Properties

Label 1400.2.a.p.1.2
Level $1400$
Weight $2$
Character 1400.1
Self dual yes
Analytic conductor $11.179$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.1790562830\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.56155\) of defining polynomial
Character \(\chi\) \(=\) 1400.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.56155 q^{3} -1.00000 q^{7} -0.561553 q^{9} +O(q^{10})\) \(q+1.56155 q^{3} -1.00000 q^{7} -0.561553 q^{9} +1.56155 q^{11} -6.68466 q^{13} -7.56155 q^{17} -7.12311 q^{19} -1.56155 q^{21} -3.12311 q^{23} -5.56155 q^{27} +0.438447 q^{29} +6.24621 q^{31} +2.43845 q^{33} +8.24621 q^{37} -10.4384 q^{39} -1.12311 q^{41} +7.12311 q^{43} -2.43845 q^{47} +1.00000 q^{49} -11.8078 q^{51} +13.1231 q^{53} -11.1231 q^{57} -4.00000 q^{59} -6.87689 q^{61} +0.561553 q^{63} -2.24621 q^{67} -4.87689 q^{69} +4.24621 q^{73} -1.56155 q^{77} +0.684658 q^{79} -7.00000 q^{81} -12.0000 q^{83} +0.684658 q^{87} +5.12311 q^{89} +6.68466 q^{91} +9.75379 q^{93} -1.31534 q^{97} -0.876894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 2q^{7} + 3q^{9} + O(q^{10}) \) \( 2q - q^{3} - 2q^{7} + 3q^{9} - q^{11} - q^{13} - 11q^{17} - 6q^{19} + q^{21} + 2q^{23} - 7q^{27} + 5q^{29} - 4q^{31} + 9q^{33} - 25q^{39} + 6q^{41} + 6q^{43} - 9q^{47} + 2q^{49} - 3q^{51} + 18q^{53} - 14q^{57} - 8q^{59} - 22q^{61} - 3q^{63} + 12q^{67} - 18q^{69} - 8q^{73} + q^{77} - 11q^{79} - 14q^{81} - 24q^{83} - 11q^{87} + 2q^{89} + q^{91} + 36q^{93} - 15q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) 1.56155 0.901563 0.450781 0.892634i \(-0.351145\pi\)
0.450781 + 0.892634i \(0.351145\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.561553 −0.187184
\(10\) 0 0
\(11\) 1.56155 0.470826 0.235413 0.971895i \(-0.424356\pi\)
0.235413 + 0.971895i \(0.424356\pi\)
\(12\) 0 0
\(13\) −6.68466 −1.85399 −0.926995 0.375073i \(-0.877618\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.56155 −1.83395 −0.916973 0.398949i \(-0.869375\pi\)
−0.916973 + 0.398949i \(0.869375\pi\)
\(18\) 0 0
\(19\) −7.12311 −1.63415 −0.817076 0.576530i \(-0.804407\pi\)
−0.817076 + 0.576530i \(0.804407\pi\)
\(20\) 0 0
\(21\) −1.56155 −0.340759
\(22\) 0 0
\(23\) −3.12311 −0.651213 −0.325606 0.945505i \(-0.605568\pi\)
−0.325606 + 0.945505i \(0.605568\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.56155 −1.07032
\(28\) 0 0
\(29\) 0.438447 0.0814176 0.0407088 0.999171i \(-0.487038\pi\)
0.0407088 + 0.999171i \(0.487038\pi\)
\(30\) 0 0
\(31\) 6.24621 1.12185 0.560926 0.827866i \(-0.310445\pi\)
0.560926 + 0.827866i \(0.310445\pi\)
\(32\) 0 0
\(33\) 2.43845 0.424479
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.24621 1.35567 0.677834 0.735215i \(-0.262919\pi\)
0.677834 + 0.735215i \(0.262919\pi\)
\(38\) 0 0
\(39\) −10.4384 −1.67149
\(40\) 0 0
\(41\) −1.12311 −0.175400 −0.0876998 0.996147i \(-0.527952\pi\)
−0.0876998 + 0.996147i \(0.527952\pi\)
\(42\) 0 0
\(43\) 7.12311 1.08626 0.543132 0.839648i \(-0.317238\pi\)
0.543132 + 0.839648i \(0.317238\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.43845 −0.355684 −0.177842 0.984059i \(-0.556912\pi\)
−0.177842 + 0.984059i \(0.556912\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −11.8078 −1.65342
\(52\) 0 0
\(53\) 13.1231 1.80260 0.901299 0.433198i \(-0.142615\pi\)
0.901299 + 0.433198i \(0.142615\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −11.1231 −1.47329
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −6.87689 −0.880496 −0.440248 0.897876i \(-0.645109\pi\)
−0.440248 + 0.897876i \(0.645109\pi\)
\(62\) 0 0
\(63\) 0.561553 0.0707490
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.24621 −0.274418 −0.137209 0.990542i \(-0.543813\pi\)
−0.137209 + 0.990542i \(0.543813\pi\)
\(68\) 0 0
\(69\) −4.87689 −0.587109
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 4.24621 0.496981 0.248491 0.968634i \(-0.420065\pi\)
0.248491 + 0.968634i \(0.420065\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.56155 −0.177955
\(78\) 0 0
