Properties

Label 2916.3.c.b.1457.10
Level $2916$
Weight $3$
Character 2916.1457
Analytic conductor $79.455$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2916,3,Mod(1457,2916)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2916, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2916.1457");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2916 = 2^{2} \cdot 3^{6} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2916.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(79.4552450875\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1457.10
Character \(\chi\) \(=\) 2916.1457
Dual form 2916.3.c.b.1457.27

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.19339i q^{5} -11.8514 q^{7} +O(q^{10})\) \(q-4.19339i q^{5} -11.8514 q^{7} -11.9234i q^{11} -2.47565 q^{13} -13.8527i q^{17} -3.77921 q^{19} +26.8663i q^{23} +7.41551 q^{25} -41.2471i q^{29} -34.8965 q^{31} +49.6975i q^{35} -67.0616 q^{37} -5.08829i q^{41} -46.3918 q^{43} -93.2950i q^{47} +91.4559 q^{49} -51.4760i q^{53} -49.9992 q^{55} +14.7036i q^{59} +51.2165 q^{61} +10.3814i q^{65} +13.5770 q^{67} -32.3246i q^{71} +40.6051 q^{73} +141.309i q^{77} +74.2963 q^{79} +153.301i q^{83} -58.0899 q^{85} +20.8675i q^{89} +29.3399 q^{91} +15.8477i q^{95} -47.7160 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 180 q^{25} + 252 q^{49} + 18 q^{61} - 90 q^{67} + 126 q^{73} - 198 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times\).

\(n\) \(1459\) \(2189\)
\(\chi(n)\) \(1\) \(-1\)

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
\(5\) − 4.19339i − 0.838677i −0.907830 0.419339i \(-0.862262\pi\)
0.907830 0.419339i \(-0.137738\pi\)
\(6\) 0 0
\(7\) −11.8514 −1.69306 −0.846529 0.532342i \(-0.821312\pi\)
−0.846529 + 0.532342i \(0.821312\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 11.9234i − 1.08394i −0.840397 0.541971i \(-0.817678\pi\)
0.840397 0.541971i \(-0.182322\pi\)
\(12\) 0 0
\(13\) −2.47565 −0.190435 −0.0952173 0.995457i \(-0.530355\pi\)
−0.0952173 + 0.995457i \(0.530355\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 13.8527i − 0.814867i −0.913235 0.407433i \(-0.866424\pi\)
0.913235 0.407433i \(-0.133576\pi\)
\(18\) 0 0
\(19\) −3.77921 −0.198906 −0.0994528 0.995042i \(-0.531709\pi\)
−0.0994528 + 0.995042i \(0.531709\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 26.8663i 1.16810i 0.811717 + 0.584051i \(0.198533\pi\)
−0.811717 + 0.584051i \(0.801467\pi\)
\(24\) 0 0
\(25\) 7.41551 0.296620
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 41.2471i − 1.42232i −0.703033 0.711158i \(-0.748171\pi\)
0.703033 0.711158i \(-0.251829\pi\)
\(30\) 0 0
\(31\) −34.8965 −1.12569 −0.562847 0.826561i \(-0.690294\pi\)
−0.562847 + 0.826561i \(0.690294\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 49.6975i 1.41993i
\(36\) 0 0
\(37\) −67.0616 −1.81248 −0.906238 0.422767i \(-0.861059\pi\)
−0.906238 + 0.422767i \(0.861059\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 5.08829i − 0.124105i −0.998073 0.0620524i \(-0.980235\pi\)
0.998073 0.0620524i \(-0.0197646\pi\)
\(42\) 0 0
\(43\) −46.3918 −1.07888 −0.539440 0.842024i \(-0.681364\pi\)
−0.539440 + 0.842024i \(0.681364\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 93.2950i − 1.98500i −0.122249 0.992499i \(-0.539011\pi\)
0.122249 0.992499i \(-0.460989\pi\)
\(48\) 0 0
\(49\) 91.4559 1.86645
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 51.4760i − 0.971245i −0.874169 0.485622i \(-0.838593\pi\)
0.874169 0.485622i \(-0.161407\pi\)
\(54\) 0 0
\(55\) −49.9992 −0.909077
