Properties

Label 7360.2.a.cl.1.3
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.7698958877\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.876604.1
Defining polynomial: \( x^{5} - x^{4} - 9x^{3} + 8x^{2} + 18x - 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 3680)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.60527\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.352411 q^{3} -1.00000 q^{5} +3.95190 q^{7} -2.87581 q^{9} +O(q^{10})\) \(q+0.352411 q^{3} -1.00000 q^{5} +3.95190 q^{7} -2.87581 q^{9} -5.63905 q^{11} -2.53457 q^{13} -0.352411 q^{15} +1.26403 q^{17} +6.83349 q^{19} +1.39270 q^{21} -1.00000 q^{23} +1.00000 q^{25} -2.07070 q^{27} -7.69701 q^{29} +9.04028 q^{31} -1.98726 q^{33} -3.95190 q^{35} +2.90308 q^{37} -0.893211 q^{39} +0.188663 q^{41} +2.97692 q^{43} +2.87581 q^{45} +4.82698 q^{47} +8.61755 q^{49} +0.445459 q^{51} -0.328956 q^{53} +5.63905 q^{55} +2.40820 q^{57} -0.966221 q^{59} -1.31009 q^{61} -11.3649 q^{63} +2.53457 q^{65} +3.94987 q^{67} -0.352411 q^{69} -7.69365 q^{71} +0.617173 q^{73} +0.352411 q^{75} -22.2850 q^{77} -15.1828 q^{79} +7.89768 q^{81} -1.30673 q^{83} -1.26403 q^{85} -2.71251 q^{87} -17.3242 q^{89} -10.0164 q^{91} +3.18590 q^{93} -6.83349 q^{95} +8.26476 q^{97} +16.2168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - q^{3} - 5 q^{5} + q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - q^{3} - 5 q^{5} + q^{7} + 6 q^{9} - 3 q^{11} - 7 q^{13} + q^{15} + 9 q^{17} - q^{19} - 20 q^{21} - 5 q^{23} + 5 q^{25} - 4 q^{27} + 10 q^{29} + 21 q^{31} + 7 q^{33} - q^{35} - 8 q^{37} - 24 q^{39} - 13 q^{41} + 6 q^{43} - 6 q^{45} + 24 q^{49} + 17 q^{51} + 6 q^{53} + 3 q^{55} + 26 q^{57} - 18 q^{59} + 11 q^{61} + 4 q^{63} + 7 q^{65} - 38 q^{67} + q^{69} - 21 q^{71} - 12 q^{73} - q^{75} - 46 q^{77} - 18 q^{79} + 9 q^{81} - 20 q^{83} - 9 q^{85} - 6 q^{87} - 16 q^{89} + 3 q^{91} - 22 q^{93} + q^{95} + 29 q^{97} - 29 q^{99}+O(q^{100}) \) 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
\(3\) 0.352411 0.203465 0.101732 0.994812i \(-0.467561\pi\)
0.101732 + 0.994812i \(0.467561\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.95190 1.49368 0.746840 0.665004i \(-0.231570\pi\)
0.746840 + 0.665004i \(0.231570\pi\)
\(8\) 0 0
\(9\) −2.87581 −0.958602
\(10\) 0 0
\(11\) −5.63905 −1.70024 −0.850118 0.526592i \(-0.823470\pi\)
−0.850118 + 0.526592i \(0.823470\pi\)
\(12\) 0 0
\(13\) −2.53457 −0.702963 −0.351481 0.936195i \(-0.614322\pi\)
−0.351481 + 0.936195i \(0.614322\pi\)
\(14\) 0 0
\(15\) −0.352411 −0.0909922
\(16\) 0 0
\(17\) 1.26403 0.306573 0.153286 0.988182i \(-0.451014\pi\)
0.153286 + 0.988182i \(0.451014\pi\)
\(18\) 0 0
\(19\) 6.83349 1.56771 0.783855 0.620944i \(-0.213251\pi\)
0.783855 + 0.620944i \(0.213251\pi\)
\(20\) 0 0
\(21\) 1.39270 0.303911
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −2.07070 −0.398506
\(28\) 0 0
\(29\) −7.69701 −1.42930 −0.714650 0.699483i \(-0.753414\pi\)
−0.714650 + 0.699483i \(0.753414\pi\)
\(30\) 0 0
\(31\) 9.04028 1.62368 0.811842 0.583878i \(-0.198465\pi\)
0.811842 + 0.583878i \(0.198465\pi\)
\(32\) 0 0
\(33\) −1.98726 −0.345938
\(34\) 0 0
\(35\) −3.95190 −0.667994
\(36\) 0 0
\(37\) 2.90308 0.477263 0.238632 0.971110i \(-0.423301\pi\)
0.238632 + 0.971110i \(0.423301\pi\)
\(38\) 0 0
\(39\) −0.893211 −0.143028
\(40\) 0 0
\(41\) 0.188663 0.0294643 0.0147321 0.999891i \(-0.495310\pi\)
0.0147321 + 0.999891i \(0.495310\pi\)
\(42\) 0 0
\(43\) 2.97692 0.453976 0.226988 0.973898i \(-0.427112\pi\)
0.226988 + 0.973898i \(0.427112\pi\)
\(44\) 0 0
\(45\) 2.87581 0.428700
\(46\) 0 0
\(47\) 4.82698 0.704088 0.352044 0.935984i \(-0.385487\pi\)
0.352044 + 0.935984i \(0.385487\pi\)
\(48\) 0 0
\(49\) 8.61755 1.23108
\(50\) 0 0
\(51\) 0.445459 0.0623767
\(52\) 0 0
\(53\) −0.328956 −0.0451856 −0.0225928 0.999745i \(-0.507192\pi\)
−0.0225928 + 0.999745i \(0.507192\pi\)
\(54\) 0 0
\(55\) 5.63905 0.760369
\(56\) 0 0
\(57\) 2.40820 0.318974
\(58\) 0 0
\(59\) −0.966221 −0.125791 −0.0628957 0.998020i \(-0.520034\pi\)
−0.0628957 + 0.998020i \(0.520034\pi\)
\(60\) 0 0
\(61\) −1.31009 −0.167740 −0.0838700 0.996477i \(-0.526728\pi\)
−0.0838700 + 0.996477i \(0.526728\pi\)
\(62\) 0 0
\(63\) −11.3649 −1.43184
\(64\) 0 0
