00788297
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0.805915 0.0664707
\(148\) 0 0
\(149\) −19.0404 −1.55985 −0.779927 0.625870i \(-0.784744\pi\)
−0.779927 + 0.625870i \(0.784744\pi\)
\(150\) 0 0
\(151\) 18.3252 1.49128 0.745640 0.666349i \(-0.232144\pi\)
0.745640 + 0.666349i \(0.232144\pi\)
\(152\) 0 0
\(153\) −15.3422 −1.24034
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.37467 −0.349137 −0.174569 0.984645i \(-0.555853\pi\)
−0.174569 + 0.984645i \(0.555853\pi\)
\(158\) 0 0
\(159\) 2.10744 0.167131
\(160\) 0 0
\(161\) 1.65661 0.130559
\(162\) 0 0
\(163\) −11.8050 −0.924639 −0.462319 0.886714i \(-0.652983\pi\)
−0.462319 + 0.886714i \(0.652983\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.19760 −0.402202 −0.201101 0.979570i \(-0.564452\pi\)
−0.201101 + 0.979570i \(0.564452\pi\)
\(168\) 0 0
\(169\) −11.4588 −0.881444
\(170\) 0 0
\(171\) 2.34837 0.179585
\(172\) 0 0
\(173\) −2.61834 −0.199069 −0.0995345 0.995034i \(-0.531735\pi\)
−0.0995345 + 0.995034i \(0.531735\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.35926 −0.177333
\(178\) 0 0
\(179\) −0.627563 −0.0469062 −0.0234531 0.999725i \(-0.507466\pi\)
−0.0234531 + 0.999725i \(0.507466\pi\)
\(180\) 0 0
\(181\) −6.15848 −0.457756 −0.228878 0.973455i \(-0.573506\pi\)
−0.228878 + 0.973455i \(0.573506\pi\)
\(182\) 0 0
\(183\) 2.27436 0.168126
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.393019 −0.0287404
\(188\) 0 0
\(189\) 1.87107 0.136101
\(190\) 0 0
\(191\) 19.1343 1.38451 0.692254 0.721654i \(-0.256618\pi\)
0.692254 + 0.721654i \(0.256618\pi\)
\(192\) 0 0
\(193\) −0.810900 −0.0583698 −0.0291849 0.999574i \(-0.509291\pi\)
−0.0291849 + 0.999574i \(0.509291\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.15110 −0.438248 −0.219124 0.975697i \(-0.570320\pi\)
−0.219124 + 0.975697i \(0.570320\pi\)
\(198\) 0 0
\(199\) −7.03061 −0.498387 −0.249193 0.968454i \(-0.580166\pi\)
−0.249193 + 0.968454i \(0.580166\pi\)
\(200\) 0 0
\(201\) −1.31818 −0.0929772
\(202\) 0 0
\(203\) −4.72797 −0.331838
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −2.96414 −0.206022
\(208\) 0 0
\(209\) 0.0601581 0.00416122
\(210\) 0 0
\(211\) −8.12120 −0.559086 −0.279543 0.960133i \(-0.590183\pi\)
−0.279543 + 0.960133i \(0.590183\pi\)
\(212\) 0 0
\(213\) −1.46131 −0.100128
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −14.7457 −1.00100
\(218\) 0 0
\(219\) 1.41932 0.0959090
\(220\) 0 0
\(221\) −6.42570 −0.432240
\(222\) 0 0
\(223\) −2.86268 −0.191699 −0.0958495 0.995396i \(-0.530557\pi\)
−0.0958495 + 0.995396i \(0.530557\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −27.4500 −1.82192 −0.910960 0.412496i \(-0.864657\pi\)
−0.910960 + 0.412496i \(0.864657\pi\)
\(228\) 0 0
\(229\) 1.11319 0.0735613 0.0367807 0.999323i \(-0.488290\pi\)
0.0367807 + 0.999323i \(0.488290\pi\)
\(230\) 0 0
\(231\) 0.0238215 0.00156734
\(232\) 0 0
\(233\) 21.2957 1.39513 0.697564 0.716523i \(-0.254267\pi\)
0.697564 + 0.716523i \(0.254267\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.96590 −0.192656
\(238\) 0 0
\(239\) −7.68036 −0.496801 −0.248401 0.968657i \(-0.579905\pi\)
−0.248401 + 0.968657i \(0.579905\pi\)
\(240\) 0 0
\(241\) 8.42476 0.542687 0.271343 0.962483i \(-0.412532\pi\)
0.271343 + 0.962483i \(0.412532\pi\)
\(242\) 0 0
\(243\) −5.03188 −0.322795