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 14.7036i 0.249214i 0.992206 + 0.124607i \(0.0397670\pi\)
−0.992206 + 0.124607i \(0.960233\pi\)
\(60\) 0 0
\(61\) 51.2165 0.839615 0.419807 0.907613i \(-0.362098\pi\)
0.419807 + 0.907613i \(0.362098\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.3814i 0.159713i
\(66\) 0 0
\(67\) 13.5770 0.202642 0.101321 0.994854i \(-0.467693\pi\)
0.101321 + 0.994854i \(0.467693\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) − 32.3246i − 0.455276i −0.973746 0.227638i \(-0.926900\pi\)
0.973746 0.227638i \(-0.0731003\pi\)
\(72\) 0 0
\(73\) 40.6051 0.556234 0.278117 0.960547i \(-0.410290\pi\)
0.278117 + 0.960547i \(0.410290\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 141.309i 1.83518i
\(78\) 0 0
\(79\) 74.2963 0.940460 0.470230 0.882544i \(-0.344171\pi\)
0.470230 + 0.882544i \(0.344171\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 153.301i 1.84700i 0.383602 + 0.923498i \(0.374683\pi\)
−0.383602 + 0.923498i \(0.625317\pi\)
\(84\) 0 0
\(85\) −58.0899 −0.683410
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 20.8675i 0.234466i 0.993104 + 0.117233i \(0.0374025\pi\)
−0.993104 + 0.117233i \(0.962598\pi\)
\(90\) 0 0
\(91\) 29.3399 0.322417
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 15.8477i 0.166818i
\(96\) 0 0
\(97\) −47.7160 −0.491918 −0.245959 0.969280i \(-0.579103\pi\)
−0.245959 + 0.969280i \(0.579103\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 47.5008i − 0.470305i −0.971959 0.235152i \(-0.924441\pi\)
0.971959 0.235152i \(-0.0755589\pi\)
\(102\) 0 0
\(103\) −105.424 −1.02353 −0.511765 0.859125i \(-0.671008\pi\)
−0.511765 + 0.859125i \(0.671008\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 189.677i 1.77268i 0.463031 + 0.886342i \(0.346762\pi\)
−0.463031 + 0.886342i \(0.653238\pi\)
\(108\) 0 0
\(109\) −86.7332 −0.795718 −0.397859 0.917447i \(-0.630247\pi\)
−0.397859 + 0.917447i \(0.630247\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 155.228i 1.37370i 0.726800 + 0.686849i \(0.241007\pi\)
−0.726800 + 0.686849i \(0.758993\pi\)
\(114\) 0 0
\(115\) 112.661 0.979660
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 164.174i 1.37962i
\(120\) 0 0
\(121\) −21.1664 −0.174929
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 135.931i − 1.08745i
\(126\) 0 0
\(127\) 200.589 1.57944 0.789720 0.613467i \(-0.210226\pi\)
0.789720 + 0.613467i \(0.210226\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 107.867i 0.823413i 0.911317 + 0.411706i \(0.135067\pi\)
−0.911317 + 0.411706i \(0.864933\pi\)
\(132\) 0 0
\(133\) 44.7889 0.336759
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 86.6872i 0.632753i 0.948634 + 0.316377i \(0.102466\pi\)
−0.948634 + 0.316377i \(0.897534\pi\)
\(138\) 0 0
\(139\) 61.2451 0.440612 0.220306 0.975431i \(-0.429294\pi\)
0.220306 + 0.975431i \(0.429294\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 29.5181i 0.206420i
\(144\) 0 0
\(145\) −172.965 −1.19286
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 0.702186i − 0.00471266i −0.999997 0.00235633i \(-0.999250\pi\)
0.999997 0.00235633i \(-0.000750043\pi\)
\(150\) 0 0
\(151\) −126.073 −0.834918 −0.417459 0.908696i \(-0.637079\pi\)
−0.417459 + 0.908696i \(0.637079\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 146.335i 0.944094i
\(156\) 0 0
\(157\) 206.324 1.31416 0.657082 0.753819i \(-0.271790\pi\)
0.657082 + 0.753819i \(0.271790\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 318.404i − 1.97766i
\(162\) 0 0
\(163\) 105.377 0.646484 0.323242 0.946316i \(-0.395227\pi\)