\(65\) 2.53457 0.314375
\(66\) 0 0
\(67\) 3.94987 0.482553 0.241277 0.970456i \(-0.422434\pi\)
0.241277 + 0.970456i \(0.422434\pi\)
\(68\) 0 0
\(69\) −0.352411 −0.0424253
\(70\) 0 0
\(71\) −7.69365 −0.913068 −0.456534 0.889706i \(-0.650909\pi\)
−0.456534 + 0.889706i \(0.650909\pi\)
\(72\) 0 0
\(73\) 0.617173 0.0722346 0.0361173 0.999348i \(-0.488501\pi\)
0.0361173 + 0.999348i \(0.488501\pi\)
\(74\) 0 0
\(75\) 0.352411 0.0406929
\(76\) 0 0
\(77\) −22.2850 −2.53961
\(78\) 0 0
\(79\) −15.1828 −1.70819 −0.854097 0.520114i \(-0.825889\pi\)
−0.854097 + 0.520114i \(0.825889\pi\)
\(80\) 0 0
\(81\) 7.89768 0.877520
\(82\) 0 0
\(83\) −1.30673 −0.143432 −0.0717161 0.997425i \(-0.522848\pi\)
−0.0717161 + 0.997425i \(0.522848\pi\)
\(84\) 0 0
\(85\) −1.26403 −0.137103
\(86\) 0 0
\(87\) −2.71251 −0.290812
\(88\) 0 0
\(89\) −17.3242 −1.83636 −0.918178 0.396167i \(-0.870340\pi\)
−0.918178 + 0.396167i \(0.870340\pi\)
\(90\) 0 0
\(91\) −10.0164 −1.05000
\(92\) 0 0
\(93\) 3.18590 0.330362
\(94\) 0 0
\(95\) −6.83349 −0.701101
\(96\) 0 0
\(97\) 8.26476 0.839159 0.419580 0.907718i \(-0.362177\pi\)
0.419580 + 0.907718i \(0.362177\pi\)
\(98\) 0 0
\(99\) 16.2168 1.62985
\(100\) 0 0
\(101\) −17.8545 −1.77659 −0.888296 0.459271i \(-0.848111\pi\)
−0.888296 + 0.459271i \(0.848111\pi\)
\(102\) 0 0
\(103\) −18.0624 −1.77974 −0.889872 0.456210i \(-0.849207\pi\)
−0.889872 + 0.456210i \(0.849207\pi\)
\(104\) 0 0
\(105\) −1.39270 −0.135913
\(106\) 0 0
\(107\) 12.7747 1.23498 0.617488 0.786580i \(-0.288150\pi\)
0.617488 + 0.786580i \(0.288150\pi\)
\(108\) 0 0
\(109\) −14.7596 −1.41372 −0.706859 0.707355i \(-0.749888\pi\)
−0.706859 + 0.707355i \(0.749888\pi\)
\(110\) 0 0
\(111\) 1.02308 0.0971062
\(112\) 0 0
\(113\) −9.11666 −0.857623 −0.428812 0.903394i \(-0.641068\pi\)
−0.428812 + 0.903394i \(0.641068\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 7.28893 0.673862
\(118\) 0 0
\(119\) 4.99533 0.457921
\(120\) 0 0
\(121\) 20.7989 1.89081
\(122\) 0 0
\(123\) 0.0664871 0.00599494
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 3.87377 0.343742 0.171871 0.985120i \(-0.445019\pi\)
0.171871 + 0.985120i \(0.445019\pi\)
\(128\) 0 0
\(129\) 1.04910 0.0923682
\(130\) 0 0
\(131\) −2.55488 −0.223221 −0.111610 0.993752i \(-0.535601\pi\)
−0.111610 + 0.993752i \(0.535601\pi\)
\(132\) 0 0
\(133\) 27.0053 2.34166
\(134\) 0 0
\(135\) 2.07070 0.178217
\(136\) 0 0
\(137\) 3.37778 0.288583 0.144292 0.989535i \(-0.453910\pi\)
0.144292 + 0.989535i \(0.453910\pi\)
\(138\) 0 0
\(139\) −1.41965 −0.120413 −0.0602064 0.998186i \(-0.519176\pi\)
−0.0602064 + 0.998186i \(0.519176\pi\)
\(140\) 0 0
\(141\) 1.70108 0.143257
\(142\) 0 0
\(143\) 14.2926 1.19520
\(144\) 0 0
\(145\) 7.69701 0.639202
\(146\) 0 0
\(147\) 3.03692 0.250481
\(148\) 0 0
\(149\) −13.3961 −1.09745 −0.548724 0.836004i \(-0.684886\pi\)
−0.548724 + 0.836004i \(0.684886\pi\)
\(150\) 0 0
\(151\) −13.6090 −1.10749 −0.553743 0.832688i \(-0.686801\pi\)
−0.553743 + 0.832688i \(0.686801\pi\)
\(152\) 0 0
\(153\) −3.63511 −0.293881
\(154\) 0 0
\(155\) −9.04028 −0.726133
\(156\) 0 0
\(157\) −19.8029 −1.58045 −0.790223 0.612819i \(-0.790035\pi\)
−0.790223 + 0.612819i \(0.790035\pi\)
\(158\) 0 0
\(159\) −0.115928 −0.00919367
\(160\) 0 0
\(161\) −3.95190 −0.311454
\(162\) 0 0
\(163\) −20.4606 −1.60260 −0.801300 0.598263i \(-0.795858\pi\)
−0.801300 + 0.598263i \(0.795858\pi\)
\(164\) 0 0
\(165\) 1.98726 0.154708
\(166\) 0 0
\(167\) −20.1227 −1.55714 −0.778569 0.627559i \(-0.784054\pi\)
−0.778569 + 0.627559i \(0.784054\pi\)
\(168\) 0 0
\(169\) −6.57596 −0.505843
\(170\) 0 0
\(171\) −19.6518 −1.50281
\(172\) 0 0
\(173\) −24.2937 −1.84702 −0.923509 0.383576i \(-0.874692\pi\)
−0.923509 + 0.383576i \(0.874692\pi\)
\(174\) 0 0
\(175\) 3.95190 0.298736
\(176\) 0 0
\(177\) −0.340507 −0.0255941
\(178\) 0 0
\(179\) −15.3672 −1.14860 −0.574299 0.818645i \(-0.694725\pi\)
−0.574299 + 0.818645i \(0.694725\pi\)
\(180\) 0 0
\(181\) 14.0440 1.04388 0.521942 0.852981i \(-0.325208\pi\)
0.521942 + 0.852981i \(0.325208\pi\)
\(182\) 0 0
\(183\) −0.461691 −0.0341292
\(184\) 0 0
\(185\) −2.90308 −0.213439
\(186\) 0 0
\(187\) −7.12793 −0.521246
\(188\) 0 0
\(189\) −8.18321 −0.595241
\(190\) 0 0
