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Properties

Label 1620.4.a.a.1.1
Level $1620$
Weight $4$
Character 1620.1
Self dual yes
Analytic conductor $95.583$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1620,4,Mod(1,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(95.5830942093\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 180)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1620.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} -7.00000 q^{7} -30.0000 q^{11} -22.0000 q^{13} +48.0000 q^{17} +68.0000 q^{19} +111.000 q^{23} +25.0000 q^{25} +87.0000 q^{29} +20.0000 q^{31} +35.0000 q^{35} +200.000 q^{37} +69.0000 q^{41} -232.000 q^{43} +243.000 q^{47} -294.000 q^{49} -498.000 q^{53} +150.000 q^{55} +66.0000 q^{59} +359.000 q^{61} +110.000 q^{65} -1063.00 q^{67} -618.000 q^{71} -532.000 q^{73} +210.000 q^{77} +410.000 q^{79} +693.000 q^{83} -240.000 q^{85} -1599.00 q^{89} +154.000 q^{91} -340.000 q^{95} +50.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 0
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −7.00000 −0.377964 −0.188982 − 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −30.0000 −0.822304 −0.411152 − 0.911567i \(-0.634873\pi\)
−0.411152 + 0.911567i \(0.634873\pi\)
\(12\) 0 0
\(13\) −22.0000 −0.469362 −0.234681 − 0.972072i \(-0.575405\pi\)
−0.234681 + 0.972072i \(0.575405\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 48.0000 0.684806 0.342403 − 0.939553i \(-0.388759\pi\)
0.342403 + 0.939553i \(0.388759\pi\)
\(18\) 0 0
\(19\) 68.0000 0.821067 0.410533 − 0.911846i \(-0.365343\pi\)
0.410533 + 0.911846i \(0.365343\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 111.000 1.00631 0.503154 − 0.864197i \(-0.332173\pi\)
0.503154 + 0.864197i \(0.332173\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 87.0000 0.557086 0.278543 − 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 0 0
\(31\) 20.0000 0.115874 0.0579372 − 0.998320i \(-0.481548\pi\)
0.0579372 + 0.998320i \(0.481548\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 35.0000 0.169031
\(36\) 0 0
\(37\) 200.000 0.888643 0.444322 − 0.895867i \(-0.353445\pi\)
0.444322 + 0.895867i \(0.353445\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 69.0000 0.262829 0.131415 − 0.991328i \(-0.458048\pi\)
0.131415 + 0.991328i \(0.458048\pi\)
\(42\) 0 0
\(43\) −232.000 −0.822783 −0.411391 − 0.911459i \(-0.634957\pi\)
−0.411391 + 0.911459i \(0.634957\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 243.000 0.754153 0.377077 − 0.926182i \(-0.376929\pi\)
0.377077 + 0.926182i \(0.376929\pi\)
\(48\) 0 0
\(49\) −294.000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −498.000 −1.29067 −0.645335 − 0.763899i \(-0.723282\pi\)
−0.645335 + 0.763899i \(0.723282\pi\)
\(54\) 0 0
\(55\) 150.000 0.367745
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 66.0000 0.145635 0.0728175 − 0.997345i \(-0.476801\pi\)
0.0728175 + 0.997345i \(0.476801\pi\)
\(60\) 0 0
\(61\) 359.000 0.753529 0.376764 − 0.926309i \(-0.377037\pi\)
0.376764 + 0.926309i \(0.377037\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 110.000 0.209905
\(66\) 0 0
\(67\) −1063.00 −1.93830 −0.969150 − 0.246471i \(-0.920729\pi\)
−0.969150 + 0.246471i \(0.920729\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −618.000 −1.03300 −0.516501 − 0.856287i \(-0.672766\pi\)
−0.516501 + 0.856287i \(0.672766\pi\)
\(72\) 0 0
\(73\) −532.000 −0.852957 −0.426479 − 0.904498i \(-0.640246\pi\)
−0.426479 + 0.904498i \(0.640246\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 210.000 0.310802
\(78\) 0 0
\(79\) 410.000 0.583906 0.291953 − 0.956433i \(-0.405695\pi\)
0.291953 + 0.956433i \(0.405695\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 693.000 0.916465 0.458233 − 0.888832i \(-0.348483\pi\)
0.458233 + 0.888832i \(0.348483\pi\)
\(84\) 0 0
\(85\) −240.000 −0.306255
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1599.00 −1.90442 −0.952212 − 0.305439i \(-0.901197\pi\)