0.323242 + 0.946316i \(0.395227\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 208.663i 1.24948i 0.780832 + 0.624741i \(0.214795\pi\)
−0.780832 + 0.624741i \(0.785205\pi\)
\(168\) 0 0
\(169\) −162.871 −0.963735
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 132.781i 0.767518i 0.923433 + 0.383759i \(0.125371\pi\)
−0.923433 + 0.383759i \(0.874629\pi\)
\(174\) 0 0
\(175\) −87.8842 −0.502196
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 142.164i 0.794212i 0.917773 + 0.397106i \(0.129986\pi\)
−0.917773 + 0.397106i \(0.870014\pi\)
\(180\) 0 0
\(181\) 2.74041 0.0151404 0.00757019 0.999971i \(-0.497590\pi\)
0.00757019 + 0.999971i \(0.497590\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 281.215i 1.52008i
\(186\) 0 0
\(187\) −165.171 −0.883268
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 37.6756i − 0.197254i −0.995124 0.0986272i \(-0.968555\pi\)
0.995124 0.0986272i \(-0.0314451\pi\)
\(192\) 0 0
\(193\) −123.736 −0.641120 −0.320560 0.947228i \(-0.603871\pi\)
−0.320560 + 0.947228i \(0.603871\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 57.9231i 0.294026i 0.989135 + 0.147013i \(0.0469659\pi\)
−0.989135 + 0.147013i \(0.953034\pi\)
\(198\) 0 0
\(199\) 311.281 1.56422 0.782112 0.623137i \(-0.214142\pi\)
0.782112 + 0.623137i \(0.214142\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 488.837i 2.40806i
\(204\) 0 0
\(205\) −21.3372 −0.104084
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 45.0608i 0.215602i
\(210\) 0 0
\(211\) −35.2227 −0.166932 −0.0834661 0.996511i \(-0.526599\pi\)
−0.0834661 + 0.996511i \(0.526599\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 194.539i 0.904832i
\(216\) 0 0
\(217\) 413.573 1.90587
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 34.2945i 0.155179i
\(222\) 0 0
\(223\) −232.310 −1.04175 −0.520874 0.853634i \(-0.674394\pi\)
−0.520874 + 0.853634i \(0.674394\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 423.639i − 1.86625i −0.359549 0.933126i \(-0.617069\pi\)
0.359549 0.933126i \(-0.382931\pi\)
\(228\) 0 0
\(229\) 267.079 1.16628 0.583141 0.812371i \(-0.301823\pi\)
0.583141 + 0.812371i \(0.301823\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 71.6122i 0.307349i 0.988122 + 0.153674i \(0.0491107\pi\)
−0.988122 + 0.153674i \(0.950889\pi\)
\(234\) 0 0
\(235\) −391.222 −1.66477
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 100.521i 0.420589i 0.977638 + 0.210295i \(0.0674423\pi\)
−0.977638 + 0.210295i \(0.932558\pi\)
\(240\) 0 0
\(241\) −29.9666 −0.124343 −0.0621715 0.998065i \(-0.519803\pi\)
−0.0621715 + 0.998065i \(0.519803\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 383.510i − 1.56535i
\(246\) 0 0
\(247\) 9.35600 0.0378785
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 159.758i − 0.636487i −0.948009 0.318243i \(-0.896907\pi\)
0.948009 0.318243i \(-0.103093\pi\)
\(252\) 0 0
\(253\) 320.337 1.26615
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 445.246i 1.73248i 0.499632 + 0.866238i \(0.333469\pi\)
−0.499632 + 0.866238i \(0.666531\pi\)
\(258\) 0 0
\(259\) 794.775 3.06863
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 98.5318i 0.374646i 0.982298 + 0.187323i \(0.0599810\pi\)
−0.982298 + 0.187323i \(0.940019\pi\)
\(264\) 0 0
\(265\) −215.859 −0.814561
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 46.7784i − 0.173898i −0.996213 0.0869488i \(-0.972288\pi\)
0.996213 0.0869488i \(-0.0277116\pi\)
\(270\) 0 0
\(271\) −262.335 −0.968026 −0.484013 0.875061i \(-0.660821\pi\)
−0.484013 + 0.875061i \(0.660821\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 88.4178i − 0.321519i
\(276\) 0 0