\(191\) 2.51098 0.181688 0.0908441 0.995865i \(-0.471044\pi\)
0.0908441 + 0.995865i \(0.471044\pi\)
\(192\) 0 0
\(193\) 18.6016 1.33897 0.669484 0.742826i \(-0.266515\pi\)
0.669484 + 0.742826i \(0.266515\pi\)
\(194\) 0 0
\(195\) 0.893211 0.0639641
\(196\) 0 0
\(197\) 17.8033 1.26843 0.634216 0.773156i \(-0.281323\pi\)
0.634216 + 0.773156i \(0.281323\pi\)
\(198\) 0 0
\(199\) 9.14740 0.648442 0.324221 0.945981i \(-0.394898\pi\)
0.324221 + 0.945981i \(0.394898\pi\)
\(200\) 0 0
\(201\) 1.39198 0.0981826
\(202\) 0 0
\(203\) −30.4179 −2.13491
\(204\) 0 0
\(205\) −0.188663 −0.0131768
\(206\) 0 0
\(207\) 2.87581 0.199882
\(208\) 0 0
\(209\) −38.5344 −2.66548
\(210\) 0 0
\(211\) −18.6161 −1.28159 −0.640793 0.767714i \(-0.721394\pi\)
−0.640793 + 0.767714i \(0.721394\pi\)
\(212\) 0 0
\(213\) −2.71133 −0.185777
\(214\) 0 0
\(215\) −2.97692 −0.203024
\(216\) 0 0
\(217\) 35.7263 2.42526
\(218\) 0 0
\(219\) 0.217499 0.0146972
\(220\) 0 0
\(221\) −3.20377 −0.215509
\(222\) 0 0
\(223\) 15.7475 1.05453 0.527267 0.849700i \(-0.323217\pi\)
0.527267 + 0.849700i \(0.323217\pi\)
\(224\) 0 0
\(225\) −2.87581 −0.191720
\(226\) 0 0
\(227\) 1.28041 0.0849835 0.0424918 0.999097i \(-0.486470\pi\)
0.0424918 + 0.999097i \(0.486470\pi\)
\(228\) 0 0
\(229\) 0.257424 0.0170110 0.00850552 0.999964i \(-0.497293\pi\)
0.00850552 + 0.999964i \(0.497293\pi\)
\(230\) 0 0
\(231\) −7.85348 −0.516721
\(232\) 0 0
\(233\) 12.2036 0.799483 0.399741 0.916628i \(-0.369100\pi\)
0.399741 + 0.916628i \(0.369100\pi\)
\(234\) 0 0
\(235\) −4.82698 −0.314878
\(236\) 0 0
\(237\) −5.35057 −0.347557
\(238\) 0 0
\(239\) −7.31120 −0.472922 −0.236461 0.971641i \(-0.575988\pi\)
−0.236461 + 0.971641i \(0.575988\pi\)
\(240\) 0 0
\(241\) −11.7293 −0.755548 −0.377774 0.925898i \(-0.623310\pi\)
−0.377774 + 0.925898i \(0.623310\pi\)
\(242\) 0 0
\(243\) 8.99533 0.577051
\(244\) 0 0
\(245\) −8.61755 −0.550555
\(246\) 0 0
\(247\) −17.3199 −1.10204
\(248\) 0 0
\(249\) −0.460506 −0.0291834
\(250\) 0 0
\(251\) 6.21099 0.392034 0.196017 0.980600i \(-0.437199\pi\)
0.196017 + 0.980600i \(0.437199\pi\)
\(252\) 0 0
\(253\) 5.63905 0.354524
\(254\) 0 0
\(255\) −0.445459 −0.0278957
\(256\) 0 0
\(257\) 27.0382 1.68660 0.843300 0.537443i \(-0.180610\pi\)
0.843300 + 0.537443i \(0.180610\pi\)
\(258\) 0 0
\(259\) 11.4727 0.712878
\(260\) 0 0
\(261\) 22.1351 1.37013
\(262\) 0 0
\(263\) −22.3100 −1.37569 −0.687846 0.725857i \(-0.741444\pi\)
−0.687846 + 0.725857i \(0.741444\pi\)
\(264\) 0 0
\(265\) 0.328956 0.0202076
\(266\) 0 0
\(267\) −6.10523 −0.373634
\(268\) 0 0
\(269\) 14.2720 0.870178 0.435089 0.900387i \(-0.356717\pi\)
0.435089 + 0.900387i \(0.356717\pi\)
\(270\) 0 0
\(271\) −18.0785 −1.09819 −0.549096 0.835759i \(-0.685028\pi\)
−0.549096 + 0.835759i \(0.685028\pi\)
\(272\) 0 0
\(273\) −3.52988 −0.213638
\(274\) 0 0
\(275\) −5.63905 −0.340047
\(276\) 0 0
\(277\) −4.97476 −0.298905 −0.149452 0.988769i \(-0.547751\pi\)
−0.149452 + 0.988769i \(0.547751\pi\)
\(278\) 0 0
\(279\) −25.9981 −1.55647
\(280\) 0 0
\(281\) −5.15895 −0.307757 −0.153878 0.988090i \(-0.549176\pi\)
−0.153878 + 0.988090i \(0.549176\pi\)
\(282\) 0 0
\(283\) −11.8800 −0.706193 −0.353096 0.935587i \(-0.614871\pi\)
−0.353096 + 0.935587i \(0.614871\pi\)
\(284\) 0 0
\(285\) −2.40820 −0.142649
\(286\) 0 0
\(287\) 0.745580 0.0440102
\(288\) 0 0
\(289\) −15.4022 −0.906013
\(290\) 0 0
\(291\) 2.91259 0.170739
\(292\) 0 0
\(293\) 24.0075 1.40253 0.701266 0.712900i \(-0.252619\pi\)
0.701266 + 0.712900i \(0.252619\pi\)
\(294\) 0 0
\(295\) 0.966221 0.0562556
\(296\) 0 0
\(297\) 11.6768 0.677555
\(298\) 0 0
\(299\) 2.53457 0.146578
\(300\) 0 0
\(301\) 11.7645 0.678095
\(302\) 0 0
\(303\) −6.29214 −0.361474
\(304\) 0 0
\(305\) 1.31009 0.0750156
\(306\) 0 0
\(307\) −20.8389 −1.18934 −0.594669 0.803971i \(-0.702717\pi\)
−0.594669 + 0.803971i \(0.702717\pi\)
\(308\) 0 0
\(309\) −6.36540 −0.362115
\(310\) 0 0
\(311\) 23.6092 1.33875 0.669376 0.742924i \(-0.266562\pi\)
0.669376 + 0.742924i \(0.266562\pi\)
\(312\) 0 0
\(313\) 15.7933 0.892692 0.446346 0.894861i \(-0.352725\pi\)
0.446346 + 0.894861i \(0.352725\pi\)
\(314\) 0 0
\(315\) 11.3649 0.640340
\(316\) 0 0
\(317\) 32.3058 1.81447 0.907236 0.420621i \(-0.138188\pi\)
0.907236 + 0.420621i \(0.138188\pi\)
