Properties

Label 7360.2.a.cr.1.4
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $0$
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: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1143052.1
Defining polynomial: \(x^{5} - x^{4} - 9 x^{3} + 11 x^{2} + 6 x - 4\)
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 1.4
Root \(-2.98054\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.80707 q^{3} +1.00000 q^{5} +4.65156 q^{7} +0.265511 q^{9} +O(q^{10})\) \(q+1.80707 q^{3} +1.00000 q^{5} +4.65156 q^{7} +0.265511 q^{9} +4.38210 q^{11} +4.79250 q^{13} +1.80707 q^{15} +0.285165 q^{17} +3.30952 q^{19} +8.40570 q^{21} -1.00000 q^{23} +1.00000 q^{25} -4.94142 q^{27} +3.47320 q^{29} -2.44557 q^{31} +7.91877 q^{33} +4.65156 q^{35} -11.0610 q^{37} +8.66039 q^{39} +11.7681 q^{41} -2.24999 q^{43} +0.265511 q^{45} -8.28422 q^{47} +14.6370 q^{49} +0.515313 q^{51} -3.81591 q^{53} +4.38210 q^{55} +5.98054 q^{57} +9.43005 q^{59} +5.54005 q^{61} +1.23504 q^{63} +4.79250 q^{65} -11.2062 q^{67} -1.80707 q^{69} -15.2464 q^{71} -9.87814 q^{73} +1.80707 q^{75} +20.3836 q^{77} +12.2402 q^{79} -9.72604 q^{81} +8.15495 q^{83} +0.285165 q^{85} +6.27633 q^{87} +1.98319 q^{89} +22.2926 q^{91} -4.41932 q^{93} +3.30952 q^{95} +4.33340 q^{97} +1.16349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + q^{3} + 5 q^{5} + q^{7} + 6 q^{9} + O(q^{10}) \) \( 5 q + q^{3} + 5 q^{5} + q^{7} + 6 q^{9} + 9 q^{11} - 3 q^{13} + q^{15} - 21 q^{17} + 7 q^{19} - 12 q^{21} - 5 q^{23} + 5 q^{25} - 20 q^{27} + 6 q^{29} - q^{31} + 17 q^{33} + q^{35} - 8 q^{37} + 4 q^{39} + 19 q^{41} + 14 q^{43} + 6 q^{45} - 8 q^{47} + 32 q^{49} + 25 q^{51} + 6 q^{53} + 9 q^{55} + 14 q^{57} + 6 q^{59} - 23 q^{61} + 48 q^{63} - 3 q^{65} - 2 q^{67} - q^{69} + 21 q^{71} + q^{75} + 26 q^{77} + 42 q^{79} + 25 q^{81} + 28 q^{83} - 21 q^{85} + 26 q^{87} + 19 q^{91} - 46 q^{93} + 7 q^{95} - 17 q^{97} + 47 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.80707 1.04331 0.521657 0.853155i \(-0.325314\pi\)
0.521657 + 0.853155i \(0.325314\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 4.65156 1.75812 0.879062 0.476708i \(-0.158170\pi\)
0.879062 + 0.476708i \(0.158170\pi\)
\(8\) 0 0
\(9\) 0.265511 0.0885036
\(10\) 0 0
\(11\) 4.38210 1.32125 0.660626 0.750715i \(-0.270291\pi\)
0.660626 + 0.750715i \(0.270291\pi\)
\(12\) 0 0
\(13\) 4.79250 1.32920 0.664600 0.747199i \(-0.268602\pi\)
0.664600 + 0.747199i \(0.268602\pi\)
\(14\) 0 0
\(15\) 1.80707 0.466584
\(16\) 0 0
\(17\) 0.285165 0.0691626 0.0345813 0.999402i \(-0.488990\pi\)
0.0345813 + 0.999402i \(0.488990\pi\)
\(18\) 0 0
\(19\) 3.30952 0.759255 0.379628 0.925139i \(-0.376052\pi\)
0.379628 + 0.925139i \(0.376052\pi\)
\(20\) 0 0
\(21\) 8.40570 1.83427
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.94142 −0.950977
\(28\) 0 0
\(29\) 3.47320 0.644958 0.322479 0.946577i \(-0.395484\pi\)
0.322479 + 0.946577i \(0.395484\pi\)
\(30\) 0 0
\(31\) −2.44557 −0.439237 −0.219619 0.975586i \(-0.570481\pi\)
−0.219619 + 0.975586i \(0.570481\pi\)
\(32\) 0 0
\(33\) 7.91877 1.37848
\(34\) 0 0
\(35\) 4.65156 0.786257
\(36\) 0 0
\(37\) −11.0610 −1.81842 −0.909210 0.416339i \(-0.863313\pi\)
−0.909210 + 0.416339i \(0.863313\pi\)
\(38\) 0 0
\(39\) 8.66039 1.38677
\(40\) 0 0
\(41\) 11.7681 1.83788 0.918938 0.394402i \(-0.129048\pi\)
0.918938 + 0.394402i \(0.129048\pi\)
\(42\) 0 0
\(43\) −2.24999 −0.343121 −0.171560 0.985174i \(-0.554881\pi\)
−0.171560 + 0.985174i \(0.554881\pi\)
\(44\) 0 0
\(45\) 0.265511 0.0395800
\(46\) 0 0
\(47\) −8.28422 −1.20838 −0.604189 0.796841i \(-0.706503\pi\)
−0.604189 + 0.796841i \(0.706503\pi\)
\(48\) 0 0
\(49\) 14.6370 2.09100
\(50\) 0 0
\(51\) 0.515313 0.0721583
\(52\) 0 0
\(53\) −3.81591 −0.524155 −0.262078 0.965047i \(-0.584408\pi\)
−0.262078 + 0.965047i \(0.584408\pi\)
\(54\) 0 0
\(55\) 4.38210 0.590882
\(56\) 0 0
\(57\) 5.98054 0.792141
\(58\) 0 0
\(59\) 9.43005 1.22769 0.613844 0.789427i \(-0.289622\pi\)
0.613844 + 0.789427i \(0.289622\pi\)
\(60\) 0 0
\(61\) 5.54005 0.709331 0.354665 0.934993i \(-0.384595\pi\)
0.354665 + 0.934993i \(0.384595\pi\)
\(62\) 0 0
\(63\) 1.23504 0.155600
\(64\) 0 0
\(65\) 4.79250 0.594436
\(66\) 0 0
