Properties

Label 7440.2.a.bl.1.1
Level $7440$
Weight $2$
Character 7440.1
Self dual yes
Analytic conductor $59.409$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7440.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4086991038\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \( x^{2} - x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 930)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 7440.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +1.00000 q^{5} -2.56155 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +1.00000 q^{5} -2.56155 q^{7} +1.00000 q^{9} -2.56155 q^{11} +2.00000 q^{13} +1.00000 q^{15} -3.12311 q^{17} +7.68466 q^{19} -2.56155 q^{21} -1.43845 q^{23} +1.00000 q^{25} +1.00000 q^{27} +7.12311 q^{29} -1.00000 q^{31} -2.56155 q^{33} -2.56155 q^{35} -3.12311 q^{37} +2.00000 q^{39} +7.12311 q^{41} -12.8078 q^{43} +1.00000 q^{45} -5.12311 q^{47} -0.438447 q^{49} -3.12311 q^{51} +7.43845 q^{53} -2.56155 q^{55} +7.68466 q^{57} +13.1231 q^{59} +6.00000 q^{61} -2.56155 q^{63} +2.00000 q^{65} +15.3693 q^{67} -1.43845 q^{69} +7.68466 q^{71} -10.8078 q^{73} +1.00000 q^{75} +6.56155 q^{77} +4.31534 q^{79} +1.00000 q^{81} -14.2462 q^{83} -3.12311 q^{85} +7.12311 q^{87} -13.6847 q^{89} -5.12311 q^{91} -1.00000 q^{93} +7.68466 q^{95} -6.00000 q^{97} -2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 2 q^{5} - q^{7} + 2 q^{9} - q^{11} + 4 q^{13} + 2 q^{15} + 2 q^{17} + 3 q^{19} - q^{21} - 7 q^{23} + 2 q^{25} + 2 q^{27} + 6 q^{29} - 2 q^{31} - q^{33} - q^{35} + 2 q^{37} + 4 q^{39} + 6 q^{41} - 5 q^{43} + 2 q^{45} - 2 q^{47} - 5 q^{49} + 2 q^{51} + 19 q^{53} - q^{55} + 3 q^{57} + 18 q^{59} + 12 q^{61} - q^{63} + 4 q^{65} + 6 q^{67} - 7 q^{69} + 3 q^{71} - q^{73} + 2 q^{75} + 9 q^{77} + 21 q^{79} + 2 q^{81} - 12 q^{83} + 2 q^{85} + 6 q^{87} - 15 q^{89} - 2 q^{91} - 2 q^{93} + 3 q^{95} - 12 q^{97} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.56155 −0.968176 −0.484088 0.875019i \(-0.660849\pi\)
−0.484088 + 0.875019i \(0.660849\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.56155 −0.772337 −0.386169 0.922428i \(-0.626202\pi\)
−0.386169 + 0.922428i \(0.626202\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) −3.12311 −0.757464 −0.378732 0.925506i \(-0.623640\pi\)
−0.378732 + 0.925506i \(0.623640\pi\)
\(18\) 0 0
\(19\) 7.68466 1.76298 0.881491 0.472201i \(-0.156540\pi\)
0.881491 + 0.472201i \(0.156540\pi\)
\(20\) 0 0
\(21\) −2.56155 −0.558977
\(22\) 0 0
\(23\) −1.43845 −0.299937 −0.149968 0.988691i \(-0.547917\pi\)
−0.149968 + 0.988691i \(0.547917\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 7.12311 1.32273 0.661364 0.750065i \(-0.269978\pi\)
0.661364 + 0.750065i \(0.269978\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) 0 0
\(33\) −2.56155 −0.445909
\(34\) 0 0
\(35\) −2.56155 −0.432981
\(36\) 0 0
\(37\) −3.12311 −0.513435 −0.256718 0.966486i \(-0.582641\pi\)
−0.256718 + 0.966486i \(0.582641\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 7.12311 1.11244 0.556221 0.831034i \(-0.312251\pi\)
0.556221 + 0.831034i \(0.312251\pi\)
\(42\) 0 0
\(43\) −12.8078 −1.95317 −0.976583 0.215142i \(-0.930979\pi\)
−0.976583 + 0.215142i \(0.930979\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −5.12311 −0.747282 −0.373641 0.927573i \(-0.621891\pi\)
−0.373641 + 0.927573i \(0.621891\pi\)
\(48\) 0 0
\(49\) −0.438447 −0.0626353
\(50\) 0 0
\(51\) −3.12311 −0.437322
\(52\) 0 0
\(53\) 7.43845 1.02175 0.510875 0.859655i \(-0.329322\pi\)
0.510875 + 0.859655i \(0.329322\pi\)
\(54\) 0 0
\(55\) −2.56155 −0.345400
\(56\) 0 0
\(57\) 7.68466 1.01786
\(58\) 0 0
\(59\) 13.1231 1.70848 0.854241 0.519877i \(-0.174022\pi\)
0.854241 + 0.519877i \(0.174022\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 0 0
\(63\) −2.56155 −0.322725
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 15.3693 1.87766 0.938830 0.344380i \(-0.111911\pi\)
0.938830 + 0.344380i \(0.111911\pi\)
\(68\) 0 0
\(69\) −1.43845 −0.173169
\(70\) 0 0