\(79\) 0.684658 0.0770301 0.0385150 0.999258i \(-0.487737\pi\)
0.0385150 + 0.999258i \(0.487737\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.684658 0.0734031
\(88\) 0 0
\(89\) 5.12311 0.543048 0.271524 0.962432i \(-0.412472\pi\)
0.271524 + 0.962432i \(0.412472\pi\)
\(90\) 0 0
\(91\) 6.68466 0.700743
\(92\) 0 0
\(93\) 9.75379 1.01142
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.31534 −0.133553 −0.0667764 0.997768i \(-0.521271\pi\)
−0.0667764 + 0.997768i \(0.521271\pi\)
\(98\) 0 0
\(99\) −0.876894 −0.0881312
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 11.8078 1.16345 0.581727 0.813384i \(-0.302377\pi\)
0.581727 + 0.813384i \(0.302377\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.1231 −1.46201 −0.731003 0.682374i \(-0.760947\pi\)
−0.731003 + 0.682374i \(0.760947\pi\)
\(108\) 0 0
\(109\) −4.43845 −0.425126 −0.212563 0.977147i \(-0.568181\pi\)
−0.212563 + 0.977147i \(0.568181\pi\)
\(110\) 0 0
\(111\) 12.8769 1.22222
\(112\) 0 0
\(113\) −8.24621 −0.775738 −0.387869 0.921714i \(-0.626789\pi\)
−0.387869 + 0.921714i \(0.626789\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.75379 0.347038
\(118\) 0 0
\(119\) 7.56155 0.693166
\(120\) 0 0
\(121\) −8.56155 −0.778323
\(122\) 0 0
\(123\) −1.75379 −0.158134
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 6.24621 0.554262 0.277131 0.960832i \(-0.410616\pi\)
0.277131 + 0.960832i \(0.410616\pi\)
\(128\) 0 0
\(129\) 11.1231 0.979335
\(130\) 0 0
\(131\) 15.1231 1.32131 0.660656 0.750689i \(-0.270278\pi\)
0.660656 + 0.750689i \(0.270278\pi\)
\(132\) 0 0
\(133\) 7.12311 0.617652
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.36932 0.629603 0.314802 0.949157i \(-0.398062\pi\)
0.314802 + 0.949157i \(0.398062\pi\)
\(138\) 0 0
\(139\) −21.3693 −1.81252 −0.906261 0.422719i \(-0.861076\pi\)
−0.906261 + 0.422719i \(0.861076\pi\)
\(140\) 0 0
\(141\) −3.80776 −0.320672
\(142\) 0 0
\(143\) −10.4384 −0.872907
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 1.56155 0.128795
\(148\) 0 0
\(149\) −0.246211 −0.0201704 −0.0100852 0.999949i \(-0.503210\pi\)
−0.0100852 + 0.999949i \(0.503210\pi\)
\(150\) 0 0
\(151\) −19.8078 −1.61193 −0.805966 0.591961i \(-0.798354\pi\)
−0.805966 + 0.591961i \(0.798354\pi\)
\(152\) 0 0
\(153\) 4.24621 0.343286
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.24621 −0.338885 −0.169442 0.985540i \(-0.554197\pi\)
−0.169442 + 0.985540i \(0.554197\pi\)
\(158\) 0 0
\(159\) 20.4924 1.62515
\(160\) 0 0
\(161\) 3.12311 0.246135
\(162\) 0 0
\(163\) −19.6155 −1.53641 −0.768203 0.640206i \(-0.778849\pi\)
−0.768203 + 0.640206i \(0.778849\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.19224 −0.324405 −0.162202 0.986757i \(-0.551860\pi\)
−0.162202 + 0.986757i \(0.551860\pi\)
\(168\) 0 0
\(169\) 31.6847 2.43728
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 0 0
\(173\) 23.1771 1.76212 0.881060 0.473004i \(-0.156830\pi\)
0.881060 + 0.473004i \(0.156830\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.24621 −0.469494
\(178\) 0 0
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 0 0
\(181\) −5.12311 −0.380797 −0.190399 0.981707i \(-0.560978\pi\)
−0.190399 + 0.981707i \(0.560978\pi\)
\(182\) 0 0
\(183\) −10.7386 −0.793823
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −11.8078 −0.863469
\(188\) 0 0
\(189\) 5.56155 0.404543
\(190\) 0 0
\(191\) −0.684658 −0.0495401 −0.0247701 0.999693i \(-0.507885\pi\)
−0.0247701 + 0.999693i \(0.507885\pi\)
\(192\) 0 0
\(193\) −13.1231 −0.944622 −0.472311 0.881432i \(-0.656580\pi\)
−0.472311 + 0.881432i \(0.656580\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.1231 0.934983 0.467491 0.883998i \(-0.345158\pi\)
0.467491 + 0.883998i \(0.345158\pi\)
\(198\) 0 0
\(199\) −14.2462 −1.00989 −0.504944 0.863152i \(-0.668487\pi\)
−0.504944 + 0.863152i \(0.668487\pi\)
\(200\) 0 0
\(201\) −3.50758 −0.247405
\(202\) 0 0
\(203\) −0.438447 −0.0307730
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.75379 0.121897
\(208\) 0 0
\(209\) −11.1231 −0.769401
\(210\) 0 0