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.983561 0.0625825
\(248\) 0 0
\(249\) 1.26601 0.0802300
\(250\) 0 0
\(251\) 2.56210 0.161718 0.0808590 0.996726i \(-0.474234\pi\)
0.0808590 + 0.996726i \(0.474234\pi\)
\(252\) 0 0
\(253\) −0.0759321 −0.00477381
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.39999 0.274464 0.137232 0.990539i \(-0.456179\pi\)
0.137232 + 0.990539i \(0.456179\pi\)
\(258\) 0 0
\(259\) 11.4648 0.712388
\(260\) 0 0
\(261\) 8.45966 0.523640
\(262\) 0 0
\(263\) −24.8510 −1.53238 −0.766191 0.642613i \(-0.777850\pi\)
−0.766191 + 0.642613i \(0.777850\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.574437 0.0351550
\(268\) 0 0
\(269\) −10.8742 −0.663012 −0.331506 0.943453i \(-0.607557\pi\)
−0.331506 + 0.943453i \(0.607557\pi\)
\(270\) 0 0
\(271\) 2.60290 0.158115 0.0790575 0.996870i \(-0.474809\pi\)
0.0790575 + 0.996870i \(0.474809\pi\)
\(272\) 0 0
\(273\) 0.389472 0.0235719
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −12.1918 −0.732537 −0.366269 0.930509i \(-0.619365\pi\)
−0.366269 + 0.930509i \(0.619365\pi\)
\(278\) 0 0
\(279\) 26.3842 1.57958
\(280\) 0 0
\(281\) 5.85068 0.349022 0.174511 0.984655i \(-0.444165\pi\)
0.174511 + 0.984655i \(0.444165\pi\)
\(282\) 0 0
\(283\) −10.7223 −0.637375 −0.318688 0.947860i \(-0.603242\pi\)
−0.318688 + 0.947860i \(0.603242\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.69129 0.454002
\(288\) 0 0
\(289\) 9.79021 0.575895
\(290\) 0 0
\(291\) 0.609309 0.0357183
\(292\) 0 0
\(293\) −2.72596 −0.159252 −0.0796261 0.996825i \(-0.525373\pi\)
−0.0796261 + 0.996825i \(0.525373\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −0.0857623 −0.00497643
\(298\) 0 0
\(299\) −1.24146 −0.0717955
\(300\) 0 0
\(301\) 2.90329 0.167343
\(302\) 0 0
\(303\) 3.14474 0.180661
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −22.4979 −1.28402 −0.642012 0.766695i \(-0.721900\pi\)
−0.642012 + 0.766695i \(0.721900\pi\)
\(308\) 0 0
\(309\) 1.38290 0.0786703
\(310\) 0 0
\(311\) −17.9597 −1.01840 −0.509200 0.860648i \(-0.670058\pi\)
−0.509200 + 0.860648i \(0.670058\pi\)
\(312\) 0 0
\(313\) −14.4728 −0.818052 −0.409026 0.912523i \(-0.634131\pi\)
−0.409026 + 0.912523i \(0.634131\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.47689 0.419944 0.209972 0.977707i \(-0.432663\pi\)
0.209972 + 0.977707i \(0.432663\pi\)
\(318\) 0 0
\(319\) 0.216711 0.0121335
\(320\) 0 0
\(321\) 0.0675949 0.00377278
\(322\) 0 0
\(323\) −4.10069 −0.228168
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.65806 −0.146991
\(328\) 0 0
\(329\) −16.5715 −0.913616
\(330\) 0 0
\(331\) 27.3565 1.50365 0.751826 0.659362i \(-0.229173\pi\)
0.751826 + 0.659362i \(0.229173\pi\)
\(332\) 0 0
\(333\) −20.5137 −1.12415
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5.65271 −0.307923 −0.153961 0.988077i \(-0.549203\pi\)
−0.153961 + 0.988077i \(0.549203\pi\)
\(338\) 0 0
\(339\) −0.223319 −0.0121290
\(340\) 0 0
\(341\) 0.675881 0.0366010
\(342\) 0 0
\(343\) −18.6462 −1.00680
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.5293 0.833658 0.416829 0.908985i \(-0.363141\pi\)
0.416829 + 0.908985i \(0.363141\pi\)
\(348\) 0 0
\(349\) 11.0559 0.591810 0.295905 0.955217i \(-0.404379\pi\)
0.295905 + 0.955217i \(0.404379\pi\)
\(350\) 0 0
\(351\) −1.40218 −0.0748428
\(352\) 0 0
\(353\) −6.85381 −0.364792 −0.182396 0.983225i \(-0.558385\pi\)