\(318\) 0 0
\(319\) 43.4038 2.43015
\(320\) 0 0
\(321\) 4.50194 0.251274
\(322\) 0 0
\(323\) 8.63774 0.480617
\(324\) 0 0
\(325\) −2.53457 −0.140593
\(326\) 0 0
\(327\) −5.20146 −0.287642
\(328\) 0 0
\(329\) 19.0758 1.05168
\(330\) 0 0
\(331\) 14.4140 0.792265 0.396132 0.918193i \(-0.370352\pi\)
0.396132 + 0.918193i \(0.370352\pi\)
\(332\) 0 0
\(333\) −8.34869 −0.457506
\(334\) 0 0
\(335\) −3.94987 −0.215804
\(336\) 0 0
\(337\) 9.34929 0.509288 0.254644 0.967035i \(-0.418042\pi\)
0.254644 + 0.967035i \(0.418042\pi\)
\(338\) 0 0
\(339\) −3.21281 −0.174496
\(340\) 0 0
\(341\) −50.9786 −2.76065
\(342\) 0 0
\(343\) 6.39240 0.345157
\(344\) 0 0
\(345\) 0.352411 0.0189732
\(346\) 0 0
\(347\) −1.13655 −0.0610133 −0.0305067 0.999535i \(-0.509712\pi\)
−0.0305067 + 0.999535i \(0.509712\pi\)
\(348\) 0 0
\(349\) 8.75535 0.468663 0.234332 0.972157i \(-0.424710\pi\)
0.234332 + 0.972157i \(0.424710\pi\)
\(350\) 0 0
\(351\) 5.24833 0.280135
\(352\) 0 0
\(353\) 22.1257 1.17763 0.588815 0.808268i \(-0.299595\pi\)
0.588815 + 0.808268i \(0.299595\pi\)
\(354\) 0 0
\(355\) 7.69365 0.408336
\(356\) 0 0
\(357\) 1.76041 0.0931708
\(358\) 0 0
\(359\) 8.55850 0.451700 0.225850 0.974162i \(-0.427484\pi\)
0.225850 + 0.974162i \(0.427484\pi\)
\(360\) 0 0
\(361\) 27.6965 1.45771
\(362\) 0 0
\(363\) 7.32975 0.384712
\(364\) 0 0
\(365\) −0.617173 −0.0323043
\(366\) 0 0
\(367\) −12.4672 −0.650784 −0.325392 0.945579i \(-0.605496\pi\)
−0.325392 + 0.945579i \(0.605496\pi\)
\(368\) 0 0
\(369\) −0.542559 −0.0282445
\(370\) 0 0
\(371\) −1.30000 −0.0674928
\(372\) 0 0
\(373\) −17.6684 −0.914837 −0.457418 0.889252i \(-0.651226\pi\)
−0.457418 + 0.889252i \(0.651226\pi\)
\(374\) 0 0
\(375\) −0.352411 −0.0181984
\(376\) 0 0
\(377\) 19.5086 1.00474
\(378\) 0 0
\(379\) −6.67680 −0.342964 −0.171482 0.985187i \(-0.554856\pi\)
−0.171482 + 0.985187i \(0.554856\pi\)
\(380\) 0 0
\(381\) 1.36516 0.0699393
\(382\) 0 0
\(383\) −4.27134 −0.218256 −0.109128 0.994028i \(-0.534806\pi\)
−0.109128 + 0.994028i \(0.534806\pi\)
\(384\) 0 0
\(385\) 22.2850 1.13575
\(386\) 0 0
\(387\) −8.56105 −0.435183
\(388\) 0 0
\(389\) 14.4378 0.732023 0.366011 0.930610i \(-0.380723\pi\)
0.366011 + 0.930610i \(0.380723\pi\)
\(390\) 0 0
\(391\) −1.26403 −0.0639248
\(392\) 0 0
\(393\) −0.900369 −0.0454176
\(394\) 0 0
\(395\) 15.1828 0.763927
\(396\) 0 0
\(397\) −9.49861 −0.476722 −0.238361 0.971177i \(-0.576610\pi\)
−0.238361 + 0.971177i \(0.576610\pi\)
\(398\) 0 0
\(399\) 9.51697 0.476444
\(400\) 0 0
\(401\) −31.6884 −1.58244 −0.791221 0.611530i \(-0.790554\pi\)
−0.791221 + 0.611530i \(0.790554\pi\)
\(402\) 0 0
\(403\) −22.9132 −1.14139
\(404\) 0 0
\(405\) −7.89768 −0.392439
\(406\) 0 0
\(407\) −16.3706 −0.811461
\(408\) 0 0
\(409\) −26.2552 −1.29824 −0.649119 0.760687i \(-0.724862\pi\)
−0.649119 + 0.760687i \(0.724862\pi\)
\(410\) 0 0
\(411\) 1.19037 0.0587165
\(412\) 0 0
\(413\) −3.81841 −0.187892
\(414\) 0 0
\(415\) 1.30673 0.0641448
\(416\) 0 0
\(417\) −0.500299 −0.0244998
\(418\) 0 0
\(419\) −25.3855 −1.24016 −0.620082 0.784537i \(-0.712901\pi\)
−0.620082 + 0.784537i \(0.712901\pi\)
\(420\) 0 0
\(421\) −16.2678 −0.792846 −0.396423 0.918068i \(-0.629749\pi\)
−0.396423 + 0.918068i \(0.629749\pi\)
\(422\) 0 0
\(423\) −13.8815 −0.674940
\(424\) 0 0
\(425\) 1.26403 0.0613145
\(426\) 0 0
\(427\) −5.17736 −0.250550
\(428\) 0 0
\(429\) 5.03686 0.243182
\(430\) 0 0
\(431\) −22.2534 −1.07191 −0.535953 0.844248i \(-0.680048\pi\)
−0.535953 + 0.844248i \(0.680048\pi\)
\(432\) 0 0
\(433\) 6.72589 0.323226 0.161613 0.986854i \(-0.448330\pi\)
0.161613 + 0.986854i \(0.448330\pi\)
\(434\) 0 0
\(435\) 2.71251 0.130055
\(436\) 0 0
\(437\) −6.83349 −0.326890
\(438\) 0 0
\(439\) −11.3391 −0.541188 −0.270594 0.962694i \(-0.587220\pi\)
−0.270594 + 0.962694i \(0.587220\pi\)
\(440\) 0 0
\(441\) −24.7824 −1.18011
\(442\) 0 0
\(443\) −6.39714 −0.303937 −0.151969 0.988385i \(-0.548561\pi\)
−0.151969 + 0.988385i \(0.548561\pi\)
\(444\) 0 0
\(445\) 17.3242 0.821244
\(446\) 0 0
\(447\) −4.72092 −0.223292
\(448\) 0 0
\(449\) 8.84945 0.417631 0.208816 0.977955i \(-0.433039\pi\)
0.208816 + 0.977955i \(0.433039\pi\)
\(450\) 0 0
\(451\) −1.06388 −0.0500962
\(452\) 0 0
\(453\) −4.79597 −0.225334