\(211\) −17.5616 −1.20899 −0.604494 0.796610i \(-0.706624\pi\)
−0.604494 + 0.796610i \(0.706624\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −6.24621 −0.424020
\(218\) 0 0
\(219\) 6.63068 0.448060
\(220\) 0 0
\(221\) 50.5464 3.40012
\(222\) 0 0
\(223\) −24.6847 −1.65301 −0.826503 0.562932i \(-0.809673\pi\)
−0.826503 + 0.562932i \(0.809673\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.3153 0.751026 0.375513 0.926817i \(-0.377467\pi\)
0.375513 + 0.926817i \(0.377467\pi\)
\(228\) 0 0
\(229\) −11.3693 −0.751306 −0.375653 0.926760i \(-0.622581\pi\)
−0.375653 + 0.926760i \(0.622581\pi\)
\(230\) 0 0
\(231\) −2.43845 −0.160438
\(232\) 0 0
\(233\) 10.8769 0.712569 0.356285 0.934378i \(-0.384043\pi\)
0.356285 + 0.934378i \(0.384043\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.06913 0.0694475
\(238\) 0 0
\(239\) −18.0540 −1.16781 −0.583907 0.811820i \(-0.698477\pi\)
−0.583907 + 0.811820i \(0.698477\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 5.75379 0.369106
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 47.6155 3.02970
\(248\) 0 0
\(249\) −18.7386 −1.18751
\(250\) 0 0
\(251\) 13.3693 0.843864 0.421932 0.906628i \(-0.361352\pi\)
0.421932 + 0.906628i \(0.361352\pi\)
\(252\) 0 0
\(253\) −4.87689 −0.306608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.4924 1.15353 0.576763 0.816912i \(-0.304316\pi\)
0.576763 + 0.816912i \(0.304316\pi\)
\(258\) 0 0
\(259\) −8.24621 −0.512395
\(260\) 0 0
\(261\) −0.246211 −0.0152401
\(262\) 0 0
\(263\) −9.36932 −0.577737 −0.288868 0.957369i \(-0.593279\pi\)
−0.288868 + 0.957369i \(0.593279\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 8.00000 0.489592
\(268\) 0 0
\(269\) 4.24621 0.258896 0.129448 0.991586i \(-0.458679\pi\)
0.129448 + 0.991586i \(0.458679\pi\)
\(270\) 0 0
\(271\) −6.24621 −0.379430 −0.189715 0.981839i \(-0.560756\pi\)
−0.189715 + 0.981839i \(0.560756\pi\)
\(272\) 0 0
\(273\) 10.4384 0.631764
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.24621 0.495467 0.247733 0.968828i \(-0.420314\pi\)
0.247733 + 0.968828i \(0.420314\pi\)
\(278\) 0 0
\(279\) −3.50758 −0.209993
\(280\) 0 0
\(281\) −19.5616 −1.16694 −0.583472 0.812133i \(-0.698306\pi\)
−0.583472 + 0.812133i \(0.698306\pi\)
\(282\) 0 0
\(283\) 4.68466 0.278474 0.139237 0.990259i \(-0.455535\pi\)
0.139237 + 0.990259i \(0.455535\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.12311 0.0662948
\(288\) 0 0
\(289\) 40.1771 2.36336
\(290\) 0 0
\(291\) −2.05398 −0.120406
\(292\) 0 0
\(293\) −32.0540 −1.87261 −0.936307 0.351184i \(-0.885779\pi\)
−0.936307 + 0.351184i \(0.885779\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −8.68466 −0.503935
\(298\) 0 0
\(299\) 20.8769 1.20734
\(300\) 0 0
\(301\) −7.12311 −0.410569
\(302\) 0 0
\(303\) 9.36932 0.538253
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 28.6847 1.63712 0.818560 0.574421i \(-0.194773\pi\)
0.818560 + 0.574421i \(0.194773\pi\)
\(308\) 0 0
\(309\) 18.4384 1.04893
\(310\) 0 0
\(311\) −12.8769 −0.730182 −0.365091 0.930972i \(-0.618962\pi\)
−0.365091 + 0.930972i \(0.618962\pi\)
\(312\) 0 0
\(313\) −26.6847 −1.50831 −0.754153 0.656699i \(-0.771952\pi\)
−0.754153 + 0.656699i \(0.771952\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.0000 0.561656 0.280828 0.959758i \(-0.409391\pi\)
0.280828 + 0.959758i \(0.409391\pi\)
\(318\) 0 0
\(319\) 0.684658 0.0383335
\(320\) 0 0
\(321\) −23.6155 −1.31809
\(322\) 0 0
\(323\) 53.8617 2.99695
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.93087 −0.383278
\(328\) 0 0
\(329\) 2.43845 0.134436
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 0 0
\(333\) −4.63068 −0.253760
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 0 0
\(339\) −12.8769 −0.699377
\(340\) 0 0
\(341\) 9.75379 0.528197
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.1231 −0.811851 −0.405925 0.913906i \(-0.633051\pi\)
−0.405925 + 0.913906i \(0.633051\pi\)
\(348\) 0 0
\(349\) −11.7538 −0.629166 −0.314583 0.949230i \(-0.601865\pi\)
−0.314583 + 0.949230i \(0.601865\pi\)