\(277\) 342.299 1.23574 0.617868 0.786282i \(-0.287996\pi\)
0.617868 + 0.786282i \(0.287996\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 255.439i − 0.909034i −0.890738 0.454517i \(-0.849812\pi\)
0.890738 0.454517i \(-0.150188\pi\)
\(282\) 0 0
\(283\) −49.0707 −0.173395 −0.0866973 0.996235i \(-0.527631\pi\)
−0.0866973 + 0.996235i \(0.527631\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 60.3035i 0.210117i
\(288\) 0 0
\(289\) 97.1017 0.335992
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 307.425i − 1.04923i −0.851339 0.524616i \(-0.824209\pi\)
0.851339 0.524616i \(-0.175791\pi\)
\(294\) 0 0
\(295\) 61.6579 0.209010
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 66.5116i − 0.222447i
\(300\) 0 0
\(301\) 549.808 1.82661
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 214.771i − 0.704166i
\(306\) 0 0
\(307\) −279.080 −0.909056 −0.454528 0.890732i \(-0.650192\pi\)
−0.454528 + 0.890732i \(0.650192\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 300.598i 0.966553i 0.875468 + 0.483277i \(0.160553\pi\)
−0.875468 + 0.483277i \(0.839447\pi\)
\(312\) 0 0
\(313\) −244.478 −0.781080 −0.390540 0.920586i \(-0.627712\pi\)
−0.390540 + 0.920586i \(0.627712\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 313.110i − 0.987728i −0.869539 0.493864i \(-0.835584\pi\)
0.869539 0.493864i \(-0.164416\pi\)
\(318\) 0 0
\(319\) −491.804 −1.54171
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 52.3524i 0.162082i
\(324\) 0 0
\(325\) −18.3582 −0.0564868
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1105.68i 3.36072i
\(330\) 0 0
\(331\) −430.034 −1.29920 −0.649599 0.760277i \(-0.725063\pi\)
−0.649599 + 0.760277i \(0.725063\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 56.9337i − 0.169951i
\(336\) 0 0
\(337\) −493.517 −1.46444 −0.732220 0.681068i \(-0.761516\pi\)
−0.732220 + 0.681068i \(0.761516\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 416.084i 1.22019i
\(342\) 0 0
\(343\) −503.162 −1.46695
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 519.549i 1.49726i 0.662988 + 0.748630i \(0.269288\pi\)
−0.662988 + 0.748630i \(0.730712\pi\)
\(348\) 0 0
\(349\) −243.092 −0.696538 −0.348269 0.937395i \(-0.613230\pi\)
−0.348269 + 0.937395i \(0.613230\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 641.701i − 1.81785i −0.416961 0.908924i \(-0.636905\pi\)
0.416961 0.908924i \(-0.363095\pi\)
\(354\) 0 0
\(355\) −135.550 −0.381830
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) − 332.130i − 0.925154i −0.886579 0.462577i \(-0.846925\pi\)
0.886579 0.462577i \(-0.153075\pi\)
\(360\) 0 0
\(361\) −346.718 −0.960437
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 170.273i − 0.466501i
\(366\) 0 0
\(367\) 71.0636 0.193634 0.0968168 0.995302i \(-0.469134\pi\)
0.0968168 + 0.995302i \(0.469134\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 610.063i 1.64437i
\(372\) 0 0
\(373\) 328.122 0.879685 0.439842 0.898075i \(-0.355034\pi\)
0.439842 + 0.898075i \(0.355034\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 102.114i 0.270858i
\(378\) 0 0
\(379\) −77.9266 −0.205611 −0.102806 0.994701i \(-0.532782\pi\)
−0.102806 + 0.994701i \(0.532782\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 206.276i 0.538578i 0.963059 + 0.269289i \(0.0867887\pi\)
−0.963059 + 0.269289i \(0.913211\pi\)
\(384\) 0 0
\(385\) 592.561 1.53912
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9.52545i 0.0244870i 0.999925 + 0.0122435i \(0.00389733\pi\)
−0.999925 + 0.0122435i \(0.996103\pi\)
\(390\) 0 0
\(391\) 372.172 0.951847