−0.952212 + 0.305439i \(0.901197\pi\)
\(90\) 0 0
\(91\) 154.000 0.177402
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −340.000 −0.367192
\(96\) 0 0
\(97\) 50.0000 0.0523374 0.0261687 − 0.999658i \(-0.491669\pi\)
0.0261687 + 0.999658i \(0.491669\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1182.00 1.16449 0.582245 − 0.813014i \(-0.302175\pi\)
0.582245 + 0.813014i \(0.302175\pi\)
\(102\) 0 0
\(103\) −1576.00 −1.50765 −0.753825 − 0.657076i \(-0.771793\pi\)
−0.753825 + 0.657076i \(0.771793\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1023.00 0.924272 0.462136 − 0.886809i \(-0.347083\pi\)
0.462136 + 0.886809i \(0.347083\pi\)
\(108\) 0 0
\(109\) −1051.00 −0.923555 −0.461778 − 0.886996i \(-0.652788\pi\)
−0.461778 + 0.886996i \(0.652788\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 864.000 0.719277 0.359638 − 0.933092i \(-0.382900\pi\)
0.359638 + 0.933092i \(0.382900\pi\)
\(114\) 0 0
\(115\) −555.000 −0.450035
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −336.000 −0.258833
\(120\) 0 0
\(121\) −431.000 −0.323817
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1991.00 1.39112 0.695562 − 0.718466i \(-0.255156\pi\)
0.695562 + 0.718466i \(0.255156\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1254.00 −0.836355 −0.418177 − 0.908365i \(-0.637331\pi\)
−0.418177 + 0.908365i \(0.637331\pi\)
\(132\) 0 0
\(133\) −476.000 −0.310334
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1596.00 −0.995295 −0.497648 − 0.867379i \(-0.665803\pi\)
−0.497648 + 0.867379i \(0.665803\pi\)
\(138\) 0 0
\(139\) 1280.00 0.781066 0.390533 − 0.920589i \(-0.372291\pi\)
0.390533 + 0.920589i \(0.372291\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 660.000 0.385958
\(144\) 0 0
\(145\) −435.000 −0.249136
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2721.00 1.49606 0.748030 − 0.663665i \(-0.231000\pi\)
0.748030 + 0.663665i \(0.231000\pi\)
\(150\) 0 0
\(151\) −2782.00 −1.49931 −0.749655 − 0.661828i \(-0.769781\pi\)
−0.749655 + 0.661828i \(0.769781\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −100.000 −0.0518206
\(156\) 0 0
\(157\) −2986.00 −1.51789 −0.758945 − 0.651155i \(-0.774285\pi\)
−0.758945 + 0.651155i \(0.774285\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −777.000 −0.380349
\(162\) 0 0
\(163\) −1132.00 −0.543958 −0.271979 − 0.962303i \(-0.587678\pi\)
−0.271979 + 0.962303i \(0.587678\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1845.00 −0.854912 −0.427456 − 0.904036i \(-0.640590\pi\)
−0.427456 + 0.904036i \(0.640590\pi\)
\(168\) 0 0
\(169\) −1713.00 −0.779700
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1080.00 −0.474629 −0.237315 − 0.971433i \(-0.576267\pi\)
−0.237315 + 0.971433i \(0.576267\pi\)
\(174\) 0 0
\(175\) −175.000 −0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 474.000 0.197924 0.0989621 − 0.995091i \(-0.468448\pi\)
0.0989621 + 0.995091i \(0.468448\pi\)
\(180\) 0 0
\(181\) −3895.00 −1.59952 −0.799760 − 0.600320i \(-0.795040\pi\)
−0.799760 + 0.600320i \(0.795040\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1000.00 −0.397413
\(186\) 0 0
\(187\) −1440.00 −0.563119
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 156.000 0.0590982 0.0295491 − 0.999563i \(-0.490593\pi\)
0.0295491 + 0.999563i \(0.490593\pi\)
\(192\) 0 0
\(193\) 818.000 0.305083 0.152541 − 0.988297i \(-0.451254\pi\)
0.152541 + 0.988297i \(0.451254\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2244.00 0.811565 0.405783 − 0.913970i \(-0.366999\pi\)
0.405783 + 0.913970i \(0.366999\pi\)
\(198\) 0 0
\(199\) −1912.00 −0.681096 −0.340548 − 0.940227i \(-0.610613\pi\)
−0.340548 + 0.940227i \(0.610613\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −609.000 −0.210559
\(204\) 0 0
\(205\) −345.000 −0.117541
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2040.00 −0.675166
\(210\) 0 0
\(211\) 5846.00 1.90737 0.953685 − 0.300806i \(-0.0972556\pi\)
0.953685 + 0.300806i \(0.0972556\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1160.00 0.367960