\(71\) 7.68466 0.912001 0.456001 0.889979i \(-0.349281\pi\)
0.456001 + 0.889979i \(0.349281\pi\)
\(72\) 0 0
\(73\) −10.8078 −1.26495 −0.632477 0.774580i \(-0.717962\pi\)
−0.632477 + 0.774580i \(0.717962\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 6.56155 0.747758
\(78\) 0 0
\(79\) 4.31534 0.485514 0.242757 0.970087i \(-0.421948\pi\)
0.242757 + 0.970087i \(0.421948\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.2462 −1.56372 −0.781862 0.623451i \(-0.785730\pi\)
−0.781862 + 0.623451i \(0.785730\pi\)
\(84\) 0 0
\(85\) −3.12311 −0.338748
\(86\) 0 0
\(87\) 7.12311 0.763677
\(88\) 0 0
\(89\) −13.6847 −1.45057 −0.725285 0.688448i \(-0.758292\pi\)
−0.725285 + 0.688448i \(0.758292\pi\)
\(90\) 0 0
\(91\) −5.12311 −0.537047
\(92\) 0 0
\(93\) −1.00000 −0.103695
\(94\) 0 0
\(95\) 7.68466 0.788429
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) −2.56155 −0.257446
\(100\) 0 0
\(101\) −0.561553 −0.0558766 −0.0279383 0.999610i \(-0.508894\pi\)
−0.0279383 + 0.999610i \(0.508894\pi\)
\(102\) 0 0
\(103\) 1.75379 0.172806 0.0864030 0.996260i \(-0.472463\pi\)
0.0864030 + 0.996260i \(0.472463\pi\)
\(104\) 0 0
\(105\) −2.56155 −0.249982
\(106\) 0 0
\(107\) 2.56155 0.247635 0.123817 0.992305i \(-0.460486\pi\)
0.123817 + 0.992305i \(0.460486\pi\)
\(108\) 0 0
\(109\) 5.36932 0.514287 0.257144 0.966373i \(-0.417219\pi\)
0.257144 + 0.966373i \(0.417219\pi\)
\(110\) 0 0
\(111\) −3.12311 −0.296432
\(112\) 0 0
\(113\) −1.68466 −0.158479 −0.0792397 0.996856i \(-0.525249\pi\)
−0.0792397 + 0.996856i \(0.525249\pi\)
\(114\) 0 0
\(115\) −1.43845 −0.134136
\(116\) 0 0
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) −4.43845 −0.403495
\(122\) 0 0
\(123\) 7.12311 0.642269
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) −12.8078 −1.12766
\(130\) 0 0
\(131\) 15.3693 1.34282 0.671412 0.741085i \(-0.265688\pi\)
0.671412 + 0.741085i \(0.265688\pi\)
\(132\) 0 0
\(133\) −19.6847 −1.70688
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) 20.2462 1.72975 0.864875 0.501987i \(-0.167397\pi\)
0.864875 + 0.501987i \(0.167397\pi\)
\(138\) 0 0
\(139\) 17.1231 1.45236 0.726181 0.687503i \(-0.241293\pi\)
0.726181 + 0.687503i \(0.241293\pi\)
\(140\) 0 0
\(141\) −5.12311 −0.431443
\(142\) 0 0
\(143\) −5.12311 −0.428416
\(144\) 0 0
\(145\) 7.12311 0.591542
\(146\) 0 0
\(147\) −0.438447 −0.0361625
\(148\) 0 0
\(149\) 17.0540 1.39712 0.698558 0.715553i \(-0.253825\pi\)
0.698558 + 0.715553i \(0.253825\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −3.12311 −0.252488
\(154\) 0 0
\(155\) −1.00000 −0.0803219
\(156\) 0 0
\(157\) 17.0540 1.36106 0.680528 0.732722i \(-0.261751\pi\)
0.680528 + 0.732722i \(0.261751\pi\)
\(158\) 0 0
\(159\) 7.43845 0.589907
\(160\) 0 0
\(161\) 3.68466 0.290392
\(162\) 0 0
\(163\) 15.3693 1.20382 0.601909 0.798565i \(-0.294407\pi\)
0.601909 + 0.798565i \(0.294407\pi\)
\(164\) 0 0
\(165\) −2.56155 −0.199417
\(166\) 0 0
\(167\) 6.56155 0.507748 0.253874 0.967237i \(-0.418295\pi\)
0.253874 + 0.967237i \(0.418295\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 7.68466 0.587661
\(172\) 0 0
\(173\) 8.24621 0.626948 0.313474 0.949597i \(-0.398507\pi\)
0.313474 + 0.949597i \(0.398507\pi\)
\(174\) 0 0
\(175\) −2.56155 −0.193635
\(176\) 0 0
\(177\) 13.1231 0.986393
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −13.0540 −0.970294 −0.485147 0.874433i \(-0.661234\pi\)
−0.485147 + 0.874433i \(0.661234\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) −3.12311 −0.229615
\(186\) 0 0
\(187\) 8.00000 0.585018
\(188\) 0 0
\(189\) −2.56155 −0.186326
\(190\) 0 0
\(191\) 14.2462 1.03082 0.515410 0.856944i \(-0.327640\pi\)
0.515410 + 0.856944i \(0.327640\pi\)
\(192\) 0 0
\(193\) 14.4924 1.04319 0.521594 0.853194i \(-0.325338\pi\)
0.521594 + 0.853194i \(0.325338\pi\)
\(194\) 0 0
\(195\) 2.00000 0.143223
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 16.8078 1.19147 0.595735 0.803181i \(-0.296861\pi\)
0.595735 + 0.803181i \(0.296861\pi\)
\(200\) 0 0
\(201\) 15.3693 1.08407