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 311.553i − 0.788742i
\(396\) 0 0
\(397\) 77.0583 0.194101 0.0970507 0.995279i \(-0.469059\pi\)
0.0970507 + 0.995279i \(0.469059\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 332.581i − 0.829379i −0.909963 0.414689i \(-0.863890\pi\)
0.909963 0.414689i \(-0.136110\pi\)
\(402\) 0 0
\(403\) 86.3916 0.214371
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 799.600i 1.96462i
\(408\) 0 0
\(409\) 420.410 1.02790 0.513948 0.857821i \(-0.328182\pi\)
0.513948 + 0.857821i \(0.328182\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 174.259i − 0.421934i
\(414\) 0 0
\(415\) 642.849 1.54903
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 156.601i 0.373749i 0.982384 + 0.186874i \(0.0598357\pi\)
−0.982384 + 0.186874i \(0.940164\pi\)
\(420\) 0 0
\(421\) 26.0089 0.0617788 0.0308894 0.999523i \(-0.490166\pi\)
0.0308894 + 0.999523i \(0.490166\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 102.725i − 0.241706i
\(426\) 0 0
\(427\) −606.988 −1.42152
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 209.889i 0.486982i 0.969903 + 0.243491i \(0.0782927\pi\)
−0.969903 + 0.243491i \(0.921707\pi\)
\(432\) 0 0
\(433\) −405.331 −0.936100 −0.468050 0.883702i \(-0.655043\pi\)
−0.468050 + 0.883702i \(0.655043\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 101.533i − 0.232342i
\(438\) 0 0
\(439\) −126.853 −0.288959 −0.144480 0.989508i \(-0.546151\pi\)
−0.144480 + 0.989508i \(0.546151\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 353.138i 0.797152i 0.917135 + 0.398576i \(0.130495\pi\)
−0.917135 + 0.398576i \(0.869505\pi\)
\(444\) 0 0
\(445\) 87.5054 0.196641
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 487.890i 1.08661i 0.839534 + 0.543307i \(0.182828\pi\)
−0.839534 + 0.543307i \(0.817172\pi\)
\(450\) 0 0
\(451\) −60.6695 −0.134522
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) − 123.034i − 0.270404i
\(456\) 0 0
\(457\) −250.541 −0.548230 −0.274115 0.961697i \(-0.588385\pi\)
−0.274115 + 0.961697i \(0.588385\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 462.832i 1.00397i 0.864875 + 0.501987i \(0.167397\pi\)
−0.864875 + 0.501987i \(0.832603\pi\)
\(462\) 0 0
\(463\) 432.508 0.934142 0.467071 0.884220i \(-0.345309\pi\)
0.467071 + 0.884220i \(0.345309\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 64.0388i − 0.137128i −0.997647 0.0685640i \(-0.978158\pi\)
0.997647 0.0685640i \(-0.0218417\pi\)
\(468\) 0 0
\(469\) −160.907 −0.343085
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 553.146i 1.16944i
\(474\) 0 0
\(475\) −28.0247 −0.0589995
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 175.100i 0.365552i 0.983155 + 0.182776i \(0.0585084\pi\)
−0.983155 + 0.182776i \(0.941492\pi\)
\(480\) 0 0
\(481\) 166.021 0.345158
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 200.092i 0.412560i
\(486\) 0 0
\(487\) −28.7536 −0.0590424 −0.0295212 0.999564i \(-0.509398\pi\)
−0.0295212 + 0.999564i \(0.509398\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 772.522i − 1.57336i −0.617358 0.786682i \(-0.711797\pi\)
0.617358 0.786682i \(-0.288203\pi\)
\(492\) 0 0
\(493\) −571.386 −1.15900
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 383.092i 0.770809i
\(498\) 0 0
\(499\) 581.705 1.16574 0.582871 0.812565i \(-0.301929\pi\)
0.582871 + 0.812565i \(0.301929\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 567.737i − 1.12870i −0.825535 0.564351i \(-0.809127\pi\)
0.825535 0.564351i \(-0.190873\pi\)
\(504\) 0 0
\(505\) −199.189 −0.394434
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 513.459i 1.00876i 0.863482 + 0.504380i \(0.168279\pi\)