\(350\) 0 0
\(351\) 37.1771 1.98437
\(352\) 0 0
\(353\) 2.19224 0.116681 0.0583405 0.998297i \(-0.481419\pi\)
0.0583405 + 0.998297i \(0.481419\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 11.8078 0.624933
\(358\) 0 0
\(359\) 32.0000 1.68890 0.844448 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 0 0
\(361\) 31.7386 1.67045
\(362\) 0 0
\(363\) −13.3693 −0.701707
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −14.9309 −0.779385 −0.389693 0.920945i \(-0.627419\pi\)
−0.389693 + 0.920945i \(0.627419\pi\)
\(368\) 0 0
\(369\) 0.630683 0.0328321
\(370\) 0 0
\(371\) −13.1231 −0.681318
\(372\) 0 0
\(373\) −15.3693 −0.795793 −0.397897 0.917430i \(-0.630260\pi\)
−0.397897 + 0.917430i \(0.630260\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.93087 −0.150947
\(378\) 0 0
\(379\) 32.4924 1.66902 0.834512 0.550990i \(-0.185750\pi\)
0.834512 + 0.550990i \(0.185750\pi\)
\(380\) 0 0
\(381\) 9.75379 0.499702
\(382\) 0 0
\(383\) 9.75379 0.498395 0.249198 0.968453i \(-0.419833\pi\)
0.249198 + 0.968453i \(0.419833\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.00000 −0.203331
\(388\) 0 0
\(389\) 22.3002 1.13066 0.565332 0.824863i \(-0.308748\pi\)
0.565332 + 0.824863i \(0.308748\pi\)
\(390\) 0 0
\(391\) 23.6155 1.19429
\(392\) 0 0
\(393\) 23.6155 1.19125
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 23.1771 1.16322 0.581612 0.813466i \(-0.302422\pi\)
0.581612 + 0.813466i \(0.302422\pi\)
\(398\) 0 0
\(399\) 11.1231 0.556852
\(400\) 0 0
\(401\) −12.9309 −0.645737 −0.322868 0.946444i \(-0.604647\pi\)
−0.322868 + 0.946444i \(0.604647\pi\)
\(402\) 0 0
\(403\) −41.7538 −2.07990
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12.8769 0.638284
\(408\) 0 0
\(409\) −18.4924 −0.914391 −0.457196 0.889366i \(-0.651146\pi\)
−0.457196 + 0.889366i \(0.651146\pi\)
\(410\) 0 0
\(411\) 11.5076 0.567627
\(412\) 0 0
\(413\) 4.00000 0.196827
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −33.3693 −1.63410
\(418\) 0 0
\(419\) −18.2462 −0.891386 −0.445693 0.895186i \(-0.647043\pi\)
−0.445693 + 0.895186i \(0.647043\pi\)
\(420\) 0 0
\(421\) 3.56155 0.173579 0.0867897 0.996227i \(-0.472339\pi\)
0.0867897 + 0.996227i \(0.472339\pi\)
\(422\) 0 0
\(423\) 1.36932 0.0665785
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.87689 0.332796
\(428\) 0 0
\(429\) −16.3002 −0.786980
\(430\) 0 0
\(431\) −22.9309 −1.10454 −0.552271 0.833665i \(-0.686238\pi\)
−0.552271 + 0.833665i \(0.686238\pi\)
\(432\) 0 0
\(433\) −19.7538 −0.949307 −0.474653 0.880173i \(-0.657427\pi\)
−0.474653 + 0.880173i \(0.657427\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 22.2462 1.06418
\(438\) 0 0
\(439\) 19.1231 0.912696 0.456348 0.889801i \(-0.349157\pi\)
0.456348 + 0.889801i \(0.349157\pi\)
\(440\) 0 0
\(441\) −0.561553 −0.0267406
\(442\) 0 0
\(443\) 19.6155 0.931962 0.465981 0.884795i \(-0.345702\pi\)
0.465981 + 0.884795i \(0.345702\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.384472 −0.0181849
\(448\) 0 0
\(449\) −21.3153 −1.00593 −0.502967 0.864306i \(-0.667758\pi\)
−0.502967 + 0.864306i \(0.667758\pi\)
\(450\) 0 0
\(451\) −1.75379 −0.0825827
\(452\) 0 0
\(453\) −30.9309 −1.45326
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.63068 −0.403726 −0.201863 0.979414i \(-0.564700\pi\)
−0.201863 + 0.979414i \(0.564700\pi\)
\(458\) 0 0
\(459\) 42.0540 1.96291
\(460\) 0 0
\(461\) 18.8769 0.879185 0.439592 0.898197i \(-0.355123\pi\)
0.439592 + 0.898197i \(0.355123\pi\)
\(462\) 0 0
\(463\) 6.24621 0.290286 0.145143 0.989411i \(-0.453636\pi\)
0.145143 + 0.989411i \(0.453636\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −25.5616 −1.18285 −0.591424 0.806361i \(-0.701434\pi\)
−0.591424 + 0.806361i \(0.701434\pi\)
\(468\) 0 0
\(469\) 2.24621 0.103720
\(470\) 0 0
\(471\) −6.63068 −0.305526
\(472\) 0 0
\(473\) 11.1231 0.511441
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −7.36932 −0.337418
\(478\) 0 0
\(479\) 17.3693 0.793624 0.396812 0.917900i \(-0.370116\pi\)