\(67\) −11.2062 −1.36905 −0.684526 0.728988i \(-0.739991\pi\)
−0.684526 + 0.728988i \(0.739991\pi\)
\(68\) 0 0
\(69\) −1.80707 −0.217546
\(70\) 0 0
\(71\) −15.2464 −1.80942 −0.904709 0.426030i \(-0.859912\pi\)
−0.904709 + 0.426030i \(0.859912\pi\)
\(72\) 0 0
\(73\) −9.87814 −1.15615 −0.578075 0.815984i \(-0.696196\pi\)
−0.578075 + 0.815984i \(0.696196\pi\)
\(74\) 0 0
\(75\) 1.80707 0.208663
\(76\) 0 0
\(77\) 20.3836 2.32293
\(78\) 0 0
\(79\) 12.2402 1.37713 0.688566 0.725174i \(-0.258241\pi\)
0.688566 + 0.725174i \(0.258241\pi\)
\(80\) 0 0
\(81\) −9.72604 −1.08067
\(82\) 0 0
\(83\) 8.15495 0.895122 0.447561 0.894254i \(-0.352293\pi\)
0.447561 + 0.894254i \(0.352293\pi\)
\(84\) 0 0
\(85\) 0.285165 0.0309305
\(86\) 0 0
\(87\) 6.27633 0.672893
\(88\) 0 0
\(89\) 1.98319 0.210217 0.105109 0.994461i \(-0.466481\pi\)
0.105109 + 0.994461i \(0.466481\pi\)
\(90\) 0 0
\(91\) 22.2926 2.33690
\(92\) 0 0
\(93\) −4.41932 −0.458262
\(94\) 0 0
\(95\) 3.30952 0.339549
\(96\) 0 0
\(97\) 4.33340 0.439990 0.219995 0.975501i \(-0.429396\pi\)
0.219995 + 0.975501i \(0.429396\pi\)
\(98\) 0 0
\(99\) 1.16349 0.116936
\(100\) 0 0
\(101\) −17.9203 −1.78313 −0.891566 0.452890i \(-0.850393\pi\)
−0.891566 + 0.452890i \(0.850393\pi\)
\(102\) 0 0
\(103\) −17.6351 −1.73764 −0.868819 0.495130i \(-0.835120\pi\)
−0.868819 + 0.495130i \(0.835120\pi\)
\(104\) 0 0
\(105\) 8.40570 0.820312
\(106\) 0 0
\(107\) −17.0535 −1.64862 −0.824312 0.566136i \(-0.808438\pi\)
−0.824312 + 0.566136i \(0.808438\pi\)
\(108\) 0 0
\(109\) −11.3174 −1.08401 −0.542006 0.840375i \(-0.682335\pi\)
−0.542006 + 0.840375i \(0.682335\pi\)
\(110\) 0 0
\(111\) −19.9881 −1.89718
\(112\) 0 0
\(113\) 4.82783 0.454164 0.227082 0.973876i \(-0.427081\pi\)
0.227082 + 0.973876i \(0.427081\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 1.27246 0.117639
\(118\) 0 0
\(119\) 1.32646 0.121596
\(120\) 0 0
\(121\) 8.20280 0.745709
\(122\) 0 0
\(123\) 21.2659 1.91748
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 7.09524 0.629601 0.314800 0.949158i \(-0.398062\pi\)
0.314800 + 0.949158i \(0.398062\pi\)
\(128\) 0 0
\(129\) −4.06590 −0.357983
\(130\) 0 0
\(131\) −11.0081 −0.961781 −0.480890 0.876781i \(-0.659686\pi\)
−0.480890 + 0.876781i \(0.659686\pi\)
\(132\) 0 0
\(133\) 15.3944 1.33486
\(134\) 0 0
\(135\) −4.94142 −0.425290
\(136\) 0 0
\(137\) −2.82861 −0.241665 −0.120832 0.992673i \(-0.538556\pi\)
−0.120832 + 0.992673i \(0.538556\pi\)
\(138\) 0 0
\(139\) −3.14536 −0.266786 −0.133393 0.991063i \(-0.542587\pi\)
−0.133393 + 0.991063i \(0.542587\pi\)
\(140\) 0 0
\(141\) −14.9702 −1.26072
\(142\) 0 0
\(143\) 21.0012 1.75621
\(144\) 0 0
\(145\) 3.47320 0.288434
\(146\) 0 0
\(147\) 26.4501 2.18157
\(148\) 0 0
\(149\) −15.6949 −1.28578 −0.642888 0.765960i \(-0.722264\pi\)
−0.642888 + 0.765960i \(0.722264\pi\)
\(150\) 0 0
\(151\) −2.48412 −0.202155 −0.101077 0.994879i \(-0.532229\pi\)
−0.101077 + 0.994879i \(0.532229\pi\)
\(152\) 0 0
\(153\) 0.0757143 0.00612114
\(154\) 0 0
\(155\) −2.44557 −0.196433
\(156\) 0 0
\(157\) −1.66989 −0.133271 −0.0666357 0.997777i \(-0.521227\pi\)
−0.0666357 + 0.997777i \(0.521227\pi\)
\(158\) 0 0
\(159\) −6.89562 −0.546858
\(160\) 0 0
\(161\) −4.65156 −0.366594
\(162\) 0 0
\(163\) −4.92836 −0.386019 −0.193009 0.981197i \(-0.561825\pi\)
−0.193009 + 0.981197i \(0.561825\pi\)
\(164\) 0 0
\(165\) 7.91877 0.616476
\(166\) 0 0
\(167\) 7.34993 0.568755 0.284377 0.958712i \(-0.408213\pi\)
0.284377 + 0.958712i \(0.408213\pi\)
\(168\) 0 0
\(169\) 9.96805 0.766773
\(170\) 0 0
\(171\) 0.878712 0.0671968
\(172\) 0 0
\(173\) −25.4824 −1.93739 −0.968696 0.248249i \(-0.920145\pi\)
−0.968696 + 0.248249i \(0.920145\pi\)
\(174\) 0 0
\(175\) 4.65156 0.351625
\(176\) 0 0
\(177\) 17.0408 1.28086
\(178\) 0 0
\(179\) 7.78168 0.581630 0.290815 0.956779i \(-0.406074\pi\)
0.290815 + 0.956779i \(0.406074\pi\)
\(180\) 0 0
\(181\) −23.7922 −1.76846 −0.884231 0.467050i \(-0.845317\pi\)
−0.884231 + 0.467050i \(0.845317\pi\)
\(182\) 0 0
\(183\) 10.0113 0.740054
\(184\) 0 0
\(185\) −11.0610 −0.813222
\(186\) 0 0
\(187\) 1.24962 0.0913813
\(188\) 0 0
\(189\) −22.9853 −1.67193
\(190\) 0 0
\(191\) −5.81402 −0.420688 −0.210344 0.977627i \(-0.567458\pi\)
−0.210344 + 0.977627i \(0.567458\pi\)