−0.863482 + 0.504380i \(0.831721\pi\)
\(510\) 0 0
\(511\) −481.228 −0.941737
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 442.082i 0.858411i
\(516\) 0 0
\(517\) −1112.39 −2.15162
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 712.101i 1.36680i 0.730046 + 0.683398i \(0.239499\pi\)
−0.730046 + 0.683398i \(0.760501\pi\)
\(522\) 0 0
\(523\) −203.216 −0.388559 −0.194279 0.980946i \(-0.562237\pi\)
−0.194279 + 0.980946i \(0.562237\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 483.412i 0.917291i
\(528\) 0 0
\(529\) −192.800 −0.364460
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 12.5968i 0.0236338i
\(534\) 0 0
\(535\) 795.390 1.48671
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 1090.46i − 2.02312i
\(540\) 0 0
\(541\) 96.3158 0.178033 0.0890165 0.996030i \(-0.471628\pi\)
0.0890165 + 0.996030i \(0.471628\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 363.706i 0.667350i
\(546\) 0 0
\(547\) −257.717 −0.471146 −0.235573 0.971857i \(-0.575697\pi\)
−0.235573 + 0.971857i \(0.575697\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 155.881i 0.282907i
\(552\) 0 0
\(553\) −880.516 −1.59225
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 289.902i − 0.520470i −0.965545 0.260235i \(-0.916200\pi\)
0.965545 0.260235i \(-0.0838000\pi\)
\(558\) 0 0
\(559\) 114.850 0.205456
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 61.2353i 0.108766i 0.998520 + 0.0543830i \(0.0173192\pi\)
−0.998520 + 0.0543830i \(0.982681\pi\)
\(564\) 0 0
\(565\) 650.930 1.15209
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 489.987i − 0.861137i −0.902558 0.430569i \(-0.858313\pi\)
0.902558 0.430569i \(-0.141687\pi\)
\(570\) 0 0
\(571\) −763.682 −1.33745 −0.668724 0.743511i \(-0.733159\pi\)
−0.668724 + 0.743511i \(0.733159\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 199.228i 0.346483i
\(576\) 0 0
\(577\) −260.905 −0.452176 −0.226088 0.974107i \(-0.572594\pi\)
−0.226088 + 0.974107i \(0.572594\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 1816.83i − 3.12707i
\(582\) 0 0
\(583\) −613.766 −1.05277
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 281.892i 0.480225i 0.970745 + 0.240113i \(0.0771844\pi\)
−0.970745 + 0.240113i \(0.922816\pi\)
\(588\) 0 0
\(589\) 131.881 0.223907
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 248.742i 0.419463i 0.977759 + 0.209731i \(0.0672590\pi\)
−0.977759 + 0.209731i \(0.932741\pi\)
\(594\) 0 0
\(595\) 688.447 1.15705
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 317.979i − 0.530850i −0.964132 0.265425i \(-0.914488\pi\)
0.964132 0.265425i \(-0.0855123\pi\)
\(600\) 0 0
\(601\) 825.574 1.37367 0.686834 0.726814i \(-0.259000\pi\)
0.686834 + 0.726814i \(0.259000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 88.7590i 0.146709i
\(606\) 0 0
\(607\) −404.868 −0.666998 −0.333499 0.942750i \(-0.608229\pi\)
−0.333499 + 0.942750i \(0.608229\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 230.966i 0.378013i
\(612\) 0 0
\(613\) 619.459 1.01054 0.505268 0.862963i \(-0.331394\pi\)
0.505268 + 0.862963i \(0.331394\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 806.726i 1.30750i 0.756712 + 0.653749i \(0.226805\pi\)
−0.756712 + 0.653749i \(0.773195\pi\)
\(618\) 0 0
\(619\) 892.691 1.44215 0.721075 0.692857i \(-0.243648\pi\)
0.721075 + 0.692857i \(0.243648\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) − 247.309i − 0.396965i
\(624\) 0 0
\(625\) −384.622 −0.615396
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 928.987i 1.47693i