\(216\) 0 0
\(217\) −140.000 −0.0437964
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1056.00 −0.321422
\(222\) 0 0
\(223\) −1087.00 −0.326417 −0.163208 − 0.986592i \(-0.552184\pi\)
−0.163208 + 0.986592i \(0.552184\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4356.00 −1.27365 −0.636824 − 0.771010i \(-0.719752\pi\)
−0.636824 + 0.771010i \(0.719752\pi\)
\(228\) 0 0
\(229\) −5569.00 −1.60703 −0.803515 − 0.595284i \(-0.797039\pi\)
−0.803515 + 0.595284i \(0.797039\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2580.00 0.725414 0.362707 − 0.931903i \(-0.381853\pi\)
0.362707 + 0.931903i \(0.381853\pi\)
\(234\) 0 0
\(235\) −1215.00 −0.337267
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3600.00 −0.974329 −0.487165 − 0.873310i \(-0.661969\pi\)
−0.487165 + 0.873310i \(0.661969\pi\)
\(240\) 0 0
\(241\) 173.000 0.0462403 0.0231201 − 0.999733i \(-0.492640\pi\)
0.0231201 + 0.999733i \(0.492640\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1470.00 0.383326
\(246\) 0 0
\(247\) −1496.00 −0.385377
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 708.000 0.178042 0.0890210 − 0.996030i \(-0.471626\pi\)
0.0890210 + 0.996030i \(0.471626\pi\)
\(252\) 0 0
\(253\) −3330.00 −0.827491
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2322.00 0.563589 0.281795 − 0.959475i \(-0.409070\pi\)
0.281795 + 0.959475i \(0.409070\pi\)
\(258\) 0 0
\(259\) −1400.00 −0.335876
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2208.00 0.517685 0.258842 − 0.965920i \(-0.416659\pi\)
0.258842 + 0.965920i \(0.416659\pi\)
\(264\) 0 0
\(265\) 2490.00 0.577206
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2481.00 0.562339 0.281170 − 0.959658i \(-0.409278\pi\)
0.281170 + 0.959658i \(0.409278\pi\)
\(270\) 0 0
\(271\) −7516.00 −1.68474 −0.842370 − 0.538900i \(-0.818840\pi\)
−0.842370 + 0.538900i \(0.818840\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −750.000 −0.164461
\(276\) 0 0
\(277\) 344.000 0.0746172 0.0373086 − 0.999304i \(-0.488122\pi\)
0.0373086 + 0.999304i \(0.488122\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 7593.00 1.61196 0.805979 − 0.591944i \(-0.201639\pi\)
0.805979 + 0.591944i \(0.201639\pi\)
\(282\) 0 0
\(283\) 2657.00 0.558100 0.279050 − 0.960277i \(-0.409981\pi\)
0.279050 + 0.960277i \(0.409981\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −483.000 −0.0993400
\(288\) 0 0
\(289\) −2609.00 −0.531040
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7392.00 1.47387 0.736937 − 0.675961i \(-0.236271\pi\)
0.736937 + 0.675961i \(0.236271\pi\)
\(294\) 0 0
\(295\) −330.000 −0.0651300
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2442.00 −0.472323
\(300\) 0 0
\(301\) 1624.00 0.310983
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1795.00 −0.336988
\(306\) 0 0
\(307\) −3877.00 −0.720756 −0.360378 − 0.932806i \(-0.617352\pi\)
−0.360378 + 0.932806i \(0.617352\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5772.00 −1.05241 −0.526206 − 0.850357i \(-0.676386\pi\)
−0.526206 + 0.850357i \(0.676386\pi\)
\(312\) 0 0
\(313\) −1438.00 −0.259682 −0.129841 − 0.991535i \(-0.541447\pi\)
−0.129841 + 0.991535i \(0.541447\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6414.00 −1.13642 −0.568212 − 0.822883i \(-0.692364\pi\)
−0.568212 + 0.822883i \(0.692364\pi\)
\(318\) 0 0
\(319\) −2610.00 −0.458094
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3264.00 0.562272
\(324\) 0 0
\(325\) −550.000 −0.0938723
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1701.00 −0.285043
\(330\) 0 0
\(331\) −11614.0 −1.92859 −0.964295 − 0.264831i \(-0.914684\pi\)
−0.964295 + 0.264831i \(0.914684\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5315.00 0.866834
\(336\) 0 0
\(337\) −9304.00 −1.50392 −0.751960 − 0.659209i \(-0.770891\pi\)
−0.751960 + 0.659209i \(0.770891\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −600.000 −0.0952839
\(342\) 0 0