\(192\) 0 0
\(193\) −8.53422 −0.614306 −0.307153 0.951660i \(-0.599376\pi\)
−0.307153 + 0.951660i \(0.599376\pi\)
\(194\) 0 0
\(195\) 8.66039 0.620184
\(196\) 0 0
\(197\) 21.9792 1.56595 0.782977 0.622051i \(-0.213700\pi\)
0.782977 + 0.622051i \(0.213700\pi\)
\(198\) 0 0
\(199\) 26.6774 1.89111 0.945556 0.325459i \(-0.105519\pi\)
0.945556 + 0.325459i \(0.105519\pi\)
\(200\) 0 0
\(201\) −20.2504 −1.42835
\(202\) 0 0
\(203\) 16.1558 1.13391
\(204\) 0 0
\(205\) 11.7681 0.821923
\(206\) 0 0
\(207\) −0.265511 −0.0184543
\(208\) 0 0
\(209\) 14.5026 1.00317
\(210\) 0 0
\(211\) −21.5831 −1.48584 −0.742921 0.669379i \(-0.766560\pi\)
−0.742921 + 0.669379i \(0.766560\pi\)
\(212\) 0 0
\(213\) −27.5514 −1.88779
\(214\) 0 0
\(215\) −2.24999 −0.153448
\(216\) 0 0
\(217\) −11.3757 −0.772233
\(218\) 0 0
\(219\) −17.8505 −1.20623
\(220\) 0 0
\(221\) 1.36665 0.0919310
\(222\) 0 0
\(223\) −5.43756 −0.364126 −0.182063 0.983287i \(-0.558278\pi\)
−0.182063 + 0.983287i \(0.558278\pi\)
\(224\) 0 0
\(225\) 0.265511 0.0177007
\(226\) 0 0
\(227\) 18.0875 1.20051 0.600256 0.799808i \(-0.295065\pi\)
0.600256 + 0.799808i \(0.295065\pi\)
\(228\) 0 0
\(229\) 4.62834 0.305849 0.152925 0.988238i \(-0.451131\pi\)
0.152925 + 0.988238i \(0.451131\pi\)
\(230\) 0 0
\(231\) 36.8346 2.42354
\(232\) 0 0
\(233\) 7.38793 0.484000 0.242000 0.970276i \(-0.422197\pi\)
0.242000 + 0.970276i \(0.422197\pi\)
\(234\) 0 0
\(235\) −8.28422 −0.540403
\(236\) 0 0
\(237\) 22.1190 1.43678
\(238\) 0 0
\(239\) 6.83735 0.442272 0.221136 0.975243i \(-0.429024\pi\)
0.221136 + 0.975243i \(0.429024\pi\)
\(240\) 0 0
\(241\) 7.95130 0.512188 0.256094 0.966652i \(-0.417564\pi\)
0.256094 + 0.966652i \(0.417564\pi\)
\(242\) 0 0
\(243\) −2.75139 −0.176502
\(244\) 0 0
\(245\) 14.6370 0.935123
\(246\) 0 0
\(247\) 15.8609 1.00920
\(248\) 0 0
\(249\) 14.7366 0.933893
\(250\) 0 0
\(251\) 29.2227 1.84452 0.922262 0.386566i \(-0.126339\pi\)
0.922262 + 0.386566i \(0.126339\pi\)
\(252\) 0 0
\(253\) −4.38210 −0.275500
\(254\) 0 0
\(255\) 0.515313 0.0322702
\(256\) 0 0
\(257\) 1.49980 0.0935548 0.0467774 0.998905i \(-0.485105\pi\)
0.0467774 + 0.998905i \(0.485105\pi\)
\(258\) 0 0
\(259\) −51.4509 −3.19701
\(260\) 0 0
\(261\) 0.922173 0.0570810
\(262\) 0 0
\(263\) −21.5869 −1.33110 −0.665552 0.746352i \(-0.731804\pi\)
−0.665552 + 0.746352i \(0.731804\pi\)
\(264\) 0 0
\(265\) −3.81591 −0.234409
\(266\) 0 0
\(267\) 3.58376 0.219322
\(268\) 0 0
\(269\) 7.49276 0.456842 0.228421 0.973562i \(-0.426644\pi\)
0.228421 + 0.973562i \(0.426644\pi\)
\(270\) 0 0
\(271\) 12.7175 0.772531 0.386265 0.922388i \(-0.373765\pi\)
0.386265 + 0.922388i \(0.373765\pi\)
\(272\) 0 0
\(273\) 40.2843 2.43812
\(274\) 0 0
\(275\) 4.38210 0.264251
\(276\) 0 0
\(277\) −27.9099 −1.67695 −0.838473 0.544943i \(-0.816551\pi\)
−0.838473 + 0.544943i \(0.816551\pi\)
\(278\) 0 0
\(279\) −0.649325 −0.0388741
\(280\) 0 0
\(281\) 21.7961 1.30024 0.650122 0.759830i \(-0.274718\pi\)
0.650122 + 0.759830i \(0.274718\pi\)
\(282\) 0 0
\(283\) −23.5235 −1.39833 −0.699163 0.714962i \(-0.746444\pi\)
−0.699163 + 0.714962i \(0.746444\pi\)
\(284\) 0 0
\(285\) 5.98054 0.354256
\(286\) 0 0
\(287\) 54.7402 3.23121
\(288\) 0 0
\(289\) −16.9187 −0.995217
\(290\) 0 0
\(291\) 7.83076 0.459047
\(292\) 0 0
\(293\) 0.675631 0.0394708 0.0197354 0.999805i \(-0.493718\pi\)
0.0197354 + 0.999805i \(0.493718\pi\)
\(294\) 0 0
\(295\) 9.43005 0.549039
\(296\) 0 0
\(297\) −21.6538 −1.25648
\(298\) 0 0
\(299\) −4.79250 −0.277157
\(300\) 0 0
\(301\) −10.4660 −0.603249
\(302\) 0 0
\(303\) −32.3832 −1.86037
\(304\) 0 0
\(305\) 5.54005 0.317222
\(306\) 0 0
\(307\) 3.23138 0.184425 0.0922123 0.995739i \(-0.470606\pi\)
0.0922123 + 0.995739i \(0.470606\pi\)
\(308\) 0 0
\(309\) −31.8679 −1.81290
\(310\) 0 0
\(311\) 21.8033 1.23635 0.618176 0.786039i \(-0.287872\pi\)
0.618176 + 0.786039i \(0.287872\pi\)
\(312\) 0 0
\(313\) 28.9311 1.63528 0.817641 0.575729i \(-0.195282\pi\)
0.817641 + 0.575729i \(0.195282\pi\)
\(314\) 0 0
\(315\) 1.23504 0.0695865
\(316\) 0 0
\(317\) 15.2017 0.853810 0.426905 0.904296i \(-0.359604\pi\)
0.426905 + 0.904296i \(0.359604\pi\)
\(318\) 0 0
\(319\) 15.2199 0.852152
\(320\) 0 0
\(321\) −30.8169 −1.72003