−0.182396 + 0.983225i \(0.558385\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.62380 −0.0859404
\(358\) 0 0
\(359\) −16.3104 −0.860832 −0.430416 0.902631i \(-0.641633\pi\)
−0.430416 + 0.902631i \(0.641633\pi\)
\(360\) 0 0
\(361\) −18.3723 −0.966964
\(362\) 0 0
\(363\) 2.08204 0.109279
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −31.6200 −1.65055 −0.825275 0.564731i \(-0.808980\pi\)
−0.825275 + 0.564731i \(0.808980\pi\)
\(368\) 0 0
\(369\) −13.7619 −0.716414
\(370\) 0 0
\(371\) −18.4354 −0.957118
\(372\) 0 0
\(373\) −28.2458 −1.46251 −0.731256 0.682104i \(-0.761065\pi\)
−0.731256 + 0.682104i \(0.761065\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.54313 0.182481
\(378\) 0 0
\(379\) −2.98772 −0.153469 −0.0767345 0.997052i \(-0.524449\pi\)
−0.0767345 + 0.997052i \(0.524449\pi\)
\(380\) 0 0
\(381\) −3.59997 −0.184432
\(382\) 0 0
\(383\) 12.5176 0.639621 0.319810 0.947482i \(-0.396381\pi\)
0.319810 + 0.947482i \(0.396381\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.19480 −0.264067
\(388\) 0 0
\(389\) −19.4861 −0.987982 −0.493991 0.869467i \(-0.664462\pi\)
−0.493991 + 0.869467i \(0.664462\pi\)
\(390\) 0 0
\(391\) 5.17593 0.261758
\(392\) 0 0
\(393\) 0.812503 0.0409853
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −17.3203 −0.869281 −0.434640 0.900604i \(-0.643124\pi\)
−0.434640 + 0.900604i \(0.643124\pi\)
\(398\) 0 0
\(399\) 0.248549 0.0124430
\(400\) 0 0
\(401\) 17.3727 0.867553 0.433777 0.901020i \(-0.357181\pi\)
0.433777 + 0.901020i \(0.357181\pi\)
\(402\) 0 0
\(403\) 11.0504 0.550459
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.525499 −0.0260480
\(408\) 0 0
\(409\) −12.6874 −0.627350 −0.313675 0.949530i \(-0.601560\pi\)
−0.313675 + 0.949530i \(0.601560\pi\)
\(410\) 0 0
\(411\) 2.31983 0.114429
\(412\) 0 0
\(413\) 20.6383 1.01554
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.495098 0.0242450
\(418\) 0 0
\(419\) 4.23468 0.206878 0.103439 0.994636i \(-0.467015\pi\)
0.103439 + 0.994636i \(0.467015\pi\)
\(420\) 0 0
\(421\) 4.17837 0.203641 0.101821 0.994803i \(-0.467533\pi\)
0.101821 + 0.994803i \(0.467533\pi\)
\(422\) 0 0
\(423\) 29.6510 1.44168
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −19.8956 −0.962813
\(428\) 0 0
\(429\) −0.0178518 −0.000861892 0
\(430\) 0 0
\(431\) 21.9197 1.05583 0.527917 0.849296i \(-0.322973\pi\)
0.527917 + 0.849296i \(0.322973\pi\)
\(432\) 0 0
\(433\) 20.2195 0.971688 0.485844 0.874046i \(-0.338512\pi\)
0.485844 + 0.874046i \(0.338512\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.792262 −0.0378990
\(438\) 0 0
\(439\) 16.3149 0.778666 0.389333 0.921097i \(-0.372706\pi\)
0.389333 + 0.921097i \(0.372706\pi\)
\(440\) 0 0
\(441\) 12.6143 0.600682
\(442\) 0 0
\(443\) 28.0868 1.33444 0.667222 0.744859i \(-0.267483\pi\)
0.667222 + 0.744859i \(0.267483\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 3.60579 0.170548
\(448\) 0 0
\(449\) −24.5071 −1.15656 −0.578282 0.815837i \(-0.696277\pi\)
−0.578282 + 0.815837i \(0.696277\pi\)
\(450\) 0 0
\(451\) −0.352537 −0.0166003
\(452\) 0 0
\(453\) −3.47033 −0.163050
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 2.87128 0.134313 0.0671564 0.997742i \(-0.478607\pi\)
0.0671564 + 0.997742i \(0.478607\pi\)
\(458\) 0 0
\(459\) 5.84601 0.272868
\(460\) 0 0