\(630\) 0 0
\(631\) −830.684 −1.31646 −0.658228 0.752819i \(-0.728694\pi\)
−0.658228 + 0.752819i \(0.728694\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 841.147i − 1.32464i
\(636\) 0 0
\(637\) −226.413 −0.355436
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 711.369i − 1.10978i −0.831924 0.554890i \(-0.812760\pi\)
0.831924 0.554890i \(-0.187240\pi\)
\(642\) 0 0
\(643\) 905.559 1.40833 0.704167 0.710034i \(-0.251320\pi\)
0.704167 + 0.710034i \(0.251320\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 175.592i − 0.271394i −0.990750 0.135697i \(-0.956673\pi\)
0.990750 0.135697i \(-0.0433273\pi\)
\(648\) 0 0
\(649\) 175.316 0.270133
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 1010.57i − 1.54758i −0.633444 0.773789i \(-0.718359\pi\)
0.633444 0.773789i \(-0.281641\pi\)
\(654\) 0 0
\(655\) 452.328 0.690578
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 262.881i 0.398909i 0.979907 + 0.199455i \(0.0639170\pi\)
−0.979907 + 0.199455i \(0.936083\pi\)
\(660\) 0 0
\(661\) 499.183 0.755194 0.377597 0.925970i \(-0.376751\pi\)
0.377597 + 0.925970i \(0.376751\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 187.817i − 0.282432i
\(666\) 0 0
\(667\) 1108.16 1.66141
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) − 610.672i − 0.910093i
\(672\) 0 0
\(673\) 892.885 1.32672 0.663362 0.748299i \(-0.269129\pi\)
0.663362 + 0.748299i \(0.269129\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 313.538i − 0.463128i −0.972820 0.231564i \(-0.925616\pi\)
0.972820 0.231564i \(-0.0743842\pi\)
\(678\) 0 0
\(679\) 565.502 0.832846
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 486.473i 0.712260i 0.934436 + 0.356130i \(0.115904\pi\)
−0.934436 + 0.356130i \(0.884096\pi\)
\(684\) 0 0
\(685\) 363.513 0.530676
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 127.437i 0.184959i
\(690\) 0 0
\(691\) 617.830 0.894110 0.447055 0.894506i \(-0.352473\pi\)
0.447055 + 0.894506i \(0.352473\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) − 256.824i − 0.369531i
\(696\) 0 0
\(697\) −70.4868 −0.101129
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 297.109i 0.423836i 0.977287 + 0.211918i \(0.0679709\pi\)
−0.977287 + 0.211918i \(0.932029\pi\)
\(702\) 0 0
\(703\) 253.440 0.360512
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 562.951i 0.796253i
\(708\) 0 0
\(709\) −881.029 −1.24264 −0.621318 0.783559i \(-0.713402\pi\)
−0.621318 + 0.783559i \(0.713402\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 937.541i − 1.31492i
\(714\) 0 0
\(715\) 123.781 0.173120
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 1179.05i − 1.63985i −0.572471 0.819925i \(-0.694015\pi\)
0.572471 0.819925i \(-0.305985\pi\)
\(720\) 0 0
\(721\) 1249.42 1.73290
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 305.869i − 0.421888i
\(726\) 0 0
\(727\) −643.311 −0.884884 −0.442442 0.896797i \(-0.645888\pi\)
−0.442442 + 0.896797i \(0.645888\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 642.654i 0.879143i
\(732\) 0 0
\(733\) 188.823 0.257602 0.128801 0.991670i \(-0.458887\pi\)
0.128801 + 0.991670i \(0.458887\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 161.884i − 0.219652i
\(738\) 0 0
\(739\) 911.207 1.23303 0.616514 0.787344i \(-0.288544\pi\)
0.616514 + 0.787344i \(0.288544\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) − 297.762i − 0.400756i −0.979719 0.200378i \(-0.935783\pi\)
0.979719 0.200378i \(-0.0642170\pi\)
\(744\) 0 0
\(745\) −2.94454 −0.00395240
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 2247.94i − 3.00126i
\(750\) 0 0