\(202\) 0 0
\(203\) −18.2462 −1.28063
\(204\) 0 0
\(205\) 7.12311 0.497499
\(206\) 0 0
\(207\) −1.43845 −0.0999790
\(208\) 0 0
\(209\) −19.6847 −1.36162
\(210\) 0 0
\(211\) 23.6847 1.63052 0.815260 0.579096i \(-0.196594\pi\)
0.815260 + 0.579096i \(0.196594\pi\)
\(212\) 0 0
\(213\) 7.68466 0.526544
\(214\) 0 0
\(215\) −12.8078 −0.873482
\(216\) 0 0
\(217\) 2.56155 0.173890
\(218\) 0 0
\(219\) −10.8078 −0.730321
\(220\) 0 0
\(221\) −6.24621 −0.420166
\(222\) 0 0
\(223\) 21.1231 1.41451 0.707254 0.706960i \(-0.249934\pi\)
0.707254 + 0.706960i \(0.249934\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −7.68466 −0.510049 −0.255024 0.966935i \(-0.582083\pi\)
−0.255024 + 0.966935i \(0.582083\pi\)
\(228\) 0 0
\(229\) −16.5616 −1.09442 −0.547209 0.836996i \(-0.684310\pi\)
−0.547209 + 0.836996i \(0.684310\pi\)
\(230\) 0 0
\(231\) 6.56155 0.431718
\(232\) 0 0
\(233\) −17.0540 −1.11724 −0.558622 0.829423i \(-0.688670\pi\)
−0.558622 + 0.829423i \(0.688670\pi\)
\(234\) 0 0
\(235\) −5.12311 −0.334195
\(236\) 0 0
\(237\) 4.31534 0.280312
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 12.2462 0.788848 0.394424 0.918929i \(-0.370944\pi\)
0.394424 + 0.918929i \(0.370944\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −0.438447 −0.0280114
\(246\) 0 0
\(247\) 15.3693 0.977926
\(248\) 0 0
\(249\) −14.2462 −0.902817
\(250\) 0 0
\(251\) −16.4924 −1.04099 −0.520496 0.853864i \(-0.674253\pi\)
−0.520496 + 0.853864i \(0.674253\pi\)
\(252\) 0 0
\(253\) 3.68466 0.231652
\(254\) 0 0
\(255\) −3.12311 −0.195576
\(256\) 0 0
\(257\) −1.68466 −0.105086 −0.0525431 0.998619i \(-0.516733\pi\)
−0.0525431 + 0.998619i \(0.516733\pi\)
\(258\) 0 0
\(259\) 8.00000 0.497096
\(260\) 0 0
\(261\) 7.12311 0.440909
\(262\) 0 0
\(263\) 20.4924 1.26362 0.631808 0.775125i \(-0.282313\pi\)
0.631808 + 0.775125i \(0.282313\pi\)
\(264\) 0 0
\(265\) 7.43845 0.456940
\(266\) 0 0
\(267\) −13.6847 −0.837487
\(268\) 0 0
\(269\) −0.246211 −0.0150118 −0.00750588 0.999972i \(-0.502389\pi\)
−0.00750588 + 0.999972i \(0.502389\pi\)
\(270\) 0 0
\(271\) −27.0540 −1.64341 −0.821706 0.569912i \(-0.806977\pi\)
−0.821706 + 0.569912i \(0.806977\pi\)
\(272\) 0 0
\(273\) −5.12311 −0.310064
\(274\) 0 0
\(275\) −2.56155 −0.154467
\(276\) 0 0
\(277\) −5.36932 −0.322611 −0.161305 0.986905i \(-0.551570\pi\)
−0.161305 + 0.986905i \(0.551570\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 4.87689 0.290931 0.145466 0.989363i \(-0.453532\pi\)
0.145466 + 0.989363i \(0.453532\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 7.68466 0.455200
\(286\) 0 0
\(287\) −18.2462 −1.07704
\(288\) 0 0
\(289\) −7.24621 −0.426248
\(290\) 0 0
\(291\) −6.00000 −0.351726
\(292\) 0 0
\(293\) 26.4924 1.54770 0.773852 0.633367i \(-0.218327\pi\)
0.773852 + 0.633367i \(0.218327\pi\)
\(294\) 0 0
\(295\) 13.1231 0.764057
\(296\) 0 0
\(297\) −2.56155 −0.148636
\(298\) 0 0
\(299\) −2.87689 −0.166375
\(300\) 0 0
\(301\) 32.8078 1.89101
\(302\) 0 0
\(303\) −0.561553 −0.0322604
\(304\) 0 0
\(305\) 6.00000 0.343559
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 1.75379 0.0997696
\(310\) 0 0
\(311\) 1.75379 0.0994482 0.0497241 0.998763i \(-0.484166\pi\)
0.0497241 + 0.998763i \(0.484166\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0 0
\(315\) −2.56155 −0.144327
\(316\) 0 0
\(317\) 16.8769 0.947901 0.473950 0.880552i \(-0.342828\pi\)
0.473950 + 0.880552i \(0.342828\pi\)
\(318\) 0 0
\(319\) −18.2462 −1.02159
\(320\) 0 0
\(321\) 2.56155 0.142972
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) 5.36932 0.296924
\(328\) 0 0
\(329\) 13.1231 0.723500
\(330\) 0 0
\(331\) 6.24621 0.343323 0.171661 0.985156i \(-0.445086\pi\)
0.171661 + 0.985156i \(0.445086\pi\)
\(332\) 0 0
\(333\) −3.12311 −0.171145
\(334\) 0 0
\(335\) 15.3693 0.839715
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 0 0
\(339\) −1.68466 −0.0914981
\(340\) 0 0
\(341\) 2.56155 0.138716
\(342\) 0 0
\(343\) 19.0540 1.02882
\(344\) 0 0
\(345\) −1.43845 −0.0774434
\(346\) 0 0