\(343\) 4459.00 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9828.00 1.52045 0.760223 − 0.649662i \(-0.225090\pi\)
0.760223 + 0.649662i \(0.225090\pi\)
\(348\) 0 0
\(349\) −1573.00 −0.241263 −0.120631 − 0.992697i \(-0.538492\pi\)
−0.120631 + 0.992697i \(0.538492\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3864.00 −0.582606 −0.291303 − 0.956631i \(-0.594089\pi\)
−0.291303 + 0.956631i \(0.594089\pi\)
\(354\) 0 0
\(355\) 3090.00 0.461972
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7596.00 1.11672 0.558359 − 0.829600i \(-0.311431\pi\)
0.558359 + 0.829600i \(0.311431\pi\)
\(360\) 0 0
\(361\) −2235.00 −0.325849
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2660.00 0.381454
\(366\) 0 0
\(367\) −3016.00 −0.428975 −0.214488 − 0.976727i \(-0.568808\pi\)
−0.214488 + 0.976727i \(0.568808\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3486.00 0.487828
\(372\) 0 0
\(373\) −9598.00 −1.33235 −0.666174 − 0.745797i \(-0.732069\pi\)
−0.666174 + 0.745797i \(0.732069\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1914.00 −0.261475
\(378\) 0 0
\(379\) 12926.0 1.75188 0.875942 − 0.482416i \(-0.160241\pi\)
0.875942 + 0.482416i \(0.160241\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9012.00 −1.20233 −0.601164 − 0.799126i \(-0.705296\pi\)
−0.601164 + 0.799126i \(0.705296\pi\)
\(384\) 0 0
\(385\) −1050.00 −0.138995
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9015.00 −1.17501 −0.587505 − 0.809221i \(-0.699890\pi\)
−0.587505 + 0.809221i \(0.699890\pi\)
\(390\) 0 0
\(391\) 5328.00 0.689127
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2050.00 −0.261131
\(396\) 0 0
\(397\) −3094.00 −0.391142 −0.195571 − 0.980690i \(-0.562656\pi\)
−0.195571 + 0.980690i \(0.562656\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12378.0 −1.54147 −0.770733 − 0.637158i \(-0.780110\pi\)
−0.770733 + 0.637158i \(0.780110\pi\)
\(402\) 0 0
\(403\) −440.000 −0.0543870
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6000.00 −0.730735
\(408\) 0 0
\(409\) −8890.00 −1.07477 −0.537387 − 0.843336i \(-0.680588\pi\)
−0.537387 + 0.843336i \(0.680588\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −462.000 −0.0550449
\(414\) 0 0
\(415\) −3465.00 −0.409856
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8118.00 0.946516 0.473258 − 0.880924i \(-0.343078\pi\)
0.473258 + 0.880924i \(0.343078\pi\)
\(420\) 0 0
\(421\) 2738.00 0.316964 0.158482 − 0.987362i \(-0.449340\pi\)
0.158482 + 0.987362i \(0.449340\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1200.00 0.136961
\(426\) 0 0
\(427\) −2513.00 −0.284807
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −16134.0 −1.80313 −0.901563 − 0.432648i \(-0.857579\pi\)
−0.901563 + 0.432648i \(0.857579\pi\)
\(432\) 0 0
\(433\) 6608.00 0.733395 0.366698 − 0.930340i \(-0.380488\pi\)
0.366698 + 0.930340i \(0.380488\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7548.00 0.826247
\(438\) 0 0
\(439\) 6428.00 0.698842 0.349421 − 0.936966i \(-0.386378\pi\)
0.349421 + 0.936966i \(0.386378\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10899.0 1.16891 0.584455 − 0.811426i \(-0.301308\pi\)
0.584455 + 0.811426i \(0.301308\pi\)
\(444\) 0 0
\(445\) 7995.00 0.851684
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −11610.0 −1.22029 −0.610145 − 0.792290i \(-0.708889\pi\)
−0.610145 + 0.792290i \(0.708889\pi\)
\(450\) 0 0
\(451\) −2070.00 −0.216125
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −770.000 −0.0793366
\(456\) 0 0
\(457\) 14600.0 1.49444 0.747220 − 0.664577i \(-0.231388\pi\)
0.747220 + 0.664577i \(0.231388\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5793.00 0.585264 0.292632 − 0.956225i \(-0.405469\pi\)
0.292632 + 0.956225i \(0.405469\pi\)
\(462\) 0 0
\(463\) −5692.00 −0.571338 −0.285669 − 0.958328i \(-0.592216\pi\)
−0.285669 + 0.958328i \(0.592216\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6708.00 −0.664688 −0.332344 − 0.943158i \(-0.607839\pi\)
−0.332344 + 0.943158i \(0.607839\pi\)