\(461\) 15.2264 0.709162 0.354581 0.935025i \(-0.384623\pi\)
0.354581 + 0.935025i \(0.384623\pi\)
\(462\) 0 0
\(463\) −36.6480 −1.70318 −0.851588 0.524212i \(-0.824360\pi\)
−0.851588 + 0.524212i \(0.824360\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.9765 0.693031 0.346516 0.938044i \(-0.387365\pi\)
0.346516 + 0.938044i \(0.387365\pi\)
\(468\) 0 0
\(469\) 11.5311 0.532457
\(470\) 0 0
\(471\) 0.828456 0.0381732
\(472\) 0 0
\(473\) −0.133075 −0.00611879
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 32.9861 1.51033
\(478\) 0 0
\(479\) −4.03398 −0.184317 −0.0921587 0.995744i \(-0.529377\pi\)
−0.0921587 + 0.995744i \(0.529377\pi\)
\(480\) 0 0
\(481\) −8.59171 −0.391748
\(482\) 0 0
\(483\) −0.313721 −0.0142748
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 4.28846 0.194329 0.0971643 0.995268i \(-0.469023\pi\)
0.0971643 + 0.995268i \(0.469023\pi\)
\(488\) 0 0
\(489\) 2.23558 0.101096
\(490\) 0 0
\(491\) 36.8754 1.66416 0.832081 0.554654i \(-0.187149\pi\)
0.832081 + 0.554654i \(0.187149\pi\)
\(492\) 0 0
\(493\) −14.7721 −0.665303
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.7832 0.573405
\(498\) 0 0
\(499\) 5.74707 0.257274 0.128637 0.991692i \(-0.458940\pi\)
0.128637 + 0.991692i \(0.458940\pi\)
\(500\) 0 0
\(501\) 0.984298 0.0439752
\(502\) 0 0
\(503\) 18.7850 0.837583 0.418792 0.908082i \(-0.362454\pi\)
0.418792 + 0.908082i \(0.362454\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.17001 0.0963735
\(508\) 0 0
\(509\) −20.2669 −0.898313 −0.449157 0.893453i \(-0.648275\pi\)
−0.449157 + 0.893453i \(0.648275\pi\)
\(510\) 0 0
\(511\) −12.4159 −0.549247
\(512\) 0 0
\(513\) −0.894829 −0.0395077
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.759568 0.0334058
\(518\) 0 0
\(519\) 0.495850 0.0217654
\(520\) 0 0
\(521\) 6.47593 0.283716 0.141858 0.989887i \(-0.454692\pi\)
0.141858 + 0.989887i \(0.454692\pi\)
\(522\) 0 0
\(523\) 0.414671 0.0181323 0.00906615 0.999959i \(-0.497114\pi\)
0.00906615 + 0.999959i \(0.497114\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −46.0716 −2.00691
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −36.9276 −1.60252
\(532\) 0 0
\(533\) −5.76384 −0.249659
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.118845 0.00512854
\(538\) 0 0
\(539\) 0.323140 0.0139186
\(540\) 0 0
\(541\) 28.5708 1.22835 0.614177 0.789169i \(-0.289488\pi\)
0.614177 + 0.789169i \(0.289488\pi\)
\(542\) 0 0
\(543\) 1.16626 0.0500492
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 39.0974 1.67168 0.835841 0.548971i \(-0.184980\pi\)
0.835841 + 0.548971i \(0.184980\pi\)
\(548\) 0 0
\(549\) 35.5987 1.51932
\(550\) 0 0
\(551\) 2.26112 0.0963270
\(552\) 0 0
\(553\) 25.9450 1.10329
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −33.9136 −1.43696 −0.718482 0.695546i \(-0.755163\pi\)
−0.718482 + 0.695546i \(0.755163\pi\)
\(558\) 0 0
\(559\) −2.17572 −0.0920232
\(560\) 0 0
\(561\) 0.0744281 0.00314236
\(562\) 0 0
\(563\) −25.6390 −1.08056 −0.540278 0.841486i \(-0.681681\pi\)
−0.540278 + 0.841486i \(0.681681\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 14.3769 0.603773
\(568\) 0 0
\(569\) −13.6257 −0.571218 −0.285609 0.958346i \(-0.592196\pi\)
−0.285609 + 0.958346i \(0.592196\pi\)
\(570\) 0 0
\(571\) −0.354294 −0.0148267 −0.00741337 0.999973i \(-0.502360\pi\)
−0.00741337 + 0.999973i \(0.502360\pi\)