\(454\) 0 0
\(455\) 10.0164 0.469575
\(456\) 0 0
\(457\) 28.8347 1.34883 0.674415 0.738353i \(-0.264396\pi\)
0.674415 + 0.738353i \(0.264396\pi\)
\(458\) 0 0
\(459\) −2.61743 −0.122171
\(460\) 0 0
\(461\) 28.5500 1.32970 0.664852 0.746975i \(-0.268495\pi\)
0.664852 + 0.746975i \(0.268495\pi\)
\(462\) 0 0
\(463\) 27.4923 1.27768 0.638838 0.769341i \(-0.279415\pi\)
0.638838 + 0.769341i \(0.279415\pi\)
\(464\) 0 0
\(465\) −3.18590 −0.147742
\(466\) 0 0
\(467\) 34.0356 1.57498 0.787490 0.616327i \(-0.211380\pi\)
0.787490 + 0.616327i \(0.211380\pi\)
\(468\) 0 0
\(469\) 15.6095 0.720780
\(470\) 0 0
\(471\) −6.97878 −0.321565
\(472\) 0 0
\(473\) −16.7870 −0.771867
\(474\) 0 0
\(475\) 6.83349 0.313542
\(476\) 0 0
\(477\) 0.946014 0.0433150
\(478\) 0 0
\(479\) −7.53712 −0.344380 −0.172190 0.985064i \(-0.555084\pi\)
−0.172190 + 0.985064i \(0.555084\pi\)
\(480\) 0 0
\(481\) −7.35805 −0.335498
\(482\) 0 0
\(483\) −1.39270 −0.0633698
\(484\) 0 0
\(485\) −8.26476 −0.375283
\(486\) 0 0
\(487\) 24.6238 1.11581 0.557906 0.829904i \(-0.311605\pi\)
0.557906 + 0.829904i \(0.311605\pi\)
\(488\) 0 0
\(489\) −7.21056 −0.326073
\(490\) 0 0
\(491\) −14.0638 −0.634692 −0.317346 0.948310i \(-0.602792\pi\)
−0.317346 + 0.948310i \(0.602792\pi\)
\(492\) 0 0
\(493\) −9.72927 −0.438184
\(494\) 0 0
\(495\) −16.2168 −0.728891
\(496\) 0 0
\(497\) −30.4046 −1.36383
\(498\) 0 0
\(499\) 26.5470 1.18841 0.594204 0.804315i \(-0.297467\pi\)
0.594204 + 0.804315i \(0.297467\pi\)
\(500\) 0 0
\(501\) −7.09145 −0.316823
\(502\) 0 0
\(503\) −36.3219 −1.61952 −0.809758 0.586764i \(-0.800401\pi\)
−0.809758 + 0.586764i \(0.800401\pi\)
\(504\) 0 0
\(505\) 17.8545 0.794516
\(506\) 0 0
\(507\) −2.31744 −0.102921
\(508\) 0 0
\(509\) −1.72157 −0.0763074 −0.0381537 0.999272i \(-0.512148\pi\)
−0.0381537 + 0.999272i \(0.512148\pi\)
\(510\) 0 0
\(511\) 2.43901 0.107895
\(512\) 0 0
\(513\) −14.1501 −0.624742
\(514\) 0 0
\(515\) 18.0624 0.795926
\(516\) 0 0
\(517\) −27.2196 −1.19712
\(518\) 0 0
\(519\) −8.56139 −0.375803
\(520\) 0 0
\(521\) −45.2230 −1.98126 −0.990629 0.136582i \(-0.956388\pi\)
−0.990629 + 0.136582i \(0.956388\pi\)
\(522\) 0 0
\(523\) −27.2150 −1.19003 −0.595013 0.803716i \(-0.702853\pi\)
−0.595013 + 0.803716i \(0.702853\pi\)
\(524\) 0 0
\(525\) 1.39270 0.0607822
\(526\) 0 0
\(527\) 11.4272 0.497777
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 2.77867 0.120584
\(532\) 0 0
\(533\) −0.478180 −0.0207123
\(534\) 0 0
\(535\) −12.7747 −0.552298
\(536\) 0 0
\(537\) −5.41558 −0.233699
\(538\) 0 0
\(539\) −48.5948 −2.09313
\(540\) 0 0
\(541\) 5.81174 0.249866 0.124933 0.992165i \(-0.460128\pi\)
0.124933 + 0.992165i \(0.460128\pi\)
\(542\) 0 0
\(543\) 4.94927 0.212394
\(544\) 0 0
\(545\) 14.7596 0.632234
\(546\) 0 0
\(547\) −25.4942 −1.09005 −0.545027 0.838419i \(-0.683481\pi\)
−0.545027 + 0.838419i \(0.683481\pi\)
\(548\) 0 0
\(549\) 3.76757 0.160796
\(550\) 0 0
\(551\) −52.5974 −2.24073
\(552\) 0 0
\(553\) −60.0008 −2.55149
\(554\) 0 0
\(555\) −1.02308 −0.0434272
\(556\) 0 0
\(557\) 0.522188 0.0221258 0.0110629 0.999939i \(-0.496478\pi\)
0.0110629 + 0.999939i \(0.496478\pi\)
\(558\) 0 0
\(559\) −7.54521 −0.319129
\(560\) 0 0
\(561\) −2.51196 −0.106055
\(562\) 0 0
\(563\) 22.8837 0.964432 0.482216 0.876052i \(-0.339832\pi\)
0.482216 + 0.876052i \(0.339832\pi\)
\(564\) 0 0
\(565\) 9.11666 0.383541
\(566\) 0 0
\(567\) 31.2109 1.31073
\(568\) 0 0
\(569\) −2.19530 −0.0920319 −0.0460159 0.998941i \(-0.514652\pi\)
−0.0460159 + 0.998941i \(0.514652\pi\)
\(570\) 0 0
\(571\) −18.5189 −0.774991 −0.387495 0.921872i \(-0.626660\pi\)
−0.387495 + 0.921872i \(0.626660\pi\)
\(572\) 0 0
\(573\) 0.884898 0.0369671
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −30.5975 −1.27379 −0.636895 0.770951i \(-0.719781\pi\)
−0.636895 + 0.770951i \(0.719781\pi\)
\(578\) 0 0
\(579\) 6.55540 0.272433
\(580\) 0 0
\(581\) −5.16407 −0.214242
\(582\) 0 0
\(583\) 1.85500 0.0768262
\(584\) 0 0
\(585\) −7.28893 −0.301360
\(586\) 0 0
\(587\) 14.0369 0.579365 0.289683 0.957123i \(-0.406450\pi\)
0.289683 + 0.957123i \(0.406450\pi\)
\(588\) 0 0
\(589\) 61.7767 2.54546
\(590\) 0 0
\(591\) 6.27408 0.258081
\(592\) 0 0
\(593\) −20.1236 −0.826376 −0.413188 0.910646i \(-0.635585\pi\)