\(322\) 0 0
\(323\) 0.943758 0.0525121
\(324\) 0 0
\(325\) 4.79250 0.265840
\(326\) 0 0
\(327\) −20.4514 −1.13096
\(328\) 0 0
\(329\) −38.5345 −2.12448
\(330\) 0 0
\(331\) −5.13558 −0.282277 −0.141138 0.989990i \(-0.545076\pi\)
−0.141138 + 0.989990i \(0.545076\pi\)
\(332\) 0 0
\(333\) −2.93682 −0.160937
\(334\) 0 0
\(335\) −11.2062 −0.612259
\(336\) 0 0
\(337\) 2.54759 0.138776 0.0693879 0.997590i \(-0.477895\pi\)
0.0693879 + 0.997590i \(0.477895\pi\)
\(338\) 0 0
\(339\) 8.72424 0.473836
\(340\) 0 0
\(341\) −10.7167 −0.580344
\(342\) 0 0
\(343\) 35.5239 1.91811
\(344\) 0 0
\(345\) −1.80707 −0.0972895
\(346\) 0 0
\(347\) −18.2462 −0.979509 −0.489755 0.871860i \(-0.662914\pi\)
−0.489755 + 0.871860i \(0.662914\pi\)
\(348\) 0 0
\(349\) −0.262585 −0.0140558 −0.00702792 0.999975i \(-0.502237\pi\)
−0.00702792 + 0.999975i \(0.502237\pi\)
\(350\) 0 0
\(351\) −23.6818 −1.26404
\(352\) 0 0
\(353\) −5.75461 −0.306287 −0.153144 0.988204i \(-0.548940\pi\)
−0.153144 + 0.988204i \(0.548940\pi\)
\(354\) 0 0
\(355\) −15.2464 −0.809197
\(356\) 0 0
\(357\) 2.39701 0.126863
\(358\) 0 0
\(359\) 16.1677 0.853296 0.426648 0.904418i \(-0.359694\pi\)
0.426648 + 0.904418i \(0.359694\pi\)
\(360\) 0 0
\(361\) −8.04710 −0.423531
\(362\) 0 0
\(363\) 14.8231 0.778009
\(364\) 0 0
\(365\) −9.87814 −0.517046
\(366\) 0 0
\(367\) −9.25214 −0.482958 −0.241479 0.970406i \(-0.577632\pi\)
−0.241479 + 0.970406i \(0.577632\pi\)
\(368\) 0 0
\(369\) 3.12457 0.162659
\(370\) 0 0
\(371\) −17.7499 −0.921530
\(372\) 0 0
\(373\) −15.4970 −0.802403 −0.401202 0.915990i \(-0.631407\pi\)
−0.401202 + 0.915990i \(0.631407\pi\)
\(374\) 0 0
\(375\) 1.80707 0.0933168
\(376\) 0 0
\(377\) 16.6453 0.857278
\(378\) 0 0
\(379\) 21.4839 1.10356 0.551778 0.833991i \(-0.313950\pi\)
0.551778 + 0.833991i \(0.313950\pi\)
\(380\) 0 0
\(381\) 12.8216 0.656871
\(382\) 0 0
\(383\) 12.3758 0.632373 0.316187 0.948697i \(-0.397597\pi\)
0.316187 + 0.948697i \(0.397597\pi\)
\(384\) 0 0
\(385\) 20.3836 1.03884
\(386\) 0 0
\(387\) −0.597397 −0.0303674
\(388\) 0 0
\(389\) 13.3944 0.679123 0.339562 0.940584i \(-0.389721\pi\)
0.339562 + 0.940584i \(0.389721\pi\)
\(390\) 0 0
\(391\) −0.285165 −0.0144214
\(392\) 0 0
\(393\) −19.8924 −1.00344
\(394\) 0 0
\(395\) 12.2402 0.615872
\(396\) 0 0
\(397\) 37.1195 1.86297 0.931487 0.363775i \(-0.118512\pi\)
0.931487 + 0.363775i \(0.118512\pi\)
\(398\) 0 0
\(399\) 27.8188 1.39268
\(400\) 0 0
\(401\) −4.40938 −0.220194 −0.110097 0.993921i \(-0.535116\pi\)
−0.110097 + 0.993921i \(0.535116\pi\)
\(402\) 0 0
\(403\) −11.7204 −0.583834
\(404\) 0 0
\(405\) −9.72604 −0.483291
\(406\) 0 0
\(407\) −48.4705 −2.40259
\(408\) 0 0
\(409\) −10.0066 −0.494793 −0.247397 0.968914i \(-0.579575\pi\)
−0.247397 + 0.968914i \(0.579575\pi\)
\(410\) 0 0
\(411\) −5.11151 −0.252132
\(412\) 0 0
\(413\) 43.8644 2.15843
\(414\) 0 0
\(415\) 8.15495 0.400311
\(416\) 0 0
\(417\) −5.68389 −0.278341
\(418\) 0 0
\(419\) 11.9583 0.584203 0.292101 0.956387i \(-0.405646\pi\)
0.292101 + 0.956387i \(0.405646\pi\)
\(420\) 0 0
\(421\) −26.4678 −1.28996 −0.644982 0.764198i \(-0.723135\pi\)
−0.644982 + 0.764198i \(0.723135\pi\)
\(422\) 0 0
\(423\) −2.19955 −0.106946
\(424\) 0 0
\(425\) 0.285165 0.0138325
\(426\) 0 0
\(427\) 25.7699 1.24709
\(428\) 0 0
\(429\) 37.9507 1.83228
\(430\) 0 0
\(431\) 12.8006 0.616582 0.308291 0.951292i \(-0.400243\pi\)
0.308291 + 0.951292i \(0.400243\pi\)
\(432\) 0 0
\(433\) 12.5437 0.602812 0.301406 0.953496i \(-0.402544\pi\)
0.301406 + 0.953496i \(0.402544\pi\)
\(434\) 0 0
\(435\) 6.27633 0.300927
\(436\) 0 0
\(437\) −3.30952 −0.158316
\(438\) 0 0
\(439\) 37.7389 1.80118 0.900590 0.434670i \(-0.143135\pi\)
0.900590 + 0.434670i \(0.143135\pi\)
\(440\) 0 0
\(441\) 3.88628 0.185061
\(442\) 0 0
\(443\) 3.89055 0.184846 0.0924228 0.995720i \(-0.470539\pi\)
0.0924228 + 0.995720i \(0.470539\pi\)
\(444\) 0 0
\(445\) 1.98319 0.0940120
\(446\) 0 0
\(447\) −28.3618 −1.34147
\(448\) 0 0
\(449\) −4.10031 −0.193506 −0.0967528 0.995308i \(-0.530846\pi\)
−0.0967528 + 0.995308i \(0.530846\pi\)
\(450\) 0 0
\(451\) 51.5692 2.42830
\(452\) 0 0
\(453\) −4.48898 −0.210911
\(454\) 0 0
\(455\) 22.2926 1.04509
\(456\) 0 0