\(347\) −14.2462 −0.764777 −0.382388 0.924002i \(-0.624898\pi\)
−0.382388 + 0.924002i \(0.624898\pi\)
\(348\) 0 0
\(349\) 5.36932 0.287413 0.143706 0.989620i \(-0.454098\pi\)
0.143706 + 0.989620i \(0.454098\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) −0.246211 −0.0131045 −0.00655225 0.999979i \(-0.502086\pi\)
−0.00655225 + 0.999979i \(0.502086\pi\)
\(354\) 0 0
\(355\) 7.68466 0.407859
\(356\) 0 0
\(357\) 8.00000 0.423405
\(358\) 0 0
\(359\) 31.6847 1.67225 0.836126 0.548537i \(-0.184815\pi\)
0.836126 + 0.548537i \(0.184815\pi\)
\(360\) 0 0
\(361\) 40.0540 2.10810
\(362\) 0 0
\(363\) −4.43845 −0.232958
\(364\) 0 0
\(365\) −10.8078 −0.565704
\(366\) 0 0
\(367\) −15.3693 −0.802272 −0.401136 0.916019i \(-0.631384\pi\)
−0.401136 + 0.916019i \(0.631384\pi\)
\(368\) 0 0
\(369\) 7.12311 0.370814
\(370\) 0 0
\(371\) −19.0540 −0.989233
\(372\) 0 0
\(373\) −5.68466 −0.294340 −0.147170 0.989111i \(-0.547017\pi\)
−0.147170 + 0.989111i \(0.547017\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) 14.2462 0.733717
\(378\) 0 0
\(379\) 7.05398 0.362338 0.181169 0.983452i \(-0.442012\pi\)
0.181169 + 0.983452i \(0.442012\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.2462 0.523557 0.261778 0.965128i \(-0.415691\pi\)
0.261778 + 0.965128i \(0.415691\pi\)
\(384\) 0 0
\(385\) 6.56155 0.334408
\(386\) 0 0
\(387\) −12.8078 −0.651055
\(388\) 0 0
\(389\) 7.75379 0.393133 0.196566 0.980491i \(-0.437021\pi\)
0.196566 + 0.980491i \(0.437021\pi\)
\(390\) 0 0
\(391\) 4.49242 0.227192
\(392\) 0 0
\(393\) 15.3693 0.775279
\(394\) 0 0
\(395\) 4.31534 0.217128
\(396\) 0 0
\(397\) 9.05398 0.454406 0.227203 0.973847i \(-0.427042\pi\)
0.227203 + 0.973847i \(0.427042\pi\)
\(398\) 0 0
\(399\) −19.6847 −0.985466
\(400\) 0 0
\(401\) −13.6847 −0.683379 −0.341690 0.939813i \(-0.610999\pi\)
−0.341690 + 0.939813i \(0.610999\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −37.3693 −1.84779 −0.923897 0.382642i \(-0.875014\pi\)
−0.923897 + 0.382642i \(0.875014\pi\)
\(410\) 0 0
\(411\) 20.2462 0.998672
\(412\) 0 0
\(413\) −33.6155 −1.65411
\(414\) 0 0
\(415\) −14.2462 −0.699319
\(416\) 0 0
\(417\) 17.1231 0.838522
\(418\) 0 0
\(419\) −5.75379 −0.281091 −0.140545 0.990074i \(-0.544886\pi\)
−0.140545 + 0.990074i \(0.544886\pi\)
\(420\) 0 0
\(421\) −14.4924 −0.706317 −0.353159 0.935563i \(-0.614892\pi\)
−0.353159 + 0.935563i \(0.614892\pi\)
\(422\) 0 0
\(423\) −5.12311 −0.249094
\(424\) 0 0
\(425\) −3.12311 −0.151493
\(426\) 0 0
\(427\) −15.3693 −0.743773
\(428\) 0 0
\(429\) −5.12311 −0.247346
\(430\) 0 0
\(431\) 30.2462 1.45691 0.728454 0.685094i \(-0.240239\pi\)
0.728454 + 0.685094i \(0.240239\pi\)
\(432\) 0 0
\(433\) 35.3002 1.69642 0.848209 0.529661i \(-0.177681\pi\)
0.848209 + 0.529661i \(0.177681\pi\)
\(434\) 0 0
\(435\) 7.12311 0.341527
\(436\) 0 0
\(437\) −11.0540 −0.528783
\(438\) 0 0
\(439\) −9.61553 −0.458924 −0.229462 0.973318i \(-0.573697\pi\)
−0.229462 + 0.973318i \(0.573697\pi\)
\(440\) 0 0
\(441\) −0.438447 −0.0208784
\(442\) 0 0
\(443\) −23.0540 −1.09533 −0.547664 0.836699i \(-0.684483\pi\)
−0.547664 + 0.836699i \(0.684483\pi\)
\(444\) 0 0
\(445\) −13.6847 −0.648715
\(446\) 0 0
\(447\) 17.0540 0.806625
\(448\) 0 0
\(449\) 10.4924 0.495168 0.247584 0.968866i \(-0.420363\pi\)
0.247584 + 0.968866i \(0.420363\pi\)
\(450\) 0 0
\(451\) −18.2462 −0.859181
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.12311 −0.240175
\(456\) 0 0
\(457\) −24.7386 −1.15722 −0.578612 0.815603i \(-0.696406\pi\)
−0.578612 + 0.815603i \(0.696406\pi\)
\(458\) 0 0
\(459\) −3.12311 −0.145774
\(460\) 0 0
\(461\) 9.36932 0.436373 0.218186 0.975907i \(-0.429986\pi\)
0.218186 + 0.975907i \(0.429986\pi\)
\(462\) 0 0
\(463\) −30.7386 −1.42855 −0.714273 0.699867i \(-0.753242\pi\)
−0.714273 + 0.699867i \(0.753242\pi\)
\(464\) 0 0
\(465\) −1.00000 −0.0463739
\(466\) 0 0
\(467\) 9.75379 0.451352 0.225676 0.974202i \(-0.427541\pi\)
0.225676 + 0.974202i \(0.427541\pi\)
\(468\) 0 0
\(469\) −39.3693 −1.81791
\(470\) 0 0
\(471\) 17.0540 0.785806