\(468\) 0 0
\(469\) 7441.00 0.732609
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6960.00 0.676577
\(474\) 0 0
\(475\) 1700.00 0.164213
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3150.00 0.300474 0.150237 − 0.988650i \(-0.451996\pi\)
0.150237 + 0.988650i \(0.451996\pi\)
\(480\) 0 0
\(481\) −4400.00 −0.417095
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −250.000 −0.0234060
\(486\) 0 0
\(487\) 11768.0 1.09499 0.547494 − 0.836810i \(-0.315582\pi\)
0.547494 + 0.836810i \(0.315582\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7404.00 −0.680525 −0.340263 − 0.940330i \(-0.610516\pi\)
−0.340263 + 0.940330i \(0.610516\pi\)
\(492\) 0 0
\(493\) 4176.00 0.381496
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4326.00 0.390438
\(498\) 0 0
\(499\) −4336.00 −0.388990 −0.194495 − 0.980904i \(-0.562307\pi\)
−0.194495 + 0.980904i \(0.562307\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 3789.00 0.335871 0.167936 − 0.985798i \(-0.446290\pi\)
0.167936 + 0.985798i \(0.446290\pi\)
\(504\) 0 0
\(505\) −5910.00 −0.520775
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1101.00 −0.0958762 −0.0479381 − 0.998850i \(-0.515265\pi\)
−0.0479381 + 0.998850i \(0.515265\pi\)
\(510\) 0 0
\(511\) 3724.00 0.322388
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7880.00 0.674241
\(516\) 0 0
\(517\) −7290.00 −0.620143
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12813.0 −1.07744 −0.538721 − 0.842484i \(-0.681092\pi\)
−0.538721 + 0.842484i \(0.681092\pi\)
\(522\) 0 0
\(523\) 9359.00 0.782487 0.391243 − 0.920287i \(-0.372045\pi\)
0.391243 + 0.920287i \(0.372045\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 960.000 0.0793515
\(528\) 0 0
\(529\) 154.000 0.0126572
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1518.00 −0.123362
\(534\) 0 0
\(535\) −5115.00 −0.413347
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8820.00 0.704832
\(540\) 0 0
\(541\) −10807.0 −0.858834 −0.429417 − 0.903106i \(-0.641281\pi\)
−0.429417 + 0.903106i \(0.641281\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5255.00 0.413027
\(546\) 0 0
\(547\) 2591.00 0.202529 0.101264 − 0.994860i \(-0.467711\pi\)
0.101264 + 0.994860i \(0.467711\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5916.00 0.457405
\(552\) 0 0
\(553\) −2870.00 −0.220696
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19662.0 −1.49570 −0.747851 − 0.663867i \(-0.768914\pi\)
−0.747851 + 0.663867i \(0.768914\pi\)
\(558\) 0 0
\(559\) 5104.00 0.386183
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9063.00 0.678437 0.339218 − 0.940708i \(-0.389837\pi\)
0.339218 + 0.940708i \(0.389837\pi\)
\(564\) 0 0
\(565\) −4320.00 −0.321670
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16554.0 1.21965 0.609824 − 0.792537i \(-0.291240\pi\)
0.609824 + 0.792537i \(0.291240\pi\)
\(570\) 0 0
\(571\) 26552.0 1.94600 0.973001 − 0.230803i \(-0.0741352\pi\)
0.973001 + 0.230803i \(0.0741352\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2775.00 0.201262
\(576\) 0 0
\(577\) 17846.0 1.28759 0.643794 − 0.765199i \(-0.277359\pi\)
0.643794 + 0.765199i \(0.277359\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4851.00 −0.346391
\(582\) 0 0
\(583\) 14940.0 1.06132
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14469.0 −1.01738 −0.508688 − 0.860951i \(-0.669869\pi\)
−0.508688 + 0.860951i \(0.669869\pi\)
\(588\) 0 0
\(589\) 1360.00 0.0951406
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5592.00 0.387244 0.193622 − 0.981076i \(-0.437976\pi\)
0.193622 + 0.981076i \(0.437976\pi\)
\(594\) 0 0
\(595\) 1680.00 0.115753
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2346.00 −0.160025 −0.0800125 − 0.996794i \(-0.525496\pi\)
−0.0800125 + 0.996794i \(0.525496\pi\)
\(600\) 0 0
\(601\) −6262.00 −0.425012 −0.212506 − 0.977160i \(-0.568163\pi\)
−0.212506 + 0.977160i \(0.568163\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2155.00 0.144815
\(606\) 0 0