0.396812 + 0.917900i \(0.370116\pi\)
\(480\) 0 0
\(481\) −55.1231 −2.51340
\(482\) 0 0
\(483\) 4.87689 0.221906
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −3.12311 −0.141521 −0.0707607 0.997493i \(-0.522543\pi\)
−0.0707607 + 0.997493i \(0.522543\pi\)
\(488\) 0 0
\(489\) −30.6307 −1.38517
\(490\) 0 0
\(491\) −3.31534 −0.149619 −0.0748096 0.997198i \(-0.523835\pi\)
−0.0748096 + 0.997198i \(0.523835\pi\)
\(492\) 0 0
\(493\) −3.31534 −0.149315
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −0.192236 −0.00860566 −0.00430283 0.999991i \(-0.501370\pi\)
−0.00430283 + 0.999991i \(0.501370\pi\)
\(500\) 0 0
\(501\) −6.54640 −0.292471
\(502\) 0 0
\(503\) 29.1771 1.30094 0.650471 0.759531i \(-0.274572\pi\)
0.650471 + 0.759531i \(0.274572\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 49.4773 2.19736
\(508\) 0 0
\(509\) 32.7386 1.45111 0.725557 0.688162i \(-0.241582\pi\)
0.725557 + 0.688162i \(0.241582\pi\)
\(510\) 0 0
\(511\) −4.24621 −0.187841
\(512\) 0 0
\(513\) 39.6155 1.74907
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −3.80776 −0.167465
\(518\) 0 0
\(519\) 36.1922 1.58866
\(520\) 0 0
\(521\) −12.2462 −0.536516 −0.268258 0.963347i \(-0.586448\pi\)
−0.268258 + 0.963347i \(0.586448\pi\)
\(522\) 0 0
\(523\) 12.0000 0.524723 0.262362 0.964970i \(-0.415499\pi\)
0.262362 + 0.964970i \(0.415499\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −47.2311 −2.05742
\(528\) 0 0
\(529\) −13.2462 −0.575922
\(530\) 0 0
\(531\) 2.24621 0.0974773
\(532\) 0 0
\(533\) 7.50758 0.325189
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −6.24621 −0.269544
\(538\) 0 0
\(539\) 1.56155 0.0672608
\(540\) 0 0
\(541\) 41.4233 1.78093 0.890463 0.455055i \(-0.150380\pi\)
0.890463 + 0.455055i \(0.150380\pi\)
\(542\) 0 0
\(543\) −8.00000 −0.343313
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 0 0
\(549\) 3.86174 0.164815
\(550\) 0 0
\(551\) −3.12311 −0.133049
\(552\) 0 0
\(553\) −0.684658 −0.0291146
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17.6155 0.746394 0.373197 0.927752i \(-0.378262\pi\)
0.373197 + 0.927752i \(0.378262\pi\)
\(558\) 0 0
\(559\) −47.6155 −2.01392
\(560\) 0 0
\(561\) −18.4384 −0.778472
\(562\) 0 0
\(563\) 7.50758 0.316407 0.158203 0.987407i \(-0.449430\pi\)
0.158203 + 0.987407i \(0.449430\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 7.00000 0.293972
\(568\) 0 0
\(569\) 18.9848 0.795886 0.397943 0.917410i \(-0.369724\pi\)
0.397943 + 0.917410i \(0.369724\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) −1.06913 −0.0446636
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 3.56155 0.148269 0.0741347 0.997248i \(-0.476381\pi\)
0.0741347 + 0.997248i \(0.476381\pi\)
\(578\) 0 0
\(579\) −20.4924 −0.851636
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) 20.4924 0.848709
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.2462 −0.422906 −0.211453 0.977388i \(-0.567820\pi\)
−0.211453 + 0.977388i \(0.567820\pi\)
\(588\) 0 0
\(589\) −44.4924 −1.83328
\(590\) 0 0
\(591\) 20.4924 0.842946
\(592\) 0 0
\(593\) −37.4233 −1.53679 −0.768395 0.639976i \(-0.778944\pi\)
−0.768395 + 0.639976i \(0.778944\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −22.2462 −0.910477
\(598\) 0 0
\(599\) −46.9309 −1.91754 −0.958772 0.284178i \(-0.908279\pi\)
−0.958772 + 0.284178i \(0.908279\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 1.26137 0.0513668
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 8.68466 0.352499 0.176250 0.984345i \(-0.443603\pi\)
0.176250 + 0.984345i \(0.443603\pi\)
\(608\) 0 0
\(609\) −0.684658 −0.0277438
\(610\) 0 0
\(611\) 16.3002 0.659435
\(612\) 0 0
\(613\) −16.7386 −0.676067 −0.338034 0.941134i \(-0.609762\pi\)
−0.338034 + 0.941134i \(0.609762\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.7538 0.634224 0.317112 0.948388i \(-0.397287\pi\)
0.317112 + 0.948388i \(0.397287\pi\)
\(618\) 0 0
\(619\) 10.6307 0.427283 0.213642 0.976912i \(-0.431468\pi\)
0.213642 + 0.976912i \(0.431468\pi\)
\(620\) 0 0
\(621\) 17.3693 0.697007