−0.413188 + 0.910646i \(0.635585\pi\)
\(594\) 0 0
\(595\) −4.99533 −0.204789
\(596\) 0 0
\(597\) 3.22365 0.131935
\(598\) 0 0
\(599\) 35.1489 1.43615 0.718073 0.695968i \(-0.245025\pi\)
0.718073 + 0.695968i \(0.245025\pi\)
\(600\) 0 0
\(601\) −13.1732 −0.537346 −0.268673 0.963231i \(-0.586585\pi\)
−0.268673 + 0.963231i \(0.586585\pi\)
\(602\) 0 0
\(603\) −11.3591 −0.462577
\(604\) 0 0
\(605\) −20.7989 −0.845594
\(606\) 0 0
\(607\) −33.4291 −1.35685 −0.678423 0.734672i \(-0.737336\pi\)
−0.678423 + 0.734672i \(0.737336\pi\)
\(608\) 0 0
\(609\) −10.7196 −0.434380
\(610\) 0 0
\(611\) −12.2343 −0.494947
\(612\) 0 0
\(613\) 18.1013 0.731103 0.365551 0.930791i \(-0.380880\pi\)
0.365551 + 0.930791i \(0.380880\pi\)
\(614\) 0 0
\(615\) −0.0664871 −0.00268102
\(616\) 0 0
\(617\) 4.09327 0.164789 0.0823944 0.996600i \(-0.473743\pi\)
0.0823944 + 0.996600i \(0.473743\pi\)
\(618\) 0 0
\(619\) 29.9861 1.20525 0.602623 0.798026i \(-0.294122\pi\)
0.602623 + 0.798026i \(0.294122\pi\)
\(620\) 0 0
\(621\) 2.07070 0.0830943
\(622\) 0 0
\(623\) −68.4634 −2.74293
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −13.5799 −0.542331
\(628\) 0 0
\(629\) 3.66958 0.146316
\(630\) 0 0
\(631\) −37.5829 −1.49615 −0.748077 0.663612i \(-0.769022\pi\)
−0.748077 + 0.663612i \(0.769022\pi\)
\(632\) 0 0
\(633\) −6.56053 −0.260758
\(634\) 0 0
\(635\) −3.87377 −0.153726
\(636\) 0 0
\(637\) −21.8418 −0.865403
\(638\) 0 0
\(639\) 22.1254 0.875269
\(640\) 0 0
\(641\) 28.9195 1.14225 0.571126 0.820863i \(-0.306507\pi\)
0.571126 + 0.820863i \(0.306507\pi\)
\(642\) 0 0
\(643\) 4.05771 0.160020 0.0800102 0.996794i \(-0.474505\pi\)
0.0800102 + 0.996794i \(0.474505\pi\)
\(644\) 0 0
\(645\) −1.04910 −0.0413083
\(646\) 0 0
\(647\) 2.81376 0.110621 0.0553103 0.998469i \(-0.482385\pi\)
0.0553103 + 0.998469i \(0.482385\pi\)
\(648\) 0 0
\(649\) 5.44857 0.213875
\(650\) 0 0
\(651\) 12.5904 0.493455
\(652\) 0 0
\(653\) −23.7672 −0.930083 −0.465041 0.885289i \(-0.653961\pi\)
−0.465041 + 0.885289i \(0.653961\pi\)
\(654\) 0 0
\(655\) 2.55488 0.0998275
\(656\) 0 0
\(657\) −1.77487 −0.0692443
\(658\) 0 0
\(659\) 22.2518 0.866807 0.433403 0.901200i \(-0.357313\pi\)
0.433403 + 0.901200i \(0.357313\pi\)
\(660\) 0 0
\(661\) −45.0505 −1.75226 −0.876131 0.482074i \(-0.839884\pi\)
−0.876131 + 0.482074i \(0.839884\pi\)
\(662\) 0 0
\(663\) −1.12905 −0.0438485
\(664\) 0 0
\(665\) −27.0053 −1.04722
\(666\) 0 0
\(667\) 7.69701 0.298029
\(668\) 0 0
\(669\) 5.54961 0.214560
\(670\) 0 0
\(671\) 7.38767 0.285198
\(672\) 0 0
\(673\) −38.8944 −1.49927 −0.749635 0.661851i \(-0.769771\pi\)
−0.749635 + 0.661851i \(0.769771\pi\)
\(674\) 0 0
\(675\) −2.07070 −0.0797013
\(676\) 0 0
\(677\) −30.7421 −1.18151 −0.590757 0.806849i \(-0.701171\pi\)
−0.590757 + 0.806849i \(0.701171\pi\)
\(678\) 0 0
\(679\) 32.6616 1.25344
\(680\) 0 0
\(681\) 0.451229 0.0172911
\(682\) 0 0
\(683\) 50.7299 1.94113 0.970564 0.240844i \(-0.0774243\pi\)
0.970564 + 0.240844i \(0.0774243\pi\)
\(684\) 0 0
\(685\) −3.37778 −0.129058
\(686\) 0 0
\(687\) 0.0907190 0.00346114
\(688\) 0 0
\(689\) 0.833762 0.0317638
\(690\) 0 0
\(691\) 11.3810 0.432954 0.216477 0.976288i \(-0.430543\pi\)
0.216477 + 0.976288i \(0.430543\pi\)
\(692\) 0 0
\(693\) 64.0873 2.43447
\(694\) 0 0
\(695\) 1.41965 0.0538503
\(696\) 0 0
\(697\) 0.238476 0.00903294
\(698\) 0 0
\(699\) 4.30068 0.162667
\(700\) 0 0
\(701\) 1.38246 0.0522149 0.0261074 0.999659i \(-0.491689\pi\)
0.0261074 + 0.999659i \(0.491689\pi\)
\(702\) 0 0
\(703\) 19.8382 0.748210
\(704\) 0 0
\(705\) −1.70108 −0.0640665
\(706\) 0 0
\(707\) −70.5594 −2.65366
\(708\) 0 0
\(709\) 35.4080 1.32978 0.664888 0.746944i \(-0.268479\pi\)
0.664888 + 0.746944i \(0.268479\pi\)
\(710\) 0 0
\(711\) 43.6627 1.63748
\(712\) 0 0
\(713\) −9.04028 −0.338561
\(714\) 0 0
\(715\) −14.2926 −0.534511
\(716\) 0 0
\(717\) −2.57655 −0.0962230
\(718\) 0 0
\(719\) 10.0867 0.376169 0.188085 0.982153i \(-0.439772\pi\)
0.188085 + 0.982153i \(0.439772\pi\)
\(720\) 0 0
\(721\) −71.3810 −2.65837
\(722\) 0 0
\(723\) −4.13352 −0.153727
\(724\) 0 0
\(725\) −7.69701 −0.285860
\(726\) 0 0
\(727\) −13.4646 −0.499374 −0.249687 0.968327i \(-0.580328\pi\)
−0.249687 + 0.968327i \(0.580328\pi\)
\(728\) 0 0