\(572\) 0 0
\(573\) −3.62356 −0.151376
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −18.5870 −0.773788 −0.386894 0.922124i \(-0.626452\pi\)
−0.386894 + 0.922124i \(0.626452\pi\)
\(578\) 0 0
\(579\) 0.153564 0.00638192
\(580\) 0 0
\(581\) −11.0747 −0.459457
\(582\) 0 0
\(583\) 0.845002 0.0349964
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.75193 −0.319956 −0.159978 0.987121i \(-0.551142\pi\)
−0.159978 + 0.987121i \(0.551142\pi\)
\(588\) 0 0
\(589\) 7.05202 0.290573
\(590\) 0 0
\(591\) 1.16487 0.0479162
\(592\) 0 0
\(593\) −23.3828 −0.960215 −0.480107 0.877210i \(-0.659402\pi\)
−0.480107 + 0.877210i \(0.659402\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.33142 0.0544916
\(598\) 0 0
\(599\) 25.6075 1.04629 0.523146 0.852243i \(-0.324758\pi\)
0.523146 + 0.852243i \(0.324758\pi\)
\(600\) 0 0
\(601\) 4.03750 0.164693 0.0823466 0.996604i \(-0.473759\pi\)
0.0823466 + 0.996604i \(0.473759\pi\)
\(602\) 0 0
\(603\) −20.6324 −0.840215
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −45.8176 −1.85968 −0.929839 0.367967i \(-0.880054\pi\)
−0.929839 + 0.367967i \(0.880054\pi\)
\(608\) 0 0
\(609\) 0.895361 0.0362819
\(610\) 0 0
\(611\) 12.4186 0.502405
\(612\) 0 0
\(613\) −29.1714 −1.17822 −0.589112 0.808052i \(-0.700522\pi\)
−0.589112 + 0.808052i \(0.700522\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 17.0562 0.686659 0.343329 0.939215i \(-0.388445\pi\)
0.343329 + 0.939215i \(0.388445\pi\)
\(618\) 0 0
\(619\) −36.0620 −1.44946 −0.724728 0.689035i \(-0.758034\pi\)
−0.724728 + 0.689035i \(0.758034\pi\)
\(620\) 0 0
\(621\) 1.12946 0.0453237
\(622\) 0 0
\(623\) −5.02503 −0.201324
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.0113925 −0.000454971 0
\(628\) 0 0
\(629\) 35.8208 1.42827
\(630\) 0 0
\(631\) −17.4958 −0.696496 −0.348248 0.937402i \(-0.613223\pi\)
−0.348248 + 0.937402i \(0.613223\pi\)
\(632\) 0 0
\(633\) 1.53795 0.0611282
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.28322 0.209329
\(638\) 0 0
\(639\) −22.8727 −0.904832
\(640\) 0 0
\(641\) −39.9200 −1.57675 −0.788373 0.615197i \(-0.789076\pi\)
−0.788373 + 0.615197i \(0.789076\pi\)
\(642\) 0 0
\(643\) −41.8187 −1.64917 −0.824584 0.565740i \(-0.808591\pi\)
−0.824584 + 0.565740i \(0.808591\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 38.8026 1.52549 0.762743 0.646702i \(-0.223852\pi\)
0.762743 + 0.646702i \(0.223852\pi\)
\(648\) 0 0
\(649\) −0.945972 −0.0371327
\(650\) 0 0
\(651\) 2.79247 0.109445
\(652\) 0 0
\(653\) −39.8995 −1.56139 −0.780694 0.624914i \(-0.785134\pi\)
−0.780694 + 0.624914i \(0.785134\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 22.2155 0.866709
\(658\) 0 0
\(659\) −22.9449 −0.893808 −0.446904 0.894582i \(-0.647473\pi\)
−0.446904 + 0.894582i \(0.647473\pi\)
\(660\) 0 0
\(661\) 19.2759 0.749745 0.374873 0.927076i \(-0.377686\pi\)
0.374873 + 0.927076i \(0.377686\pi\)
\(662\) 0 0
\(663\) 1.21687 0.0472593
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.85401 −0.110508
\(668\) 0 0
\(669\) 0.542121 0.0209596
\(670\) 0 0
\(671\) 0.911930 0.0352047
\(672\) 0 0
\(673\) 38.0041 1.46495 0.732476 0.680793i \(-0.238365\pi\)
0.732476 + 0.680793i \(0.238365\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −41.0387 −1.57725 −0.788623 0.614878i \(-0.789205\pi\)
−0.788623 + 0.614878i \(0.789205\pi\)