\(607\) 5411.00 0.361822 0.180911 − 0.983500i \(-0.442095\pi\)
0.180911 + 0.983500i \(0.442095\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5346.00 −0.353971
\(612\) 0 0
\(613\) −23176.0 −1.52703 −0.763515 − 0.645790i \(-0.776528\pi\)
−0.763515 + 0.645790i \(0.776528\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4404.00 −0.287356 −0.143678 − 0.989625i \(-0.545893\pi\)
−0.143678 + 0.989625i \(0.545893\pi\)
\(618\) 0 0
\(619\) 13544.0 0.879450 0.439725 − 0.898133i \(-0.355076\pi\)
0.439725 + 0.898133i \(0.355076\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11193.0 0.719804
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9600.00 0.608549
\(630\) 0 0
\(631\) 14240.0 0.898392 0.449196 − 0.893433i \(-0.351710\pi\)
0.449196 + 0.893433i \(0.351710\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9955.00 −0.622129
\(636\) 0 0
\(637\) 6468.00 0.402310
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −11199.0 −0.690068 −0.345034 − 0.938590i \(-0.612133\pi\)
−0.345034 + 0.938590i \(0.612133\pi\)
\(642\) 0 0
\(643\) 8867.00 0.543826 0.271913 − 0.962322i \(-0.412344\pi\)
0.271913 + 0.962322i \(0.412344\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24363.0 1.48038 0.740192 − 0.672396i \(-0.234735\pi\)
0.740192 + 0.672396i \(0.234735\pi\)
\(648\) 0 0
\(649\) −1980.00 −0.119756
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17328.0 1.03843 0.519217 − 0.854643i \(-0.326224\pi\)
0.519217 + 0.854643i \(0.326224\pi\)
\(654\) 0 0
\(655\) 6270.00 0.374029
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −20256.0 −1.19736 −0.598681 − 0.800987i \(-0.704308\pi\)
−0.598681 + 0.800987i \(0.704308\pi\)
\(660\) 0 0
\(661\) 12410.0 0.730247 0.365123 − 0.930959i \(-0.381027\pi\)
0.365123 + 0.930959i \(0.381027\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2380.00 0.138786
\(666\) 0 0
\(667\) 9657.00 0.560600
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −10770.0 −0.619629
\(672\) 0 0
\(673\) −23134.0 −1.32504 −0.662519 − 0.749045i \(-0.730512\pi\)
−0.662519 + 0.749045i \(0.730512\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −21750.0 −1.23474 −0.617371 − 0.786672i \(-0.711802\pi\)
−0.617371 + 0.786672i \(0.711802\pi\)
\(678\) 0 0
\(679\) −350.000 −0.0197817
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 13284.0 0.744214 0.372107 − 0.928190i \(-0.378635\pi\)
0.372107 + 0.928190i \(0.378635\pi\)
\(684\) 0 0
\(685\) 7980.00 0.445110
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 10956.0 0.605792
\(690\) 0 0
\(691\) 9650.00 0.531264 0.265632 − 0.964075i \(-0.414419\pi\)
0.265632 + 0.964075i \(0.414419\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6400.00 −0.349303
\(696\) 0 0
\(697\) 3312.00 0.179987
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 519.000 0.0279634 0.0139817 − 0.999902i \(-0.495549\pi\)
0.0139817 + 0.999902i \(0.495549\pi\)
\(702\) 0 0
\(703\) 13600.0 0.729635
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8274.00 −0.440135
\(708\) 0 0
\(709\) −10345.0 −0.547976 −0.273988 − 0.961733i \(-0.588343\pi\)
−0.273988 + 0.961733i \(0.588343\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2220.00 0.116605
\(714\) 0 0
\(715\) −3300.00 −0.172606
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2502.00 0.129776 0.0648879 − 0.997893i \(-0.479331\pi\)
0.0648879 + 0.997893i \(0.479331\pi\)
\(720\) 0 0
\(721\) 11032.0 0.569838
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2175.00 0.111417
\(726\) 0 0
\(727\) −2653.00 −0.135343 −0.0676715 − 0.997708i \(-0.521557\pi\)
−0.0676715 + 0.997708i \(0.521557\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11136.0 −0.563447
\(732\) 0 0
\(733\) 31142.0 1.56924 0.784622 − 0.619974i \(-0.212857\pi\)
0.784622 + 0.619974i \(0.212857\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31890.0 1.59387
\(738\) 0 0
\(739\) −10042.0 −0.499866 −0.249933 − 0.968263i \(-0.580409\pi\)