\(472\) 0 0
\(473\) 32.8078 1.50850
\(474\) 0 0
\(475\) 7.68466 0.352596
\(476\) 0 0
\(477\) 7.43845 0.340583
\(478\) 0 0
\(479\) −10.5616 −0.482570 −0.241285 0.970454i \(-0.577569\pi\)
−0.241285 + 0.970454i \(0.577569\pi\)
\(480\) 0 0
\(481\) −6.24621 −0.284803
\(482\) 0 0
\(483\) 3.68466 0.167658
\(484\) 0 0
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) −24.0000 −1.08754 −0.543772 0.839233i \(-0.683004\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) 0 0
\(489\) 15.3693 0.695025
\(490\) 0 0
\(491\) 25.9309 1.17024 0.585122 0.810945i \(-0.301047\pi\)
0.585122 + 0.810945i \(0.301047\pi\)
\(492\) 0 0
\(493\) −22.2462 −1.00192
\(494\) 0 0
\(495\) −2.56155 −0.115133
\(496\) 0 0
\(497\) −19.6847 −0.882978
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) 6.56155 0.293149
\(502\) 0 0
\(503\) −26.2462 −1.17026 −0.585130 0.810939i \(-0.698957\pi\)
−0.585130 + 0.810939i \(0.698957\pi\)
\(504\) 0 0
\(505\) −0.561553 −0.0249888
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) 0 0
\(509\) 19.6155 0.869443 0.434721 0.900565i \(-0.356847\pi\)
0.434721 + 0.900565i \(0.356847\pi\)
\(510\) 0 0
\(511\) 27.6847 1.22470
\(512\) 0 0
\(513\) 7.68466 0.339286
\(514\) 0 0
\(515\) 1.75379 0.0772812
\(516\) 0 0
\(517\) 13.1231 0.577154
\(518\) 0 0
\(519\) 8.24621 0.361968
\(520\) 0 0
\(521\) −32.2462 −1.41273 −0.706366 0.707847i \(-0.749667\pi\)
−0.706366 + 0.707847i \(0.749667\pi\)
\(522\) 0 0
\(523\) 22.4233 0.980502 0.490251 0.871581i \(-0.336905\pi\)
0.490251 + 0.871581i \(0.336905\pi\)
\(524\) 0 0
\(525\) −2.56155 −0.111795
\(526\) 0 0
\(527\) 3.12311 0.136045
\(528\) 0 0
\(529\) −20.9309 −0.910038
\(530\) 0 0
\(531\) 13.1231 0.569494
\(532\) 0 0
\(533\) 14.2462 0.617072
\(534\) 0 0
\(535\) 2.56155 0.110746
\(536\) 0 0
\(537\) 12.0000 0.517838
\(538\) 0 0
\(539\) 1.12311 0.0483756
\(540\) 0 0
\(541\) 19.7538 0.849282 0.424641 0.905362i \(-0.360400\pi\)
0.424641 + 0.905362i \(0.360400\pi\)
\(542\) 0 0
\(543\) −13.0540 −0.560200
\(544\) 0 0
\(545\) 5.36932 0.229996
\(546\) 0 0
\(547\) −26.8769 −1.14917 −0.574587 0.818444i \(-0.694837\pi\)
−0.574587 + 0.818444i \(0.694837\pi\)
\(548\) 0 0
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) 54.7386 2.33194
\(552\) 0 0
\(553\) −11.0540 −0.470063
\(554\) 0 0
\(555\) −3.12311 −0.132568
\(556\) 0 0
\(557\) −26.8078 −1.13588 −0.567941 0.823069i \(-0.692260\pi\)
−0.567941 + 0.823069i \(0.692260\pi\)
\(558\) 0 0
\(559\) −25.6155 −1.08342
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 0 0
\(563\) −16.4924 −0.695073 −0.347536 0.937667i \(-0.612982\pi\)
−0.347536 + 0.937667i \(0.612982\pi\)
\(564\) 0 0
\(565\) −1.68466 −0.0708741
\(566\) 0 0
\(567\) −2.56155 −0.107575
\(568\) 0 0
\(569\) 30.8078 1.29153 0.645764 0.763537i \(-0.276539\pi\)
0.645764 + 0.763537i \(0.276539\pi\)
\(570\) 0 0
\(571\) −41.1231 −1.72095 −0.860474 0.509494i \(-0.829833\pi\)
−0.860474 + 0.509494i \(0.829833\pi\)
\(572\) 0 0
\(573\) 14.2462 0.595144
\(574\) 0 0
\(575\) −1.43845 −0.0599874
\(576\) 0 0
\(577\) 15.1231 0.629583 0.314792 0.949161i \(-0.398065\pi\)
0.314792 + 0.949161i \(0.398065\pi\)
\(578\) 0 0
\(579\) 14.4924 0.602285
\(580\) 0 0
\(581\) 36.4924 1.51396
\(582\) 0 0
\(583\) −19.0540 −0.789135
\(584\) 0 0
\(585\) 2.00000 0.0826898
\(586\) 0 0
\(587\) 0.492423 0.0203245 0.0101622 0.999948i \(-0.496765\pi\)
0.0101622 + 0.999948i \(0.496765\pi\)
\(588\) 0 0
\(589\) −7.68466 −0.316641
\(590\) 0 0
\(591\) 6.00000 0.246807
\(592\) 0 0
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 8.00000 0.327968
\(596\) 0 0
\(597\) 16.8078 0.687896
\(598\) 0 0
\(599\) −38.4233 −1.56993 −0.784967 0.619538i \(-0.787320\pi\)
−0.784967 + 0.619538i \(0.787320\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 0 0
\(603\) 15.3693 0.625887
\(604\) 0 0
\(605\) −4.43845 −0.180449
\(606\) 0 0
\(607\) −7.05398 −0.286312 −0.143156 0.989700i \(-0.545725\pi\)
−0.143156 + 0.989700i \(0.545725\pi\)
\(608\) 0 0
\(609\) −18.2462 −0.739374
\(610\) 0 0