\(678\) 0 0
\(679\) −5.33008 −0.204550
\(680\) 0 0
\(681\) 5.19835 0.199201
\(682\) 0 0
\(683\) 27.6705 1.05878 0.529390 0.848378i \(-0.322421\pi\)
0.529390 + 0.848378i \(0.322421\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.210810 −0.00804290
\(688\) 0 0
\(689\) 13.8155 0.526327
\(690\) 0 0
\(691\) −33.8078 −1.28611 −0.643056 0.765820i \(-0.722334\pi\)
−0.643056 + 0.765820i \(0.722334\pi\)
\(692\) 0 0
\(693\) 0.372858 0.0141637
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 24.0307 0.910229
\(698\) 0 0
\(699\) −4.03288 −0.152538
\(700\) 0 0
\(701\) −46.4878 −1.75582 −0.877909 0.478827i \(-0.841062\pi\)
−0.877909 + 0.478827i \(0.841062\pi\)
\(702\) 0 0
\(703\) −5.48297 −0.206794
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −27.5094 −1.03460
\(708\) 0 0
\(709\) −13.5298 −0.508122 −0.254061 0.967188i \(-0.581766\pi\)
−0.254061 + 0.967188i \(0.581766\pi\)
\(710\) 0 0
\(711\) −46.4229 −1.74099
\(712\) 0 0
\(713\) −8.90112 −0.333350
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.45447 0.0543182
\(718\) 0 0
\(719\) 2.64955 0.0988115 0.0494057 0.998779i \(-0.484267\pi\)
0.0494057 + 0.998779i \(0.484267\pi\)
\(720\) 0 0
\(721\) −12.0972 −0.450525
\(722\) 0 0
\(723\) −1.59544 −0.0593351
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 46.8796 1.73867 0.869334 0.494226i \(-0.164548\pi\)
0.869334 + 0.494226i \(0.164548\pi\)
\(728\) 0 0
\(729\) −25.0826 −0.928987
\(730\) 0 0
\(731\) 9.07108 0.335506
\(732\) 0 0
\(733\) −36.1389 −1.33482 −0.667410 0.744691i \(-0.732597\pi\)
−0.667410 + 0.744691i \(0.732597\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.528538 −0.0194690
\(738\) 0 0
\(739\) −22.6473 −0.833095 −0.416547 0.909114i \(-0.636760\pi\)
−0.416547 + 0.909114i \(0.636760\pi\)
\(740\) 0 0
\(741\) −0.186262 −0.00684252
\(742\) 0 0
\(743\) 7.04015 0.258278 0.129139 0.991627i \(-0.458779\pi\)
0.129139 + 0.991627i \(0.458779\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 19.8158 0.725021
\(748\) 0 0
\(749\) −0.591304 −0.0216058
\(750\) 0 0
\(751\) 5.94539 0.216950 0.108475 0.994099i \(-0.465403\pi\)
0.108475 + 0.994099i \(0.465403\pi\)
\(752\) 0 0
\(753\) −0.485198 −0.0176816
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −43.9519 −1.59746 −0.798729 0.601691i \(-0.794494\pi\)
−0.798729 + 0.601691i \(0.794494\pi\)
\(758\) 0 0
\(759\) 0.0143797 0.000521949 0
\(760\) 0 0
\(761\) 22.0290 0.798549 0.399274 0.916831i \(-0.369262\pi\)
0.399274 + 0.916831i \(0.369262\pi\)
\(762\) 0 0
\(763\) 23.2520 0.841779
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15.4663 −0.558455
\(768\) 0 0
\(769\) −17.6958 −0.638128 −0.319064 0.947733i \(-0.603368\pi\)
−0.319064 + 0.947733i \(0.603368\pi\)
\(770\) 0 0
\(771\) −0.833250 −0.0300088
\(772\) 0 0
\(773\) −1.63758 −0.0588997 −0.0294498 0.999566i \(-0.509376\pi\)
−0.0294498 + 0.999566i \(0.509376\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −2.17115 −0.0778896
\(778\) 0 0
\(779\) −3.67831 −0.131789
\(780\) 0 0
\(781\) −0.585930 −0.0209662
\(782\) 0 0
\(783\) −3.22349 −0.115198
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 27.6760 0.986543 0.493272 0.869875i \(-0.335801\pi\)
0.493272 + 0.869875i \(0.335801\pi\)
\(788\) 0 0
\(789\) 4.70618 0.167544
\(790\) 0 0
\(791\) 1.95354 0.0694598
\(792\) 0 0
\(793\) 14.9097 0.529459