\(457\) 14.8783 0.695979 0.347990 0.937498i \(-0.386864\pi\)
0.347990 + 0.937498i \(0.386864\pi\)
\(458\) 0 0
\(459\) −1.40912 −0.0657720
\(460\) 0 0
\(461\) −1.90588 −0.0887655 −0.0443828 0.999015i \(-0.514132\pi\)
−0.0443828 + 0.999015i \(0.514132\pi\)
\(462\) 0 0
\(463\) −21.2271 −0.986509 −0.493255 0.869885i \(-0.664193\pi\)
−0.493255 + 0.869885i \(0.664193\pi\)
\(464\) 0 0
\(465\) −4.41932 −0.204941
\(466\) 0 0
\(467\) −12.0609 −0.558114 −0.279057 0.960275i \(-0.590022\pi\)
−0.279057 + 0.960275i \(0.590022\pi\)
\(468\) 0 0
\(469\) −52.1262 −2.40696
\(470\) 0 0
\(471\) −3.01760 −0.139044
\(472\) 0 0
\(473\) −9.85970 −0.453349
\(474\) 0 0
\(475\) 3.30952 0.151851
\(476\) 0 0
\(477\) −1.01316 −0.0463896
\(478\) 0 0
\(479\) 8.96710 0.409717 0.204859 0.978792i \(-0.434327\pi\)
0.204859 + 0.978792i \(0.434327\pi\)
\(480\) 0 0
\(481\) −53.0099 −2.41704
\(482\) 0 0
\(483\) −8.40570 −0.382473
\(484\) 0 0
\(485\) 4.33340 0.196769
\(486\) 0 0
\(487\) −23.3799 −1.05945 −0.529723 0.848171i \(-0.677704\pi\)
−0.529723 + 0.848171i \(0.677704\pi\)
\(488\) 0 0
\(489\) −8.90590 −0.402739
\(490\) 0 0
\(491\) 13.2821 0.599412 0.299706 0.954032i \(-0.403111\pi\)
0.299706 + 0.954032i \(0.403111\pi\)
\(492\) 0 0
\(493\) 0.990435 0.0446070
\(494\) 0 0
\(495\) 1.16349 0.0522952
\(496\) 0 0
\(497\) −70.9196 −3.18118
\(498\) 0 0
\(499\) 18.9496 0.848301 0.424150 0.905592i \(-0.360573\pi\)
0.424150 + 0.905592i \(0.360573\pi\)
\(500\) 0 0
\(501\) 13.2819 0.593390
\(502\) 0 0
\(503\) 30.1400 1.34388 0.671938 0.740607i \(-0.265462\pi\)
0.671938 + 0.740607i \(0.265462\pi\)
\(504\) 0 0
\(505\) −17.9203 −0.797441
\(506\) 0 0
\(507\) 18.0130 0.799985
\(508\) 0 0
\(509\) −8.77973 −0.389155 −0.194577 0.980887i \(-0.562333\pi\)
−0.194577 + 0.980887i \(0.562333\pi\)
\(510\) 0 0
\(511\) −45.9487 −2.03265
\(512\) 0 0
\(513\) −16.3537 −0.722034
\(514\) 0 0
\(515\) −17.6351 −0.777095
\(516\) 0 0
\(517\) −36.3023 −1.59657
\(518\) 0 0
\(519\) −46.0486 −2.02131
\(520\) 0 0
\(521\) 37.6420 1.64912 0.824562 0.565771i \(-0.191421\pi\)
0.824562 + 0.565771i \(0.191421\pi\)
\(522\) 0 0
\(523\) 20.7013 0.905204 0.452602 0.891713i \(-0.350496\pi\)
0.452602 + 0.891713i \(0.350496\pi\)
\(524\) 0 0
\(525\) 8.40570 0.366855
\(526\) 0 0
\(527\) −0.697390 −0.0303788
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 2.50378 0.108655
\(532\) 0 0
\(533\) 56.3988 2.44290
\(534\) 0 0
\(535\) −17.0535 −0.737287
\(536\) 0 0
\(537\) 14.0621 0.606823
\(538\) 0 0
\(539\) 64.1407 2.76274
\(540\) 0 0
\(541\) −22.2767 −0.957751 −0.478875 0.877883i \(-0.658955\pi\)
−0.478875 + 0.877883i \(0.658955\pi\)
\(542\) 0 0
\(543\) −42.9943 −1.84506
\(544\) 0 0
\(545\) −11.3174 −0.484785
\(546\) 0 0
\(547\) 33.4571 1.43052 0.715262 0.698857i \(-0.246308\pi\)
0.715262 + 0.698857i \(0.246308\pi\)
\(548\) 0 0
\(549\) 1.47094 0.0627783
\(550\) 0 0
\(551\) 11.4946 0.489687
\(552\) 0 0
\(553\) 56.9361 2.42117
\(554\) 0 0
\(555\) −19.9881 −0.848446
\(556\) 0 0
\(557\) −19.7297 −0.835974 −0.417987 0.908453i \(-0.637264\pi\)
−0.417987 + 0.908453i \(0.637264\pi\)
\(558\) 0 0
\(559\) −10.7831 −0.456076
\(560\) 0 0
\(561\) 2.25816 0.0953394
\(562\) 0 0
\(563\) 8.44680 0.355990 0.177995 0.984031i \(-0.443039\pi\)
0.177995 + 0.984031i \(0.443039\pi\)
\(564\) 0 0
\(565\) 4.82783 0.203108
\(566\) 0 0
\(567\) −45.2412 −1.89995
\(568\) 0 0
\(569\) 27.8345 1.16688 0.583442 0.812155i \(-0.301706\pi\)
0.583442 + 0.812155i \(0.301706\pi\)
\(570\) 0 0
\(571\) −17.8837 −0.748409 −0.374204 0.927346i \(-0.622084\pi\)
−0.374204 + 0.927346i \(0.622084\pi\)
\(572\) 0 0
\(573\) −10.5064 −0.438909
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −8.19106 −0.340998 −0.170499 0.985358i \(-0.554538\pi\)
−0.170499 + 0.985358i \(0.554538\pi\)
\(578\) 0 0
\(579\) −15.4219 −0.640914
\(580\) 0 0
\(581\) 37.9332 1.57373
\(582\) 0 0
\(583\) −16.7217 −0.692542
\(584\) 0 0
\(585\) 1.27246 0.0526097
\(586\) 0 0
\(587\) 39.9336 1.64824 0.824119 0.566417i \(-0.191671\pi\)
0.824119 + 0.566417i \(0.191671\pi\)
\(588\) 0 0
\(589\) −8.09365 −0.333493
\(590\) 0 0
\(591\) 39.7180 1.63378
\(592\) 0 0
\(593\) −17.4592 −0.716963 −0.358482 0.933537i \(-0.616705\pi\)
−0.358482 + 0.933537i \(0.616705\pi\)
\(594\) 0 0