\(611\) −10.2462 −0.414517
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) 0 0
\(615\) 7.12311 0.287231
\(616\) 0 0
\(617\) −15.4384 −0.621528 −0.310764 0.950487i \(-0.600585\pi\)
−0.310764 + 0.950487i \(0.600585\pi\)
\(618\) 0 0
\(619\) −11.3693 −0.456971 −0.228486 0.973547i \(-0.573377\pi\)
−0.228486 + 0.973547i \(0.573377\pi\)
\(620\) 0 0
\(621\) −1.43845 −0.0577229
\(622\) 0 0
\(623\) 35.0540 1.40441
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −19.6847 −0.786130
\(628\) 0 0
\(629\) 9.75379 0.388909
\(630\) 0 0
\(631\) −29.3002 −1.16642 −0.583211 0.812321i \(-0.698204\pi\)
−0.583211 + 0.812321i \(0.698204\pi\)
\(632\) 0 0
\(633\) 23.6847 0.941381
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.876894 −0.0347438
\(638\) 0 0
\(639\) 7.68466 0.304000
\(640\) 0 0
\(641\) −5.50758 −0.217536 −0.108768 0.994067i \(-0.534691\pi\)
−0.108768 + 0.994067i \(0.534691\pi\)
\(642\) 0 0
\(643\) 7.05398 0.278182 0.139091 0.990280i \(-0.455582\pi\)
0.139091 + 0.990280i \(0.455582\pi\)
\(644\) 0 0
\(645\) −12.8078 −0.504305
\(646\) 0 0
\(647\) 45.9309 1.80573 0.902864 0.429925i \(-0.141460\pi\)
0.902864 + 0.429925i \(0.141460\pi\)
\(648\) 0 0
\(649\) −33.6155 −1.31952
\(650\) 0 0
\(651\) 2.56155 0.100395
\(652\) 0 0
\(653\) 40.2462 1.57496 0.787478 0.616343i \(-0.211386\pi\)
0.787478 + 0.616343i \(0.211386\pi\)
\(654\) 0 0
\(655\) 15.3693 0.600529
\(656\) 0 0
\(657\) −10.8078 −0.421651
\(658\) 0 0
\(659\) 30.7386 1.19741 0.598704 0.800971i \(-0.295683\pi\)
0.598704 + 0.800971i \(0.295683\pi\)
\(660\) 0 0
\(661\) 26.4924 1.03044 0.515218 0.857059i \(-0.327711\pi\)
0.515218 + 0.857059i \(0.327711\pi\)
\(662\) 0 0
\(663\) −6.24621 −0.242583
\(664\) 0 0
\(665\) −19.6847 −0.763338
\(666\) 0 0
\(667\) −10.2462 −0.396735
\(668\) 0 0
\(669\) 21.1231 0.816666
\(670\) 0 0
\(671\) −15.3693 −0.593326
\(672\) 0 0
\(673\) 11.7538 0.453075 0.226538 0.974002i \(-0.427259\pi\)
0.226538 + 0.974002i \(0.427259\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 32.4233 1.24613 0.623064 0.782171i \(-0.285888\pi\)
0.623064 + 0.782171i \(0.285888\pi\)
\(678\) 0 0
\(679\) 15.3693 0.589820
\(680\) 0 0
\(681\) −7.68466 −0.294477
\(682\) 0 0
\(683\) −31.6847 −1.21238 −0.606190 0.795320i \(-0.707303\pi\)
−0.606190 + 0.795320i \(0.707303\pi\)
\(684\) 0 0
\(685\) 20.2462 0.773568
\(686\) 0 0
\(687\) −16.5616 −0.631863
\(688\) 0 0
\(689\) 14.8769 0.566765
\(690\) 0 0
\(691\) −15.0540 −0.572680 −0.286340 0.958128i \(-0.592439\pi\)
−0.286340 + 0.958128i \(0.592439\pi\)
\(692\) 0 0
\(693\) 6.56155 0.249253
\(694\) 0 0
\(695\) 17.1231 0.649516
\(696\) 0 0
\(697\) −22.2462 −0.842635
\(698\) 0 0
\(699\) −17.0540 −0.645041
\(700\) 0 0
\(701\) 5.19224 0.196108 0.0980540 0.995181i \(-0.468738\pi\)
0.0980540 + 0.995181i \(0.468738\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 0 0
\(705\) −5.12311 −0.192947
\(706\) 0 0
\(707\) 1.43845 0.0540984
\(708\) 0 0
\(709\) 17.0540 0.640475 0.320238 0.947337i \(-0.396237\pi\)
0.320238 + 0.947337i \(0.396237\pi\)
\(710\) 0 0
\(711\) 4.31534 0.161838
\(712\) 0 0
\(713\) 1.43845 0.0538703
\(714\) 0 0
\(715\) −5.12311 −0.191593
\(716\) 0 0
\(717\) −24.0000 −0.896296
\(718\) 0 0
\(719\) 34.8769 1.30069 0.650344 0.759640i \(-0.274625\pi\)
0.650344 + 0.759640i \(0.274625\pi\)
\(720\) 0 0
\(721\) −4.49242 −0.167307
\(722\) 0 0
\(723\) 12.2462 0.455441
\(724\) 0 0
\(725\) 7.12311 0.264546
\(726\) 0 0
\(727\) −23.0540 −0.855025 −0.427512 0.904010i \(-0.640610\pi\)
−0.427512 + 0.904010i \(0.640610\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 40.0000 1.47945
\(732\) 0 0
\(733\) −6.49242 −0.239803 −0.119902 0.992786i \(-0.538258\pi\)
−0.119902 + 0.992786i \(0.538258\pi\)
\(734\) 0 0
\(735\) −0.438447 −0.0161724
\(736\) 0 0
\(737\) −39.3693 −1.45019
\(738\) 0 0
\(739\) −52.9848 −1.94908 −0.974540 0.224216i \(-0.928018\pi\)
−0.974540 + 0.224216i \(0.928018\pi\)
\(740\) 0 0
\(741\) 15.3693 0.564606
\(742\) 0 0
\(743\) 50.4233 1.84985 0.924926 0.380148i \(-0.124127\pi\)