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9.29831 0.329363 0.164681 0.986347i \(-0.447340\pi\)
0.164681 + 0.986347i \(0.447340\pi\)
\(798\) 0 0
\(799\) −51.7761 −1.83171
\(800\) 0 0
\(801\) 8.99119 0.317688
\(802\) 0 0
\(803\) 0.569093 0.0200829
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.05931 0.0724911
\(808\) 0 0
\(809\) 48.8800 1.71853 0.859264 0.511532i \(-0.170922\pi\)
0.859264 + 0.511532i \(0.170922\pi\)
\(810\) 0 0
\(811\) −44.0615 −1.54721 −0.773604 0.633669i \(-0.781548\pi\)
−0.773604 + 0.633669i \(0.781548\pi\)
\(812\) 0 0
\(813\) −0.492926 −0.0172877
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1.38848 −0.0485768
\(818\) 0 0
\(819\) 6.09608 0.213014
\(820\) 0 0
\(821\) 30.1832 1.05340 0.526700 0.850051i \(-0.323429\pi\)
0.526700 + 0.850051i \(0.323429\pi\)
\(822\) 0 0
\(823\) −32.0171 −1.11605 −0.558023 0.829826i \(-0.688440\pi\)
−0.558023 + 0.829826i \(0.688440\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20.5192 −0.713523 −0.356761 0.934196i \(-0.616119\pi\)
−0.356761 + 0.934196i \(0.616119\pi\)
\(828\) 0 0
\(829\) 38.0551 1.32171 0.660854 0.750515i \(-0.270194\pi\)
0.660854 + 0.750515i \(0.270194\pi\)
\(830\) 0 0
\(831\) 2.30884 0.0800926
\(832\) 0 0
\(833\) −22.0269 −0.763188
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −10.0535 −0.347499
\(838\) 0 0
\(839\) −24.6946 −0.852553 −0.426277 0.904593i \(-0.640175\pi\)
−0.426277 + 0.904593i \(0.640175\pi\)
\(840\) 0 0
\(841\) −20.8547 −0.719126
\(842\) 0 0
\(843\) −1.10797 −0.0381607
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −18.2131 −0.625811
\(848\) 0 0
\(849\) 2.03054 0.0696880
\(850\) 0 0
\(851\) 6.92065 0.237237
\(852\) 0 0
\(853\) 23.4770 0.803837 0.401919 0.915675i \(-0.368343\pi\)
0.401919 + 0.915675i \(0.368343\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 20.9632 0.716090 0.358045 0.933704i \(-0.383443\pi\)
0.358045 + 0.933704i \(0.383443\pi\)
\(858\) 0 0
\(859\) −35.7273 −1.21900 −0.609500 0.792786i \(-0.708630\pi\)
−0.609500 + 0.792786i \(0.708630\pi\)
\(860\) 0 0
\(861\) −1.45654 −0.0496388
\(862\) 0 0
\(863\) −19.5880 −0.666784 −0.333392 0.942788i \(-0.608193\pi\)
−0.333392 + 0.942788i \(0.608193\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.85403 −0.0629660
\(868\) 0 0
\(869\) −1.18921 −0.0403412
\(870\) 0 0
\(871\) −8.64139 −0.292802
\(872\) 0 0
\(873\) 9.53702 0.322779
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −49.5791 −1.67417 −0.837084 0.547074i \(-0.815741\pi\)
−0.837084 + 0.547074i \(0.815741\pi\)
\(878\) 0 0
\(879\) 0.516230 0.0174120
\(880\) 0 0
\(881\) 21.4406 0.722353 0.361177 0.932497i \(-0.382375\pi\)
0.361177 + 0.932497i \(0.382375\pi\)
\(882\) 0 0
\(883\) −52.7646 −1.77567 −0.887836 0.460161i \(-0.847792\pi\)
−0.887836 + 0.460161i \(0.847792\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 30.1462 1.01221 0.506105 0.862472i \(-0.331085\pi\)
0.506105 + 0.862472i \(0.331085\pi\)
\(888\) 0 0
\(889\) 31.4917 1.05620
\(890\) 0 0
\(891\) −0.658978 −0.0220766
\(892\) 0 0
\(893\) 7.92520 0.265207
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0.235102 0.00784982
\(898\) 0 0
\(899\) 25.4039 0.847266
\(900\) 0 0
\(901\) −57.5998 −1.91893
\(902\) 0 0
\(903\) −0.549812 −0.0182966
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 20.3987 0.677329 0.338665 0.940907i \(-0.390025\pi\)