\(595\) 1.32646 0.0543796
\(596\) 0 0
\(597\) 48.2080 1.97302
\(598\) 0 0
\(599\) −9.83913 −0.402016 −0.201008 0.979590i \(-0.564422\pi\)
−0.201008 + 0.979590i \(0.564422\pi\)
\(600\) 0 0
\(601\) 20.1621 0.822428 0.411214 0.911539i \(-0.365105\pi\)
0.411214 + 0.911539i \(0.365105\pi\)
\(602\) 0 0
\(603\) −2.97536 −0.121166
\(604\) 0 0
\(605\) 8.20280 0.333491
\(606\) 0 0
\(607\) −7.64121 −0.310147 −0.155074 0.987903i \(-0.549561\pi\)
−0.155074 + 0.987903i \(0.549561\pi\)
\(608\) 0 0
\(609\) 29.1947 1.18303
\(610\) 0 0
\(611\) −39.7021 −1.60618
\(612\) 0 0
\(613\) 0.518216 0.0209305 0.0104653 0.999945i \(-0.496669\pi\)
0.0104653 + 0.999945i \(0.496669\pi\)
\(614\) 0 0
\(615\) 21.2659 0.857524
\(616\) 0 0
\(617\) −22.5090 −0.906180 −0.453090 0.891465i \(-0.649678\pi\)
−0.453090 + 0.891465i \(0.649678\pi\)
\(618\) 0 0
\(619\) 15.7750 0.634052 0.317026 0.948417i \(-0.397316\pi\)
0.317026 + 0.948417i \(0.397316\pi\)
\(620\) 0 0
\(621\) 4.94142 0.198292
\(622\) 0 0
\(623\) 9.22490 0.369588
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 26.2073 1.04662
\(628\) 0 0
\(629\) −3.15421 −0.125767
\(630\) 0 0
\(631\) 36.1022 1.43721 0.718603 0.695421i \(-0.244782\pi\)
0.718603 + 0.695421i \(0.244782\pi\)
\(632\) 0 0
\(633\) −39.0022 −1.55020
\(634\) 0 0
\(635\) 7.09524 0.281566
\(636\) 0 0
\(637\) 70.1477 2.77935
\(638\) 0 0
\(639\) −4.04809 −0.160140
\(640\) 0 0
\(641\) −2.17328 −0.0858395 −0.0429198 0.999079i \(-0.513666\pi\)
−0.0429198 + 0.999079i \(0.513666\pi\)
\(642\) 0 0
\(643\) −15.5752 −0.614227 −0.307113 0.951673i \(-0.599363\pi\)
−0.307113 + 0.951673i \(0.599363\pi\)
\(644\) 0 0
\(645\) −4.06590 −0.160095
\(646\) 0 0
\(647\) 8.47998 0.333382 0.166691 0.986009i \(-0.446692\pi\)
0.166691 + 0.986009i \(0.446692\pi\)
\(648\) 0 0
\(649\) 41.3234 1.62209
\(650\) 0 0
\(651\) −20.5567 −0.805682
\(652\) 0 0
\(653\) 16.3027 0.637973 0.318986 0.947759i \(-0.396658\pi\)
0.318986 + 0.947759i \(0.396658\pi\)
\(654\) 0 0
\(655\) −11.0081 −0.430121
\(656\) 0 0
\(657\) −2.62275 −0.102323
\(658\) 0 0
\(659\) 0.674301 0.0262670 0.0131335 0.999914i \(-0.495819\pi\)
0.0131335 + 0.999914i \(0.495819\pi\)
\(660\) 0 0
\(661\) −3.55427 −0.138245 −0.0691225 0.997608i \(-0.522020\pi\)
−0.0691225 + 0.997608i \(0.522020\pi\)
\(662\) 0 0
\(663\) 2.46964 0.0959128
\(664\) 0 0
\(665\) 15.3944 0.596970
\(666\) 0 0
\(667\) −3.47320 −0.134483
\(668\) 0 0
\(669\) −9.82607 −0.379898
\(670\) 0 0
\(671\) 24.2770 0.937205
\(672\) 0 0
\(673\) 14.4874 0.558448 0.279224 0.960226i \(-0.409923\pi\)
0.279224 + 0.960226i \(0.409923\pi\)
\(674\) 0 0
\(675\) −4.94142 −0.190195
\(676\) 0 0
\(677\) −13.4408 −0.516571 −0.258285 0.966069i \(-0.583157\pi\)
−0.258285 + 0.966069i \(0.583157\pi\)
\(678\) 0 0
\(679\) 20.1570 0.773556
\(680\) 0 0
\(681\) 32.6855 1.25251
\(682\) 0 0
\(683\) 12.6694 0.484783 0.242391 0.970179i \(-0.422068\pi\)
0.242391 + 0.970179i \(0.422068\pi\)
\(684\) 0 0
\(685\) −2.82861 −0.108076
\(686\) 0 0
\(687\) 8.36374 0.319097
\(688\) 0 0
\(689\) −18.2877 −0.696707
\(690\) 0 0
\(691\) −47.0038 −1.78811 −0.894054 0.447960i \(-0.852151\pi\)
−0.894054 + 0.447960i \(0.852151\pi\)
\(692\) 0 0
\(693\) 5.41206 0.205587
\(694\) 0 0
\(695\) −3.14536 −0.119310
\(696\) 0 0
\(697\) 3.35586 0.127112
\(698\) 0 0
\(699\) 13.3505 0.504963
\(700\) 0 0
\(701\) −37.3330 −1.41005 −0.705024 0.709184i \(-0.749064\pi\)
−0.705024 + 0.709184i \(0.749064\pi\)
\(702\) 0 0
\(703\) −36.6066 −1.38064
\(704\) 0 0
\(705\) −14.9702 −0.563810
\(706\) 0 0
\(707\) −83.3571 −3.13497
\(708\) 0 0
\(709\) −38.0927 −1.43060 −0.715301 0.698817i \(-0.753710\pi\)
−0.715301 + 0.698817i \(0.753710\pi\)
\(710\) 0 0
\(711\) 3.24991 0.121881
\(712\) 0 0
\(713\) 2.44557 0.0915873
\(714\) 0 0
\(715\) 21.0012 0.785401
\(716\) 0 0
\(717\) 12.3556 0.461428
\(718\) 0 0
\(719\) 25.5206 0.951757 0.475879 0.879511i \(-0.342130\pi\)
0.475879 + 0.879511i \(0.342130\pi\)
\(720\) 0 0
\(721\) −82.0307 −3.05498
\(722\) 0 0
\(723\) 14.3686 0.534373
\(724\) 0 0
\(725\) 3.47320 0.128992
\(726\) 0 0
\(727\) 41.6377 1.54426 0.772129 0.635465i \(-0.219192\pi\)
0.772129 + 0.635465i \(0.219192\pi\)
\(728\) 0 0
\(729\) 24.2061 0.896524
\(730\) 0 0
\(731\) −0.641619 −0.0237311