0.924926 + 0.380148i \(0.124127\pi\)
\(744\) 0 0
\(745\) 17.0540 0.624809
\(746\) 0 0
\(747\) −14.2462 −0.521242
\(748\) 0 0
\(749\) −6.56155 −0.239754
\(750\) 0 0
\(751\) −45.1231 −1.64657 −0.823283 0.567631i \(-0.807860\pi\)
−0.823283 + 0.567631i \(0.807860\pi\)
\(752\) 0 0
\(753\) −16.4924 −0.601017
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 3.68466 0.133745
\(760\) 0 0
\(761\) −20.4233 −0.740344 −0.370172 0.928963i \(-0.620701\pi\)
−0.370172 + 0.928963i \(0.620701\pi\)
\(762\) 0 0
\(763\) −13.7538 −0.497921
\(764\) 0 0
\(765\) −3.12311 −0.112916
\(766\) 0 0
\(767\) 26.2462 0.947696
\(768\) 0 0
\(769\) −20.5616 −0.741469 −0.370734 0.928739i \(-0.620894\pi\)
−0.370734 + 0.928739i \(0.620894\pi\)
\(770\) 0 0
\(771\) −1.68466 −0.0606715
\(772\) 0 0
\(773\) −11.4384 −0.411412 −0.205706 0.978614i \(-0.565949\pi\)
−0.205706 + 0.978614i \(0.565949\pi\)
\(774\) 0 0
\(775\) −1.00000 −0.0359211
\(776\) 0 0
\(777\) 8.00000 0.286998
\(778\) 0 0
\(779\) 54.7386 1.96122
\(780\) 0 0
\(781\) −19.6847 −0.704372
\(782\) 0 0
\(783\) 7.12311 0.254559
\(784\) 0 0
\(785\) 17.0540 0.608682
\(786\) 0 0
\(787\) 17.9309 0.639166 0.319583 0.947558i \(-0.396457\pi\)
0.319583 + 0.947558i \(0.396457\pi\)
\(788\) 0 0
\(789\) 20.4924 0.729550
\(790\) 0 0
\(791\) 4.31534 0.153436
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) 0 0
\(795\) 7.43845 0.263815
\(796\) 0 0
\(797\) −26.9848 −0.955852 −0.477926 0.878400i \(-0.658611\pi\)
−0.477926 + 0.878400i \(0.658611\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) −13.6847 −0.483524
\(802\) 0 0
\(803\) 27.6847 0.976970
\(804\) 0 0
\(805\) 3.68466 0.129867
\(806\) 0 0
\(807\) −0.246211 −0.00866705
\(808\) 0 0
\(809\) −37.6847 −1.32492 −0.662461 0.749096i \(-0.730488\pi\)
−0.662461 + 0.749096i \(0.730488\pi\)
\(810\) 0 0
\(811\) 24.6695 0.866263 0.433132 0.901331i \(-0.357408\pi\)
0.433132 + 0.901331i \(0.357408\pi\)
\(812\) 0 0
\(813\) −27.0540 −0.948824
\(814\) 0 0
\(815\) 15.3693 0.538364
\(816\) 0 0
\(817\) −98.4233 −3.44340
\(818\) 0 0
\(819\) −5.12311 −0.179016
\(820\) 0 0
\(821\) 19.6155 0.684587 0.342293 0.939593i \(-0.388796\pi\)
0.342293 + 0.939593i \(0.388796\pi\)
\(822\) 0 0
\(823\) 25.6155 0.892901 0.446451 0.894808i \(-0.352688\pi\)
0.446451 + 0.894808i \(0.352688\pi\)
\(824\) 0 0
\(825\) −2.56155 −0.0891818
\(826\) 0 0
\(827\) −1.75379 −0.0609852 −0.0304926 0.999535i \(-0.509708\pi\)
−0.0304926 + 0.999535i \(0.509708\pi\)
\(828\) 0 0
\(829\) 24.4233 0.848256 0.424128 0.905602i \(-0.360581\pi\)
0.424128 + 0.905602i \(0.360581\pi\)
\(830\) 0 0
\(831\) −5.36932 −0.186260
\(832\) 0 0
\(833\) 1.36932 0.0474440
\(834\) 0 0
\(835\) 6.56155 0.227072
\(836\) 0 0
\(837\) −1.00000 −0.0345651
\(838\) 0 0
\(839\) −6.06913 −0.209530 −0.104765 0.994497i \(-0.533409\pi\)
−0.104765 + 0.994497i \(0.533409\pi\)
\(840\) 0 0
\(841\) 21.7386 0.749608
\(842\) 0 0
\(843\) 4.87689 0.167969
\(844\) 0 0
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) 11.3693 0.390654
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.49242 0.153998
\(852\) 0 0
\(853\) 47.7926 1.63639 0.818194 0.574942i \(-0.194976\pi\)
0.818194 + 0.574942i \(0.194976\pi\)
\(854\) 0 0
\(855\) 7.68466 0.262810
\(856\) 0 0
\(857\) 29.2311 0.998514 0.499257 0.866454i \(-0.333606\pi\)
0.499257 + 0.866454i \(0.333606\pi\)
\(858\) 0 0
\(859\) −26.7386 −0.912310 −0.456155 0.889900i \(-0.650774\pi\)
−0.456155 + 0.889900i \(0.650774\pi\)
\(860\) 0 0
\(861\) −18.2462 −0.621829
\(862\) 0 0
\(863\) −39.5464 −1.34618 −0.673088 0.739563i \(-0.735032\pi\)
−0.673088 + 0.739563i \(0.735032\pi\)
\(864\) 0 0
\(865\) 8.24621 0.280380
\(866\) 0 0
\(867\) −7.24621 −0.246094
\(868\) 0 0
\(869\) −11.0540 −0.374980
\(870\) 0 0
\(871\) 30.7386 1.04154
\(872\) 0 0
\(873\) −6.00000 −0.203069
\(874\) 0 0
\(875\) −2.56155 −0.0865963
\(876\) 0 0
\(877\) −50.0000 −1.68838 −0.844190 0.536044i \(-0.819918\pi\)
−0.844190 + 0.536044i \(0.819918\pi\)
\(878\) 0 0
\(879\) 26.4924 0.893567
\(880\) 0 0