0.338665 + 0.940907i \(0.390025\pi\)
\(908\) 0 0
\(909\) 49.2221 1.63259
\(910\) 0 0
\(911\) 57.7921 1.91474 0.957369 0.288869i \(-0.0932792\pi\)
0.957369 + 0.288869i \(0.0932792\pi\)
\(912\) 0 0
\(913\) 0.507619 0.0167998
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.10757 −0.234713
\(918\) 0 0
\(919\) 26.0255 0.858502 0.429251 0.903185i \(-0.358778\pi\)
0.429251 + 0.903185i \(0.358778\pi\)
\(920\) 0 0
\(921\) 4.26055 0.140390
\(922\) 0 0
\(923\) −9.57972 −0.315320
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 21.6454 0.710927
\(928\) 0 0
\(929\) 26.9839 0.885313 0.442656 0.896691i \(-0.354036\pi\)
0.442656 + 0.896691i \(0.354036\pi\)
\(930\) 0 0
\(931\) 3.37159 0.110499
\(932\) 0 0
\(933\) 3.40112 0.111348
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 35.8201 1.17019 0.585096 0.810964i \(-0.301057\pi\)
0.585096 + 0.810964i \(0.301057\pi\)
\(938\) 0 0
\(939\) 2.74079 0.0894424
\(940\) 0 0
\(941\) −32.0416 −1.04453 −0.522263 0.852785i \(-0.674912\pi\)
−0.522263 + 0.852785i \(0.674912\pi\)
\(942\) 0 0
\(943\) 4.64279 0.151190
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.53256 0.277271 0.138635 0.990343i \(-0.455728\pi\)
0.138635 + 0.990343i \(0.455728\pi\)
\(948\) 0 0
\(949\) 9.30445 0.302035
\(950\) 0 0
\(951\) −1.41594 −0.0459150
\(952\) 0 0
\(953\) 42.4054 1.37365 0.686823 0.726825i \(-0.259005\pi\)
0.686823 + 0.726825i \(0.259005\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −0.0410397 −0.00132662
\(958\) 0 0
\(959\) −20.2933 −0.655305
\(960\) 0 0
\(961\) 48.2300 1.55581
\(962\) 0 0
\(963\) 1.05801 0.0340938
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −10.0988 −0.324755 −0.162377 0.986729i \(-0.551916\pi\)
−0.162377 + 0.986729i \(0.551916\pi\)
\(968\) 0 0
\(969\) 0.776570 0.0249470
\(970\) 0 0
\(971\) 15.7943 0.506863 0.253431 0.967353i \(-0.418441\pi\)
0.253431 + 0.967353i \(0.418441\pi\)
\(972\) 0 0
\(973\) −4.33099 −0.138845
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 27.0055 0.863984 0.431992 0.901877i \(-0.357811\pi\)
0.431992 + 0.901877i \(0.357811\pi\)
\(978\) 0 0
\(979\) 0.230327 0.00736128
\(980\) 0 0
\(981\) −41.6043 −1.32832
\(982\) 0 0
\(983\) −16.0647 −0.512384 −0.256192 0.966626i \(-0.582468\pi\)
−0.256192 + 0.966626i \(0.582468\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 3.13823 0.0998910
\(988\) 0 0
\(989\) 1.75255 0.0557279
\(990\) 0 0
\(991\) −51.4433 −1.63415 −0.817075 0.576532i \(-0.804406\pi\)
−0.817075 + 0.576532i \(0.804406\pi\)
\(992\) 0 0
\(993\) −5.18066 −0.164403
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 39.2639 1.24350 0.621751 0.783215i \(-0.286422\pi\)
0.621751 + 0.783215i \(0.286422\pi\)
\(998\) 0 0
\(999\) 7.81660 0.247306
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 9200.2.a.cz.1.5 7
4.3 odd 2 4600.2.a.bi.1.3 7
5.2 odd 4 1840.2.e.g.369.8 14
5.3 odd 4 1840.2.e.g.369.7 14
5.4 even 2 9200.2.a.dc.1.3 7
20.3 even 4 920.2.e.b.369.8 yes 14
20.7 even 4 920.2.e.b.369.7 14
20.19 odd 2 4600.2.a.bh.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.7 14 20.7 even 4
920.2.e.b.369.8 yes 14 20.3 even 4
1840.2.e.g.369.7 14 5.3 odd 4
1840.2.e.g.369.8 14 5.2 odd 4
4600.2.a.bh.1.5 7 20.19 odd 2
4600.2.a.bi.1.3 7 4.3 odd 2
9200.2.a.cz.1.5 7 1.1 even 1 trivial
9200.2.a.dc.1.3 7 5.4 even 2