−0.249933 + 0.968263i \(0.580409\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 20439.0 1.00920 0.504599 − 0.863354i \(-0.331640\pi\)
0.504599 + 0.863354i \(0.331640\pi\)
\(744\) 0 0
\(745\) −13605.0 −0.669059
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7161.00 −0.349342
\(750\) 0 0
\(751\) 24014.0 1.16682 0.583411 − 0.812177i \(-0.301718\pi\)
0.583411 + 0.812177i \(0.301718\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 13910.0 0.670512
\(756\) 0 0
\(757\) −10630.0 −0.510375 −0.255188 − 0.966892i \(-0.582137\pi\)
−0.255188 + 0.966892i \(0.582137\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −24345.0 −1.15967 −0.579833 − 0.814735i \(-0.696882\pi\)
−0.579833 + 0.814735i \(0.696882\pi\)
\(762\) 0 0
\(763\) 7357.00 0.349071
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1452.00 −0.0683555
\(768\) 0 0
\(769\) 34781.0 1.63099 0.815497 − 0.578761i \(-0.196464\pi\)
0.815497 + 0.578761i \(0.196464\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 29232.0 1.36016 0.680079 − 0.733139i \(-0.261946\pi\)
0.680079 + 0.733139i \(0.261946\pi\)
\(774\) 0 0
\(775\) 500.000 0.0231749
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4692.00 0.215800
\(780\) 0 0
\(781\) 18540.0 0.849441
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14930.0 0.678821
\(786\) 0 0
\(787\) 4220.00 0.191139 0.0955697 − 0.995423i \(-0.469533\pi\)
0.0955697 + 0.995423i \(0.469533\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6048.00 −0.271861
\(792\) 0 0
\(793\) −7898.00 −0.353677
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −35298.0 −1.56878 −0.784391 − 0.620267i \(-0.787024\pi\)
−0.784391 + 0.620267i \(0.787024\pi\)
\(798\) 0 0
\(799\) 11664.0 0.516449
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 15960.0 0.701390
\(804\) 0 0
\(805\) 3885.00 0.170097
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −39966.0 −1.73687 −0.868436 − 0.495801i \(-0.834875\pi\)
−0.868436 + 0.495801i \(0.834875\pi\)
\(810\) 0 0
\(811\) 14438.0 0.625138 0.312569 − 0.949895i \(-0.398810\pi\)
0.312569 + 0.949895i \(0.398810\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 5660.00 0.243265
\(816\) 0 0
\(817\) −15776.0 −0.675560
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15657.0 −0.665570 −0.332785 − 0.943003i \(-0.607988\pi\)
−0.332785 + 0.943003i \(0.607988\pi\)
\(822\) 0 0
\(823\) 16673.0 0.706178 0.353089 − 0.935590i \(-0.385131\pi\)
0.353089 + 0.935590i \(0.385131\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −17871.0 −0.751434 −0.375717 − 0.926735i \(-0.622603\pi\)
−0.375717 + 0.926735i \(0.622603\pi\)
\(828\) 0 0
\(829\) −21163.0 −0.886636 −0.443318 − 0.896364i \(-0.646199\pi\)
−0.443318 + 0.896364i \(0.646199\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −14112.0 −0.586977
\(834\) 0 0
\(835\) 9225.00 0.382328
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −900.000 −0.0370339 −0.0185170 − 0.999829i \(-0.505894\pi\)
−0.0185170 + 0.999829i \(0.505894\pi\)
\(840\) 0 0
\(841\) −16820.0 −0.689655
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8565.00 0.348692
\(846\) 0 0
\(847\) 3017.00 0.122391
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 22200.0 0.894249
\(852\) 0 0
\(853\) 20798.0 0.834830 0.417415 − 0.908716i \(-0.362936\pi\)
0.417415 + 0.908716i \(0.362936\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 54.0000 0.00215240 0.00107620 − 0.999999i \(-0.499657\pi\)
0.00107620 + 0.999999i \(0.499657\pi\)
\(858\) 0 0
\(859\) 41690.0 1.65593 0.827965 − 0.560779i \(-0.189498\pi\)
0.827965 + 0.560779i \(0.189498\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −26115.0 −1.03009 −0.515043 − 0.857164i \(-0.672224\pi\)
−0.515043 + 0.857164i \(0.672224\pi\)
\(864\) 0 0
\(865\) 5400.00 0.212261
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −12300.0 −0.480148
\(870\) 0 0
\(871\) 23386.0 0.909764
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 875.000 0.0338062
\(876\) 0 0
\(877\) −4318.00 −0.166258 −0.0831291 − 0.996539i \(-0.526491\pi\)