\(622\) 0 0
\(623\) −5.12311 −0.205253
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −17.3693 −0.693664
\(628\) 0 0
\(629\) −62.3542 −2.48622
\(630\) 0 0
\(631\) −27.4233 −1.09170 −0.545852 0.837882i \(-0.683794\pi\)
−0.545852 + 0.837882i \(0.683794\pi\)
\(632\) 0 0
\(633\) −27.4233 −1.08998
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.68466 −0.264856
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −22.9848 −0.907847 −0.453923 0.891041i \(-0.649976\pi\)
−0.453923 + 0.891041i \(0.649976\pi\)
\(642\) 0 0
\(643\) 30.0540 1.18521 0.592607 0.805492i \(-0.298099\pi\)
0.592607 + 0.805492i \(0.298099\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) 0 0
\(649\) −6.24621 −0.245185
\(650\) 0 0
\(651\) −9.75379 −0.382281
\(652\) 0 0
\(653\) 38.4924 1.50632 0.753162 0.657835i \(-0.228527\pi\)
0.753162 + 0.657835i \(0.228527\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2.38447 −0.0930271
\(658\) 0 0
\(659\) −0.192236 −0.00748845 −0.00374422 0.999993i \(-0.501192\pi\)
−0.00374422 + 0.999993i \(0.501192\pi\)
\(660\) 0 0
\(661\) −17.6155 −0.685165 −0.342582 0.939488i \(-0.611302\pi\)
−0.342582 + 0.939488i \(0.611302\pi\)
\(662\) 0 0
\(663\) 78.9309 3.06542
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.36932 −0.0530202
\(668\) 0 0
\(669\) −38.5464 −1.49029
\(670\) 0 0
\(671\) −10.7386 −0.414560
\(672\) 0 0
\(673\) −41.6155 −1.60416 −0.802080 0.597216i \(-0.796273\pi\)
−0.802080 + 0.597216i \(0.796273\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.31534 0.0505527 0.0252763 0.999681i \(-0.491953\pi\)
0.0252763 + 0.999681i \(0.491953\pi\)
\(678\) 0 0
\(679\) 1.31534 0.0504782
\(680\) 0 0
\(681\) 17.6695 0.677097
\(682\) 0 0
\(683\) −44.9848 −1.72130 −0.860649 0.509199i \(-0.829942\pi\)
−0.860649 + 0.509199i \(0.829942\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −17.7538 −0.677349
\(688\) 0 0
\(689\) −87.7235 −3.34200
\(690\) 0 0
\(691\) 16.4924 0.627401 0.313701 0.949522i \(-0.398431\pi\)
0.313701 + 0.949522i \(0.398431\pi\)
\(692\) 0 0
\(693\) 0.876894 0.0333105
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 8.49242 0.321673
\(698\) 0 0
\(699\) 16.9848 0.642426
\(700\) 0 0
\(701\) −9.31534 −0.351836 −0.175918 0.984405i \(-0.556289\pi\)
−0.175918 + 0.984405i \(0.556289\pi\)
\(702\) 0 0
\(703\) −58.7386 −2.21537
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.00000 −0.225653
\(708\) 0 0
\(709\) −4.05398 −0.152250 −0.0761251 0.997098i \(-0.524255\pi\)
−0.0761251 + 0.997098i \(0.524255\pi\)
\(710\) 0 0
\(711\) −0.384472 −0.0144188
\(712\) 0 0
\(713\) −19.5076 −0.730565
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −28.1922 −1.05286
\(718\) 0 0
\(719\) −23.6155 −0.880711 −0.440355 0.897824i \(-0.645148\pi\)
−0.440355 + 0.897824i \(0.645148\pi\)
\(720\) 0 0
\(721\) −11.8078 −0.439744
\(722\) 0 0
\(723\) 3.12311 0.116150
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −48.9848 −1.81675 −0.908374 0.418159i \(-0.862675\pi\)
−0.908374 + 0.418159i \(0.862675\pi\)
\(728\) 0 0
\(729\) 29.9848 1.11055
\(730\) 0 0
\(731\) −53.8617 −1.99215
\(732\) 0 0
\(733\) −16.4384 −0.607168 −0.303584 0.952805i \(-0.598183\pi\)
−0.303584 + 0.952805i \(0.598183\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.50758 −0.129203
\(738\) 0 0
\(739\) −6.43845 −0.236842 −0.118421 0.992963i \(-0.537783\pi\)
−0.118421 + 0.992963i \(0.537783\pi\)
\(740\) 0 0
\(741\) 74.3542 2.73147
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6.73863 0.246554
\(748\) 0 0
\(749\) 15.1231 0.552586
\(750\) 0 0
\(751\) −31.3153 −1.14271 −0.571357 0.820702i \(-0.693583\pi\)
−0.571357 + 0.820702i \(0.693583\pi\)
\(752\) 0 0
\(753\) 20.8769 0.760796
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −15.3693 −0.558607 −0.279304 0.960203i \(-0.590104\pi\)
−0.279304 + 0.960203i \(0.590104\pi\)
\(758\) 0 0
\(759\) −7.61553 −0.276426
\(760\) 0 0
\(761\) 26.0000 0.942499 0.471250 0.882000i \(-0.343803\pi\)
0.471250 + 0.882000i \(0.343803\pi\)
\(762\) 0 0
\(763\) 4.43845 0.160683