\(729\) −20.5230 −0.760111
\(730\) 0 0
\(731\) 3.76292 0.139177
\(732\) 0 0
\(733\) −19.2923 −0.712577 −0.356289 0.934376i \(-0.615958\pi\)
−0.356289 + 0.934376i \(0.615958\pi\)
\(734\) 0 0
\(735\) −3.03692 −0.112019
\(736\) 0 0
\(737\) −22.2735 −0.820455
\(738\) 0 0
\(739\) 41.9597 1.54351 0.771756 0.635918i \(-0.219379\pi\)
0.771756 + 0.635918i \(0.219379\pi\)
\(740\) 0 0
\(741\) −6.10374 −0.224227
\(742\) 0 0
\(743\) 26.2397 0.962640 0.481320 0.876545i \(-0.340157\pi\)
0.481320 + 0.876545i \(0.340157\pi\)
\(744\) 0 0
\(745\) 13.3961 0.490794
\(746\) 0 0
\(747\) 3.75790 0.137494
\(748\) 0 0
\(749\) 50.4844 1.84466
\(750\) 0 0
\(751\) −43.8563 −1.60034 −0.800170 0.599773i \(-0.795258\pi\)
−0.800170 + 0.599773i \(0.795258\pi\)
\(752\) 0 0
\(753\) 2.18882 0.0797652
\(754\) 0 0
\(755\) 13.6090 0.495283
\(756\) 0 0
\(757\) −26.2435 −0.953835 −0.476918 0.878948i \(-0.658246\pi\)
−0.476918 + 0.878948i \(0.658246\pi\)
\(758\) 0 0
\(759\) 1.98726 0.0721331
\(760\) 0 0
\(761\) −45.7738 −1.65930 −0.829650 0.558283i \(-0.811460\pi\)
−0.829650 + 0.558283i \(0.811460\pi\)
\(762\) 0 0
\(763\) −58.3287 −2.11164
\(764\) 0 0
\(765\) 3.63511 0.131428
\(766\) 0 0
\(767\) 2.44895 0.0884266
\(768\) 0 0
\(769\) 26.7930 0.966181 0.483091 0.875570i \(-0.339514\pi\)
0.483091 + 0.875570i \(0.339514\pi\)
\(770\) 0 0
\(771\) 9.52858 0.343164
\(772\) 0 0
\(773\) 40.8103 1.46784 0.733922 0.679234i \(-0.237688\pi\)
0.733922 + 0.679234i \(0.237688\pi\)
\(774\) 0 0
\(775\) 9.04028 0.324737
\(776\) 0 0
\(777\) 4.04311 0.145046
\(778\) 0 0
\(779\) 1.28923 0.0461914
\(780\) 0 0
\(781\) 43.3849 1.55243
\(782\) 0 0
\(783\) 15.9382 0.569585
\(784\) 0 0
\(785\) 19.8029 0.706797
\(786\) 0 0
\(787\) −7.34419 −0.261792 −0.130896 0.991396i \(-0.541785\pi\)
−0.130896 + 0.991396i \(0.541785\pi\)
\(788\) 0 0
\(789\) −7.86228 −0.279905
\(790\) 0 0
\(791\) −36.0282 −1.28101
\(792\) 0 0
\(793\) 3.32052 0.117915
\(794\) 0 0
\(795\) 0.115928 0.00411154
\(796\) 0 0
\(797\) 3.62790 0.128507 0.0642535 0.997934i \(-0.479533\pi\)
0.0642535 + 0.997934i \(0.479533\pi\)
\(798\) 0 0
\(799\) 6.10146 0.215854
\(800\) 0 0
\(801\) 49.8209 1.76034
\(802\) 0 0
\(803\) −3.48027 −0.122816
\(804\) 0 0
\(805\) 3.95190 0.139286
\(806\) 0 0
\(807\) 5.02961 0.177051
\(808\) 0 0
\(809\) 8.82493 0.310268 0.155134 0.987893i \(-0.450419\pi\)
0.155134 + 0.987893i \(0.450419\pi\)
\(810\) 0 0
\(811\) 17.9422 0.630035 0.315018 0.949086i \(-0.397990\pi\)
0.315018 + 0.949086i \(0.397990\pi\)
\(812\) 0 0
\(813\) −6.37108 −0.223443
\(814\) 0 0
\(815\) 20.4606 0.716705
\(816\) 0 0
\(817\) 20.3428 0.711703
\(818\) 0 0
\(819\) 28.8052 1.00653
\(820\) 0 0
\(821\) 38.7051 1.35082 0.675409 0.737444i \(-0.263967\pi\)
0.675409 + 0.737444i \(0.263967\pi\)
\(822\) 0 0
\(823\) −25.7406 −0.897259 −0.448630 0.893718i \(-0.648088\pi\)
−0.448630 + 0.893718i \(0.648088\pi\)
\(824\) 0 0
\(825\) −1.98726 −0.0691876
\(826\) 0 0
\(827\) −54.3061 −1.88841 −0.944205 0.329359i \(-0.893167\pi\)
−0.944205 + 0.329359i \(0.893167\pi\)
\(828\) 0 0
\(829\) −44.6143 −1.54952 −0.774759 0.632257i \(-0.782129\pi\)
−0.774759 + 0.632257i \(0.782129\pi\)
\(830\) 0 0
\(831\) −1.75316 −0.0608165
\(832\) 0 0
\(833\) 10.8929 0.377415
\(834\) 0 0
\(835\) 20.1227 0.696373
\(836\) 0 0
\(837\) −18.7197 −0.647048
\(838\) 0 0
\(839\) −26.1843 −0.903984 −0.451992 0.892022i \(-0.649286\pi\)
−0.451992 + 0.892022i \(0.649286\pi\)
\(840\) 0 0
\(841\) 30.2440 1.04290
\(842\) 0 0
\(843\) −1.81807 −0.0626177
\(844\) 0 0
\(845\) 6.57596 0.226220
\(846\) 0 0
\(847\) 82.1951 2.82426
\(848\) 0 0
\(849\) −4.18665 −0.143685
\(850\) 0 0
\(851\) −2.90308 −0.0995163
\(852\) 0 0
\(853\) −8.97182 −0.307189 −0.153595 0.988134i \(-0.549085\pi\)
−0.153595 + 0.988134i \(0.549085\pi\)
\(854\) 0 0
\(855\) 19.6518 0.672077
\(856\) 0 0
\(857\) 7.25709 0.247898 0.123949 0.992289i \(-0.460444\pi\)
0.123949 + 0.992289i \(0.460444\pi\)
\(858\) 0 0
\(859\) 34.9010 1.19081 0.595403 0.803427i \(-0.296993\pi\)
0.595403 + 0.803427i \(0.296993\pi\)
\(860\) 0 0
\(861\) 0.262751 0.00895452
\(862\) 0 0
\(863\) 15.7663 0.536690 0.268345 0.963323i \(-0.413523\pi\)
0.268345 + 0.963323i \(0.413523\pi\)
\(864\) 0 0
\(865\) 24.2937 0.826012
\(866\) 0 0
\(867\) −5.42792 −0.184342