−0.0831291 + 0.996539i \(0.526491\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 16485.0 0.630413 0.315206 − 0.949023i \(-0.397926\pi\)
0.315206 + 0.949023i \(0.397926\pi\)
\(882\) 0 0
\(883\) 17267.0 0.658076 0.329038 − 0.944317i \(-0.393276\pi\)
0.329038 + 0.944317i \(0.393276\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −6276.00 −0.237573 −0.118787 − 0.992920i \(-0.537900\pi\)
−0.118787 + 0.992920i \(0.537900\pi\)
\(888\) 0 0
\(889\) −13937.0 −0.525795
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 16524.0 0.619210
\(894\) 0 0
\(895\) −2370.00 −0.0885144
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1740.00 0.0645520
\(900\) 0 0
\(901\) −23904.0 −0.883860
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 19475.0 0.715327
\(906\) 0 0
\(907\) 38633.0 1.41432 0.707160 − 0.707054i \(-0.249976\pi\)
0.707160 + 0.707054i \(0.249976\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −53586.0 −1.94883 −0.974415 − 0.224758i \(-0.927841\pi\)
−0.974415 + 0.224758i \(0.927841\pi\)
\(912\) 0 0
\(913\) −20790.0 −0.753613
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8778.00 0.316112
\(918\) 0 0
\(919\) −16486.0 −0.591755 −0.295878 − 0.955226i \(-0.595612\pi\)
−0.295878 + 0.955226i \(0.595612\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 13596.0 0.484851
\(924\) 0 0
\(925\) 5000.00 0.177729
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 18054.0 0.637602 0.318801 − 0.947822i \(-0.396720\pi\)
0.318801 + 0.947822i \(0.396720\pi\)
\(930\) 0 0
\(931\) −19992.0 −0.703772
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 7200.00 0.251834
\(936\) 0 0
\(937\) 30728.0 1.07133 0.535667 − 0.844429i \(-0.320060\pi\)
0.535667 + 0.844429i \(0.320060\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −17295.0 −0.599151 −0.299575 − 0.954073i \(-0.596845\pi\)
−0.299575 + 0.954073i \(0.596845\pi\)
\(942\) 0 0
\(943\) 7659.00 0.264487
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 32805.0 1.12568 0.562840 − 0.826566i \(-0.309709\pi\)
0.562840 + 0.826566i \(0.309709\pi\)
\(948\) 0 0
\(949\) 11704.0 0.400346
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 55962.0 1.90219 0.951095 − 0.308899i \(-0.0999604\pi\)
0.951095 + 0.308899i \(0.0999604\pi\)
\(954\) 0 0
\(955\) −780.000 −0.0264295
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 11172.0 0.376186
\(960\) 0 0
\(961\) −29391.0 −0.986573
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −4090.00 −0.136437
\(966\) 0 0
\(967\) 30653.0 1.01937 0.509687 − 0.860360i \(-0.329761\pi\)
0.509687 + 0.860360i \(0.329761\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −28008.0 −0.925664 −0.462832 − 0.886446i \(-0.653167\pi\)
−0.462832 + 0.886446i \(0.653167\pi\)
\(972\) 0 0
\(973\) −8960.00 −0.295215
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −39642.0 −1.29812 −0.649058 − 0.760739i \(-0.724837\pi\)
−0.649058 + 0.760739i \(0.724837\pi\)
\(978\) 0 0
\(979\) 47970.0 1.56601
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 33807.0 1.09692 0.548462 − 0.836176i \(-0.315214\pi\)
0.548462 + 0.836176i \(0.315214\pi\)
\(984\) 0 0
\(985\) −11220.0 −0.362943
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −25752.0 −0.827974
\(990\) 0 0
\(991\) 7082.00 0.227010 0.113505 − 0.993537i \(-0.463792\pi\)
0.113505 + 0.993537i \(0.463792\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 9560.00 0.304595
\(996\) 0 0
\(997\) −43090.0 −1.36878 −0.684390 − 0.729116i \(-0.739931\pi\)
−0.684390 + 0.729116i \(0.739931\pi\)
\(998\) 0 0
\(999\) 0 0
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 1620.4.a.a.1.1 1
3.2 odd 2 1620.4.a.b.1.1 1
9.2 odd 6 540.4.i.a.361.1 2
9.4 even 3 180.4.i.a.61.1 ✓ 2
9.5 odd 6 540.4.i.a.181.1 2
9.7 even 3 180.4.i.a.121.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.4.i.a.61.1 ✓ 2 9.4 even 3
180.4.i.a.121.1 yes 2 9.7 even 3
540.4.i.a.181.1 2 9.5 odd 6
540.4.i.a.361.1 2 9.2 odd 6
1620.4.a.a.1.1 1 1.1 even 1 trivial
1620.4.a.b.1.1 1 3.2 odd 2