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.7386 0.965476
\(768\) 0 0
\(769\) 42.9848 1.55007 0.775037 0.631916i \(-0.217731\pi\)
0.775037 + 0.631916i \(0.217731\pi\)
\(770\) 0 0
\(771\) 28.8769 1.03998
\(772\) 0 0
\(773\) 29.8078 1.07211 0.536055 0.844183i \(-0.319914\pi\)
0.536055 + 0.844183i \(0.319914\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −12.8769 −0.461956
\(778\) 0 0
\(779\) 8.00000 0.286630
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −2.43845 −0.0871430
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −33.1771 −1.18264 −0.591318 0.806439i \(-0.701392\pi\)
−0.591318 + 0.806439i \(0.701392\pi\)
\(788\) 0 0
\(789\) −14.6307 −0.520866
\(790\) 0 0
\(791\) 8.24621 0.293202
\(792\) 0 0
\(793\) 45.9697 1.63243
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −17.8078 −0.630783 −0.315392 0.948962i \(-0.602136\pi\)
−0.315392 + 0.948962i \(0.602136\pi\)
\(798\) 0 0
\(799\) 18.4384 0.652305
\(800\) 0 0
\(801\) −2.87689 −0.101650
\(802\) 0 0
\(803\) 6.63068 0.233992
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.63068 0.233411
\(808\) 0 0
\(809\) 4.05398 0.142530 0.0712651 0.997457i \(-0.477296\pi\)
0.0712651 + 0.997457i \(0.477296\pi\)
\(810\) 0 0
\(811\) −27.6155 −0.969712 −0.484856 0.874594i \(-0.661128\pi\)
−0.484856 + 0.874594i \(0.661128\pi\)
\(812\) 0 0
\(813\) −9.75379 −0.342080
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −50.7386 −1.77512
\(818\) 0 0
\(819\) −3.75379 −0.131168
\(820\) 0 0
\(821\) 54.3002 1.89509 0.947545 0.319623i \(-0.103556\pi\)
0.947545 + 0.319623i \(0.103556\pi\)
\(822\) 0 0
\(823\) 17.7538 0.618858 0.309429 0.950923i \(-0.399862\pi\)
0.309429 + 0.950923i \(0.399862\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −24.8769 −0.865054 −0.432527 0.901621i \(-0.642378\pi\)
−0.432527 + 0.901621i \(0.642378\pi\)
\(828\) 0 0
\(829\) 5.61553 0.195035 0.0975177 0.995234i \(-0.468910\pi\)
0.0975177 + 0.995234i \(0.468910\pi\)
\(830\) 0 0
\(831\) 12.8769 0.446695
\(832\) 0 0
\(833\) −7.56155 −0.261992
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −34.7386 −1.20074
\(838\) 0 0
\(839\) 19.1231 0.660203 0.330101 0.943945i \(-0.392917\pi\)
0.330101 + 0.943945i \(0.392917\pi\)
\(840\) 0 0
\(841\) −28.8078 −0.993371
\(842\) 0 0
\(843\) −30.5464 −1.05207
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 8.56155 0.294178
\(848\) 0 0
\(849\) 7.31534 0.251062
\(850\) 0 0
\(851\) −25.7538 −0.882829
\(852\) 0 0
\(853\) −15.7538 −0.539399 −0.269700 0.962944i \(-0.586924\pi\)
−0.269700 + 0.962944i \(0.586924\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −52.7386 −1.80152 −0.900759 0.434320i \(-0.856989\pi\)
−0.900759 + 0.434320i \(0.856989\pi\)
\(858\) 0 0
\(859\) 36.9848 1.26191 0.630953 0.775821i \(-0.282664\pi\)
0.630953 + 0.775821i \(0.282664\pi\)
\(860\) 0 0
\(861\) 1.75379 0.0597690
\(862\) 0 0
\(863\) −28.4924 −0.969893 −0.484947 0.874544i \(-0.661161\pi\)
−0.484947 + 0.874544i \(0.661161\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 62.7386 2.13072
\(868\) 0 0
\(869\) 1.06913 0.0362678
\(870\) 0 0
\(871\) 15.0152 0.508769
\(872\) 0 0
\(873\) 0.738634 0.0249990
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 13.5076 0.456118 0.228059 0.973647i \(-0.426762\pi\)
0.228059 + 0.973647i \(0.426762\pi\)
\(878\) 0 0
\(879\) −50.0540 −1.68828
\(880\) 0 0
\(881\) 54.1080 1.82294 0.911472 0.411363i \(-0.134947\pi\)
0.911472 + 0.411363i \(0.134947\pi\)
\(882\) 0 0
\(883\) −21.7538 −0.732073 −0.366037 0.930600i \(-0.619286\pi\)
−0.366037 + 0.930600i \(0.619286\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 36.4924 1.22530 0.612648 0.790356i \(-0.290104\pi\)
0.612648 + 0.790356i \(0.290104\pi\)
\(888\) 0 0
\(889\) −6.24621 −0.209491
\(890\) 0 0
\(891\) −10.9309 −0.366198
\(892\) 0 0
\(893\) 17.3693 0.581242
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 32.6004 1.08849
\(898\) 0 0
\(899\) 2.73863 0.0913385
\(900\) 0 0
\(901\) −99.2311 −3.30587
\(902\) 0 0
\(903\) −11.1231 −0.370154