\(732\) 0 0
\(733\) −26.6076 −0.982773 −0.491386 0.870942i \(-0.663510\pi\)
−0.491386 + 0.870942i \(0.663510\pi\)
\(734\) 0 0
\(735\) 26.4501 0.975626
\(736\) 0 0
\(737\) −49.1066 −1.80886
\(738\) 0 0
\(739\) −0.749723 −0.0275790 −0.0137895 0.999905i \(-0.504389\pi\)
−0.0137895 + 0.999905i \(0.504389\pi\)
\(740\) 0 0
\(741\) 28.6617 1.05291
\(742\) 0 0
\(743\) −27.3965 −1.00508 −0.502540 0.864554i \(-0.667601\pi\)
−0.502540 + 0.864554i \(0.667601\pi\)
\(744\) 0 0
\(745\) −15.6949 −0.575017
\(746\) 0 0
\(747\) 2.16523 0.0792214
\(748\) 0 0
\(749\) −79.3253 −2.89848
\(750\) 0 0
\(751\) 7.46662 0.272461 0.136230 0.990677i \(-0.456501\pi\)
0.136230 + 0.990677i \(0.456501\pi\)
\(752\) 0 0
\(753\) 52.8076 1.92442
\(754\) 0 0
\(755\) −2.48412 −0.0904063
\(756\) 0 0
\(757\) −20.1426 −0.732096 −0.366048 0.930596i \(-0.619289\pi\)
−0.366048 + 0.930596i \(0.619289\pi\)
\(758\) 0 0
\(759\) −7.91877 −0.287433
\(760\) 0 0
\(761\) −49.9203 −1.80961 −0.904804 0.425828i \(-0.859983\pi\)
−0.904804 + 0.425828i \(0.859983\pi\)
\(762\) 0 0
\(763\) −52.6436 −1.90583
\(764\) 0 0
\(765\) 0.0757143 0.00273746
\(766\) 0 0
\(767\) 45.1935 1.63184
\(768\) 0 0
\(769\) −31.7567 −1.14517 −0.572587 0.819844i \(-0.694060\pi\)
−0.572587 + 0.819844i \(0.694060\pi\)
\(770\) 0 0
\(771\) 2.71024 0.0976070
\(772\) 0 0
\(773\) 28.3113 1.01829 0.509143 0.860682i \(-0.329962\pi\)
0.509143 + 0.860682i \(0.329962\pi\)
\(774\) 0 0
\(775\) −2.44557 −0.0878475
\(776\) 0 0
\(777\) −92.9756 −3.33548
\(778\) 0 0
\(779\) 38.9469 1.39542
\(780\) 0 0
\(781\) −66.8114 −2.39070
\(782\) 0 0
\(783\) −17.1626 −0.613340
\(784\) 0 0
\(785\) −1.66989 −0.0596008
\(786\) 0 0
\(787\) 14.2157 0.506735 0.253367 0.967370i \(-0.418462\pi\)
0.253367 + 0.967370i \(0.418462\pi\)
\(788\) 0 0
\(789\) −39.0090 −1.38876
\(790\) 0 0
\(791\) 22.4569 0.798477
\(792\) 0 0
\(793\) 26.5507 0.942842
\(794\) 0 0
\(795\) −6.89562 −0.244563
\(796\) 0 0
\(797\) 4.27296 0.151356 0.0756780 0.997132i \(-0.475888\pi\)
0.0756780 + 0.997132i \(0.475888\pi\)
\(798\) 0 0
\(799\) −2.36237 −0.0835746
\(800\) 0 0
\(801\) 0.526557 0.0186050
\(802\) 0 0
\(803\) −43.2870 −1.52757
\(804\) 0 0
\(805\) −4.65156 −0.163946
\(806\) 0 0
\(807\) 13.5400 0.476629
\(808\) 0 0
\(809\) 2.97019 0.104426 0.0522132 0.998636i \(-0.483372\pi\)
0.0522132 + 0.998636i \(0.483372\pi\)
\(810\) 0 0
\(811\) 24.4381 0.858139 0.429070 0.903271i \(-0.358842\pi\)
0.429070 + 0.903271i \(0.358842\pi\)
\(812\) 0 0
\(813\) 22.9814 0.805992
\(814\) 0 0
\(815\) −4.92836 −0.172633
\(816\) 0 0
\(817\) −7.44639 −0.260516
\(818\) 0 0
\(819\) 5.91892 0.206824
\(820\) 0 0
\(821\) 7.88814 0.275298 0.137649 0.990481i \(-0.456045\pi\)
0.137649 + 0.990481i \(0.456045\pi\)
\(822\) 0 0
\(823\) 14.3154 0.499005 0.249503 0.968374i \(-0.419733\pi\)
0.249503 + 0.968374i \(0.419733\pi\)
\(824\) 0 0
\(825\) 7.91877 0.275696
\(826\) 0 0
\(827\) 22.4641 0.781153 0.390576 0.920570i \(-0.372276\pi\)
0.390576 + 0.920570i \(0.372276\pi\)
\(828\) 0 0
\(829\) 42.8763 1.48915 0.744577 0.667536i \(-0.232651\pi\)
0.744577 + 0.667536i \(0.232651\pi\)
\(830\) 0 0
\(831\) −50.4353 −1.74958
\(832\) 0 0
\(833\) 4.17395 0.144619
\(834\) 0 0
\(835\) 7.34993 0.254355
\(836\) 0 0
\(837\) 12.0846 0.417704
\(838\) 0 0
\(839\) 20.1216 0.694673 0.347337 0.937741i \(-0.387086\pi\)
0.347337 + 0.937741i \(0.387086\pi\)
\(840\) 0 0
\(841\) −16.9369 −0.584030
\(842\) 0 0
\(843\) 39.3871 1.35656
\(844\) 0 0
\(845\) 9.96805 0.342911
\(846\) 0 0
\(847\) 38.1558 1.31105
\(848\) 0 0
\(849\) −42.5086 −1.45889
\(850\) 0 0
\(851\) 11.0610 0.379167
\(852\) 0 0
\(853\) 48.2488 1.65201 0.826004 0.563664i \(-0.190609\pi\)
0.826004 + 0.563664i \(0.190609\pi\)
\(854\) 0 0
\(855\) 0.878712 0.0300513
\(856\) 0 0
\(857\) −35.6234 −1.21687 −0.608436 0.793603i \(-0.708203\pi\)
−0.608436 + 0.793603i \(0.708203\pi\)
\(858\) 0 0
\(859\) 30.4312 1.03830 0.519149 0.854684i \(-0.326249\pi\)
0.519149 + 0.854684i \(0.326249\pi\)
\(860\) 0 0
\(861\) 98.9195 3.37117
\(862\) 0 0
\(863\) 13.6755 0.465520 0.232760 0.972534i \(-0.425224\pi\)
0.232760 + 0.972534i \(0.425224\pi\)
\(864\) 0 0
\(865\) −25.4824 −0.866428
\(866\) 0 0
\(867\) −30.5733 −1.03832
\(868\) 0 0