\(868\) 0 0
\(869\) 85.6163 2.90433
\(870\) 0 0
\(871\) −10.0112 −0.339217
\(872\) 0 0
\(873\) −23.7679 −0.804420
\(874\) 0 0
\(875\) −3.95190 −0.133599
\(876\) 0 0
\(877\) 3.07478 0.103828 0.0519139 0.998652i \(-0.483468\pi\)
0.0519139 + 0.998652i \(0.483468\pi\)
\(878\) 0 0
\(879\) 8.46051 0.285366
\(880\) 0 0
\(881\) 8.27798 0.278892 0.139446 0.990230i \(-0.455468\pi\)
0.139446 + 0.990230i \(0.455468\pi\)
\(882\) 0 0
\(883\) −11.5521 −0.388758 −0.194379 0.980927i \(-0.562269\pi\)
−0.194379 + 0.980927i \(0.562269\pi\)
\(884\) 0 0
\(885\) 0.340507 0.0114460
\(886\) 0 0
\(887\) −44.6832 −1.50031 −0.750157 0.661260i \(-0.770022\pi\)
−0.750157 + 0.661260i \(0.770022\pi\)
\(888\) 0 0
\(889\) 15.3088 0.513440
\(890\) 0 0
\(891\) −44.5354 −1.49199
\(892\) 0 0
\(893\) 32.9851 1.10380
\(894\) 0 0
\(895\) 15.3672 0.513669
\(896\) 0 0
\(897\) 0.893211 0.0298234
\(898\) 0 0
\(899\) −69.5832 −2.32073
\(900\) 0 0
\(901\) −0.415811 −0.0138527
\(902\) 0 0
\(903\) 4.14595 0.137968
\(904\) 0 0
\(905\) −14.0440 −0.466839
\(906\) 0 0
\(907\) 5.55427 0.184426 0.0922132 0.995739i \(-0.470606\pi\)
0.0922132 + 0.995739i \(0.470606\pi\)
\(908\) 0 0
\(909\) 51.3462 1.70304
\(910\) 0 0
\(911\) 13.1325 0.435100 0.217550 0.976049i \(-0.430193\pi\)
0.217550 + 0.976049i \(0.430193\pi\)
\(912\) 0 0
\(913\) 7.36871 0.243869
\(914\) 0 0
\(915\) 0.461691 0.0152630
\(916\) 0 0
\(917\) −10.0966 −0.333421
\(918\) 0 0
\(919\) −12.5417 −0.413712 −0.206856 0.978371i \(-0.566323\pi\)
−0.206856 + 0.978371i \(0.566323\pi\)
\(920\) 0 0
\(921\) −7.34386 −0.241988
\(922\) 0 0
\(923\) 19.5001 0.641853
\(924\) 0 0
\(925\) 2.90308 0.0954527
\(926\) 0 0
\(927\) 51.9441 1.70607
\(928\) 0 0
\(929\) −8.24051 −0.270362 −0.135181 0.990821i \(-0.543162\pi\)
−0.135181 + 0.990821i \(0.543162\pi\)
\(930\) 0 0
\(931\) 58.8879 1.92997
\(932\) 0 0
\(933\) 8.32013 0.272389
\(934\) 0 0
\(935\) 7.12793 0.233108
\(936\) 0 0
\(937\) 11.4798 0.375030 0.187515 0.982262i \(-0.439957\pi\)
0.187515 + 0.982262i \(0.439957\pi\)
\(938\) 0 0
\(939\) 5.56575 0.181631
\(940\) 0 0
\(941\) 28.3769 0.925061 0.462531 0.886603i \(-0.346942\pi\)
0.462531 + 0.886603i \(0.346942\pi\)
\(942\) 0 0
\(943\) −0.188663 −0.00614373
\(944\) 0 0
\(945\) 8.18321 0.266200
\(946\) 0 0
\(947\) 7.88882 0.256352 0.128176 0.991751i \(-0.459088\pi\)
0.128176 + 0.991751i \(0.459088\pi\)
\(948\) 0 0
\(949\) −1.56427 −0.0507783
\(950\) 0 0
\(951\) 11.3849 0.369181
\(952\) 0 0
\(953\) −9.20245 −0.298096 −0.149048 0.988830i \(-0.547621\pi\)
−0.149048 + 0.988830i \(0.547621\pi\)
\(954\) 0 0
\(955\) −2.51098 −0.0812534
\(956\) 0 0
\(957\) 15.2960 0.494449
\(958\) 0 0
\(959\) 13.3487 0.431051
\(960\) 0 0
\(961\) 50.7267 1.63635
\(962\) 0 0
\(963\) −36.7375 −1.18385
\(964\) 0 0
\(965\) −18.6016 −0.598805
\(966\) 0 0
\(967\) −19.6278 −0.631186 −0.315593 0.948895i \(-0.602203\pi\)
−0.315593 + 0.948895i \(0.602203\pi\)
\(968\) 0 0
\(969\) 3.04404 0.0977886
\(970\) 0 0
\(971\) −7.09502 −0.227690 −0.113845 0.993499i \(-0.536317\pi\)
−0.113845 + 0.993499i \(0.536317\pi\)
\(972\) 0 0
\(973\) −5.61031 −0.179858
\(974\) 0 0
\(975\) −0.893211 −0.0286056
\(976\) 0 0
\(977\) 40.5255 1.29652 0.648262 0.761417i \(-0.275496\pi\)
0.648262 + 0.761417i \(0.275496\pi\)
\(978\) 0 0
\(979\) 97.6917 3.12224
\(980\) 0 0
\(981\) 42.4459 1.35519
\(982\) 0 0
\(983\) −48.8845 −1.55917 −0.779587 0.626294i \(-0.784571\pi\)
−0.779587 + 0.626294i \(0.784571\pi\)
\(984\) 0 0
\(985\) −17.8033 −0.567260
\(986\) 0 0
\(987\) 6.72251 0.213980
\(988\) 0 0
\(989\) −2.97692 −0.0946606
\(990\) 0 0
\(991\) 44.9031 1.42639 0.713197 0.700963i \(-0.247246\pi\)
0.713197 + 0.700963i \(0.247246\pi\)
\(992\) 0 0
\(993\) 5.07965 0.161198
\(994\) 0 0
\(995\) −9.14740 −0.289992
\(996\) 0 0
\(997\) −55.6027 −1.76096 −0.880478 0.474087i \(-0.842778\pi\)
−0.880478 + 0.474087i \(0.842778\pi\)
\(998\) 0 0
\(999\) −6.01141 −0.190192
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 7360.2.a.cl.1.3 5
4.3 odd 2 7360.2.a.cq.1.3 5
8.3 odd 2 3680.2.a.x.1.3 5
8.5 even 2 3680.2.a.ba.1.3 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.x.1.3 5 8.3 odd 2
3680.2.a.ba.1.3 yes 5 8.5 even 2
7360.2.a.cl.1.3 5 1.1 even 1 trivial
7360.2.a.cq.1.3 5 4.3 odd 2