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 48.1080 1.59740 0.798699 0.601731i \(-0.205522\pi\)
0.798699 + 0.601731i \(0.205522\pi\)
\(908\) 0 0
\(909\) −3.36932 −0.111753
\(910\) 0 0
\(911\) 8.00000 0.265052 0.132526 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) 0 0
\(913\) −18.7386 −0.620158
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15.1231 −0.499409
\(918\) 0 0
\(919\) 2.43845 0.0804370 0.0402185 0.999191i \(-0.487195\pi\)
0.0402185 + 0.999191i \(0.487195\pi\)
\(920\) 0 0
\(921\) 44.7926 1.47597
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −6.63068 −0.217780
\(928\) 0 0
\(929\) −2.87689 −0.0943878 −0.0471939 0.998886i \(-0.515028\pi\)
−0.0471939 + 0.998886i \(0.515028\pi\)
\(930\) 0 0
\(931\) −7.12311 −0.233450
\(932\) 0 0
\(933\) −20.1080 −0.658305
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −37.8078 −1.23513 −0.617563 0.786521i \(-0.711880\pi\)
−0.617563 + 0.786521i \(0.711880\pi\)
\(938\) 0 0
\(939\) −41.6695 −1.35983
\(940\) 0 0
\(941\) 28.6307 0.933334 0.466667 0.884433i \(-0.345455\pi\)
0.466667 + 0.884433i \(0.345455\pi\)
\(942\) 0 0
\(943\) 3.50758 0.114222
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 35.2311 1.14486 0.572428 0.819955i \(-0.306002\pi\)
0.572428 + 0.819955i \(0.306002\pi\)
\(948\) 0 0
\(949\) −28.3845 −0.921399
\(950\) 0 0
\(951\) 15.6155 0.506368
\(952\) 0 0
\(953\) 51.8617 1.67997 0.839983 0.542612i \(-0.182565\pi\)
0.839983 + 0.542612i \(0.182565\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.06913 0.0345601
\(958\) 0 0
\(959\) −7.36932 −0.237968
\(960\) 0 0
\(961\) 8.01515 0.258553
\(962\) 0 0
\(963\) 8.49242 0.273664
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −44.1080 −1.41842 −0.709208 0.704999i \(-0.750947\pi\)
−0.709208 + 0.704999i \(0.750947\pi\)
\(968\) 0 0
\(969\) 84.1080 2.70194
\(970\) 0 0
\(971\) −22.7386 −0.729717 −0.364859 0.931063i \(-0.618883\pi\)
−0.364859 + 0.931063i \(0.618883\pi\)
\(972\) 0 0
\(973\) 21.3693 0.685069
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −10.9848 −0.351436 −0.175718 0.984441i \(-0.556225\pi\)
−0.175718 + 0.984441i \(0.556225\pi\)
\(978\) 0 0
\(979\) 8.00000 0.255681
\(980\) 0 0
\(981\) 2.49242 0.0795769
\(982\) 0 0
\(983\) 29.1771 0.930604 0.465302 0.885152i \(-0.345946\pi\)
0.465302 + 0.885152i \(0.345946\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 3.80776 0.121202
\(988\) 0 0
\(989\) −22.2462 −0.707388
\(990\) 0 0
\(991\) −20.4924 −0.650963 −0.325482 0.945548i \(-0.605526\pi\)
−0.325482 + 0.945548i \(0.605526\pi\)
\(992\) 0 0
\(993\) −18.7386 −0.594653
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 56.9309 1.80302 0.901509 0.432760i \(-0.142460\pi\)
0.901509 + 0.432760i \(0.142460\pi\)
\(998\) 0 0
\(999\) −45.8617 −1.45100
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 1400.2.a.p.1.2 2
4.3 odd 2 2800.2.a.bn.1.1 2
5.2 odd 4 1400.2.g.k.449.2 4
5.3 odd 4 1400.2.g.k.449.3 4
5.4 even 2 280.2.a.d.1.1 2
7.6 odd 2 9800.2.a.by.1.1 2
15.14 odd 2 2520.2.a.w.1.1 2
20.3 even 4 2800.2.g.u.449.2 4
20.7 even 4 2800.2.g.u.449.3 4
20.19 odd 2 560.2.a.g.1.2 2
35.4 even 6 1960.2.q.s.961.2 4
35.9 even 6 1960.2.q.s.361.2 4
35.19 odd 6 1960.2.q.u.361.1 4
35.24 odd 6 1960.2.q.u.961.1 4
35.34 odd 2 1960.2.a.r.1.2 2
40.19 odd 2 2240.2.a.bi.1.1 2
40.29 even 2 2240.2.a.be.1.2 2
60.59 even 2 5040.2.a.bq.1.2 2
140.139 even 2 3920.2.a.bu.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.a.d.1.1 2 5.4 even 2
560.2.a.g.1.2 2 20.19 odd 2
1400.2.a.p.1.2 2 1.1 even 1 trivial
1400.2.g.k.449.2 4 5.2 odd 4
1400.2.g.k.449.3 4 5.3 odd 4
1960.2.a.r.1.2 2 35.34 odd 2
1960.2.q.s.361.2 4 35.9 even 6
1960.2.q.s.961.2 4 35.4 even 6
1960.2.q.u.361.1 4 35.19 odd 6
1960.2.q.u.961.1 4 35.24 odd 6
2240.2.a.be.1.2 2 40.29 even 2
2240.2.a.bi.1.1 2 40.19 odd 2
2520.2.a.w.1.1 2 15.14 odd 2
2800.2.a.bn.1.1 2 4.3 odd 2
2800.2.g.u.449.2 4 20.3 even 4
2800.2.g.u.449.3 4 20.7 even 4
3920.2.a.bu.1.1 2 140.139 even 2
5040.2.a.bq.1.2 2 60.59 even 2
9800.2.a.by.1.1 2 7.6 odd 2