\(869\) 53.6378 1.81954
\(870\) 0 0
\(871\) −53.7056 −1.81974
\(872\) 0 0
\(873\) 1.15056 0.0389407
\(874\) 0 0
\(875\) 4.65156 0.157251
\(876\) 0 0
\(877\) 28.4382 0.960291 0.480145 0.877189i \(-0.340584\pi\)
0.480145 + 0.877189i \(0.340584\pi\)
\(878\) 0 0
\(879\) 1.22091 0.0411804
\(880\) 0 0
\(881\) 14.0086 0.471963 0.235982 0.971758i \(-0.424170\pi\)
0.235982 + 0.971758i \(0.424170\pi\)
\(882\) 0 0
\(883\) −13.5629 −0.456429 −0.228214 0.973611i \(-0.573289\pi\)
−0.228214 + 0.973611i \(0.573289\pi\)
\(884\) 0 0
\(885\) 17.0408 0.572820
\(886\) 0 0
\(887\) −1.73459 −0.0582418 −0.0291209 0.999576i \(-0.509271\pi\)
−0.0291209 + 0.999576i \(0.509271\pi\)
\(888\) 0 0
\(889\) 33.0039 1.10692
\(890\) 0 0
\(891\) −42.6205 −1.42784
\(892\) 0 0
\(893\) −27.4168 −0.917467
\(894\) 0 0
\(895\) 7.78168 0.260113
\(896\) 0 0
\(897\) −8.66039 −0.289162
\(898\) 0 0
\(899\) −8.49396 −0.283289
\(900\) 0 0
\(901\) −1.08816 −0.0362520
\(902\) 0 0
\(903\) −18.9128 −0.629378
\(904\) 0 0
\(905\) −23.7922 −0.790880
\(906\) 0 0
\(907\) 18.2428 0.605743 0.302871 0.953031i \(-0.402055\pi\)
0.302871 + 0.953031i \(0.402055\pi\)
\(908\) 0 0
\(909\) −4.75802 −0.157814
\(910\) 0 0
\(911\) −16.9469 −0.561475 −0.280738 0.959785i \(-0.590579\pi\)
−0.280738 + 0.959785i \(0.590579\pi\)
\(912\) 0 0
\(913\) 35.7358 1.18268
\(914\) 0 0
\(915\) 10.0113 0.330962
\(916\) 0 0
\(917\) −51.2047 −1.69093
\(918\) 0 0
\(919\) −28.5266 −0.941007 −0.470503 0.882398i \(-0.655928\pi\)
−0.470503 + 0.882398i \(0.655928\pi\)
\(920\) 0 0
\(921\) 5.83933 0.192413
\(922\) 0 0
\(923\) −73.0685 −2.40508
\(924\) 0 0
\(925\) −11.0610 −0.363684
\(926\) 0 0
\(927\) −4.68231 −0.153787
\(928\) 0 0
\(929\) −19.7391 −0.647620 −0.323810 0.946122i \(-0.604964\pi\)
−0.323810 + 0.946122i \(0.604964\pi\)
\(930\) 0 0
\(931\) 48.4413 1.58760
\(932\) 0 0
\(933\) 39.4002 1.28990
\(934\) 0 0
\(935\) 1.24962 0.0408670
\(936\) 0 0
\(937\) −46.4289 −1.51677 −0.758383 0.651809i \(-0.774010\pi\)
−0.758383 + 0.651809i \(0.774010\pi\)
\(938\) 0 0
\(939\) 52.2806 1.70611
\(940\) 0 0
\(941\) 54.6408 1.78124 0.890619 0.454751i \(-0.150272\pi\)
0.890619 + 0.454751i \(0.150272\pi\)
\(942\) 0 0
\(943\) −11.7681 −0.383224
\(944\) 0 0
\(945\) −22.9853 −0.747712
\(946\) 0 0
\(947\) −23.3385 −0.758399 −0.379200 0.925315i \(-0.623801\pi\)
−0.379200 + 0.925315i \(0.623801\pi\)
\(948\) 0 0
\(949\) −47.3410 −1.53675
\(950\) 0 0
\(951\) 27.4705 0.890792
\(952\) 0 0
\(953\) 34.6233 1.12156 0.560779 0.827966i \(-0.310502\pi\)
0.560779 + 0.827966i \(0.310502\pi\)
\(954\) 0 0
\(955\) −5.81402 −0.188137
\(956\) 0 0
\(957\) 27.5035 0.889062
\(958\) 0 0
\(959\) −13.1575 −0.424876
\(960\) 0 0
\(961\) −25.0192 −0.807071
\(962\) 0 0
\(963\) −4.52789 −0.145909
\(964\) 0 0
\(965\) −8.53422 −0.274726
\(966\) 0 0
\(967\) 22.2831 0.716576 0.358288 0.933611i \(-0.383361\pi\)
0.358288 + 0.933611i \(0.383361\pi\)
\(968\) 0 0
\(969\) 1.70544 0.0547866
\(970\) 0 0
\(971\) −40.8981 −1.31248 −0.656242 0.754551i \(-0.727855\pi\)
−0.656242 + 0.754551i \(0.727855\pi\)
\(972\) 0 0
\(973\) −14.6308 −0.469042
\(974\) 0 0
\(975\) 8.66039 0.277355
\(976\) 0 0
\(977\) 9.11906 0.291744 0.145872 0.989303i \(-0.453401\pi\)
0.145872 + 0.989303i \(0.453401\pi\)
\(978\) 0 0
\(979\) 8.69052 0.277750
\(980\) 0 0
\(981\) −3.00489 −0.0959389
\(982\) 0 0
\(983\) 1.55459 0.0495838 0.0247919 0.999693i \(-0.492108\pi\)
0.0247919 + 0.999693i \(0.492108\pi\)
\(984\) 0 0
\(985\) 21.9792 0.700316
\(986\) 0 0
\(987\) −69.6347 −2.21650
\(988\) 0 0
\(989\) 2.24999 0.0715456
\(990\) 0 0
\(991\) −19.6635 −0.624631 −0.312316 0.949978i \(-0.601105\pi\)
−0.312316 + 0.949978i \(0.601105\pi\)
\(992\) 0 0
\(993\) −9.28036 −0.294503
\(994\) 0 0
\(995\) 26.6774 0.845731
\(996\) 0 0
\(997\) −21.0904 −0.667941 −0.333970 0.942584i \(-0.608389\pi\)
−0.333970 + 0.942584i \(0.608389\pi\)
\(998\) 0 0
\(999\) 54.6571 1.72927
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.cr.1.4 5
4.3 odd 2 7360.2.a.cn.1.2 5
8.3 odd 2 3680.2.a.z.1.4 yes 5
8.5 even 2 3680.2.a.v.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3680.2.a.v.1.2 5 8.5 even 2
3680.2.a.z.1.4 yes 5 8.3 odd 2
7360.2.a.cn.1.2 5 4.3 odd 2
7360.2.a.cr.1.4 5 1.1 even 1 trivial