\(881\) 9.50758 0.320318 0.160159 0.987091i \(-0.448799\pi\)
0.160159 + 0.987091i \(0.448799\pi\)
\(882\) 0 0
\(883\) −30.4233 −1.02383 −0.511913 0.859038i \(-0.671063\pi\)
−0.511913 + 0.859038i \(0.671063\pi\)
\(884\) 0 0
\(885\) 13.1231 0.441128
\(886\) 0 0
\(887\) 32.6307 1.09563 0.547816 0.836599i \(-0.315460\pi\)
0.547816 + 0.836599i \(0.315460\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −2.56155 −0.0858152
\(892\) 0 0
\(893\) −39.3693 −1.31744
\(894\) 0 0
\(895\) 12.0000 0.401116
\(896\) 0 0
\(897\) −2.87689 −0.0960567
\(898\) 0 0
\(899\) −7.12311 −0.237569
\(900\) 0 0
\(901\) −23.2311 −0.773939
\(902\) 0 0
\(903\) 32.8078 1.09177
\(904\) 0 0
\(905\) −13.0540 −0.433929
\(906\) 0 0
\(907\) −24.0000 −0.796907 −0.398453 0.917189i \(-0.630453\pi\)
−0.398453 + 0.917189i \(0.630453\pi\)
\(908\) 0 0
\(909\) −0.561553 −0.0186255
\(910\) 0 0
\(911\) 11.5076 0.381263 0.190632 0.981662i \(-0.438946\pi\)
0.190632 + 0.981662i \(0.438946\pi\)
\(912\) 0 0
\(913\) 36.4924 1.20772
\(914\) 0 0
\(915\) 6.00000 0.198354
\(916\) 0 0
\(917\) −39.3693 −1.30009
\(918\) 0 0
\(919\) 1.61553 0.0532914 0.0266457 0.999645i \(-0.491517\pi\)
0.0266457 + 0.999645i \(0.491517\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 15.3693 0.505887
\(924\) 0 0
\(925\) −3.12311 −0.102687
\(926\) 0 0
\(927\) 1.75379 0.0576020
\(928\) 0 0
\(929\) 7.43845 0.244048 0.122024 0.992527i \(-0.461062\pi\)
0.122024 + 0.992527i \(0.461062\pi\)
\(930\) 0 0
\(931\) −3.36932 −0.110425
\(932\) 0 0
\(933\) 1.75379 0.0574165
\(934\) 0 0
\(935\) 8.00000 0.261628
\(936\) 0 0
\(937\) 41.3693 1.35148 0.675738 0.737142i \(-0.263825\pi\)
0.675738 + 0.737142i \(0.263825\pi\)
\(938\) 0 0
\(939\) −10.0000 −0.326338
\(940\) 0 0
\(941\) 2.63068 0.0857578 0.0428789 0.999080i \(-0.486347\pi\)
0.0428789 + 0.999080i \(0.486347\pi\)
\(942\) 0 0
\(943\) −10.2462 −0.333663
\(944\) 0 0
\(945\) −2.56155 −0.0833273
\(946\) 0 0
\(947\) 9.12311 0.296461 0.148231 0.988953i \(-0.452642\pi\)
0.148231 + 0.988953i \(0.452642\pi\)
\(948\) 0 0
\(949\) −21.6155 −0.701670
\(950\) 0 0
\(951\) 16.8769 0.547271
\(952\) 0 0
\(953\) 16.1080 0.521788 0.260894 0.965367i \(-0.415983\pi\)
0.260894 + 0.965367i \(0.415983\pi\)
\(954\) 0 0
\(955\) 14.2462 0.460997
\(956\) 0 0
\(957\) −18.2462 −0.589816
\(958\) 0 0
\(959\) −51.8617 −1.67470
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) 0 0
\(963\) 2.56155 0.0825449
\(964\) 0 0
\(965\) 14.4924 0.466528
\(966\) 0 0
\(967\) 42.2462 1.35855 0.679273 0.733885i \(-0.262295\pi\)
0.679273 + 0.733885i \(0.262295\pi\)
\(968\) 0 0
\(969\) −24.0000 −0.770991
\(970\) 0 0
\(971\) 37.1231 1.19134 0.595669 0.803230i \(-0.296887\pi\)
0.595669 + 0.803230i \(0.296887\pi\)
\(972\) 0 0
\(973\) −43.8617 −1.40614
\(974\) 0 0
\(975\) 2.00000 0.0640513
\(976\) 0 0
\(977\) 42.9848 1.37521 0.687604 0.726086i \(-0.258663\pi\)
0.687604 + 0.726086i \(0.258663\pi\)
\(978\) 0 0
\(979\) 35.0540 1.12033
\(980\) 0 0
\(981\) 5.36932 0.171429
\(982\) 0 0
\(983\) −40.9848 −1.30721 −0.653607 0.756834i \(-0.726745\pi\)
−0.653607 + 0.756834i \(0.726745\pi\)
\(984\) 0 0
\(985\) 6.00000 0.191176
\(986\) 0 0
\(987\) 13.1231 0.417713
\(988\) 0 0
\(989\) 18.4233 0.585827
\(990\) 0 0
\(991\) −35.6847 −1.13356 −0.566780 0.823869i \(-0.691811\pi\)
−0.566780 + 0.823869i \(0.691811\pi\)
\(992\) 0 0
\(993\) 6.24621 0.198218
\(994\) 0 0
\(995\) 16.8078 0.532842
\(996\) 0 0
\(997\) −29.5076 −0.934514 −0.467257 0.884121i \(-0.654758\pi\)
−0.467257 + 0.884121i \(0.654758\pi\)
\(998\) 0 0
\(999\) −3.12311 −0.0988107
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 7440.2.a.bl.1.1 2
4.3 odd 2 930.2.a.p.1.2 2
12.11 even 2 2790.2.a.be.1.2 2
20.3 even 4 4650.2.d.bd.3349.1 4
20.7 even 4 4650.2.d.bd.3349.4 4
20.19 odd 2 4650.2.a.ce.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.p.1.2 2 4.3 odd 2
2790.2.a.be.1.2 2 12.11 even 2
4650.2.a.ce.1.1 2 20.19 odd 2
4650.2.d.bd.3349.1 4 20.3 even 4
4650.2.d.bd.3349.4 4 20.7 even 4
7440.2.a.bl.1.1 2 1.1 even 1 trivial