\(751\) −5.31339 −0.00707508 −0.00353754 0.999994i \(-0.501126\pi\)
−0.00353754 + 0.999994i \(0.501126\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 528.671i 0.700227i
\(756\) 0 0
\(757\) −678.131 −0.895813 −0.447907 0.894080i \(-0.647830\pi\)
−0.447907 + 0.894080i \(0.647830\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 914.492i − 1.20170i −0.799363 0.600849i \(-0.794829\pi\)
0.799363 0.600849i \(-0.205171\pi\)
\(762\) 0 0
\(763\) 1027.91 1.34720
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 36.4010i − 0.0474590i
\(768\) 0 0
\(769\) 355.672 0.462512 0.231256 0.972893i \(-0.425717\pi\)
0.231256 + 0.972893i \(0.425717\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 727.920i − 0.941681i −0.882218 0.470841i \(-0.843951\pi\)
0.882218 0.470841i \(-0.156049\pi\)
\(774\) 0 0
\(775\) −258.775 −0.333904
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 19.2297i 0.0246851i
\(780\) 0 0
\(781\) −385.418 −0.493493
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 865.195i − 1.10216i
\(786\) 0 0
\(787\) 45.9632 0.0584031 0.0292015 0.999574i \(-0.490704\pi\)
0.0292015 + 0.999574i \(0.490704\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 1839.67i − 2.32575i
\(792\) 0 0
\(793\) −126.794 −0.159892
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 394.806i − 0.495365i −0.968841 0.247682i \(-0.920331\pi\)
0.968841 0.247682i \(-0.0796690\pi\)
\(798\) 0 0
\(799\) −1292.39 −1.61751
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 484.149i − 0.602925i
\(804\) 0 0
\(805\) −1335.19 −1.65862
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 333.349i − 0.412050i −0.978547 0.206025i \(-0.933947\pi\)
0.978547 0.206025i \(-0.0660529\pi\)
\(810\) 0 0
\(811\) −1156.01 −1.42541 −0.712705 0.701464i \(-0.752530\pi\)
−0.712705 + 0.701464i \(0.752530\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 441.886i − 0.542191i
\(816\) 0 0
\(817\) 175.324 0.214595
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 1239.86i − 1.51018i −0.655623 0.755088i \(-0.727594\pi\)
0.655623 0.755088i \(-0.272406\pi\)
\(822\) 0 0
\(823\) 47.6805 0.0579350 0.0289675 0.999580i \(-0.490778\pi\)
0.0289675 + 0.999580i \(0.490778\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1056.26i 1.27722i 0.769529 + 0.638612i \(0.220491\pi\)
−0.769529 + 0.638612i \(0.779509\pi\)
\(828\) 0 0
\(829\) −1288.49 −1.55427 −0.777137 0.629331i \(-0.783329\pi\)
−0.777137 + 0.629331i \(0.783329\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 1266.91i − 1.52091i
\(834\) 0 0
\(835\) 875.007 1.04791
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 952.960i 1.13583i 0.823088 + 0.567914i \(0.192249\pi\)
−0.823088 + 0.567914i \(0.807751\pi\)
\(840\) 0 0
\(841\) −860.327 −1.02298
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 682.982i 0.808262i
\(846\) 0 0
\(847\) 250.852 0.296165
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 1801.70i − 2.11716i
\(852\) 0 0
\(853\) −349.667 −0.409926 −0.204963 0.978770i \(-0.565707\pi\)
−0.204963 + 0.978770i \(0.565707\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 605.317i 0.706321i 0.935563 + 0.353160i \(0.114893\pi\)
−0.935563 + 0.353160i \(0.885107\pi\)
\(858\) 0 0
\(859\) 381.186 0.443755 0.221878 0.975075i \(-0.428781\pi\)
0.221878 + 0.975075i \(0.428781\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 634.987i 0.735791i 0.929867 + 0.367895i \(0.119922\pi\)
−0.929867 + 0.367895i \(0.880078\pi\)
\(864\) 0 0
\(865\) 556.800 0.643700
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 885.862i − 1.01940i
\(870\) 0 0
\(871\) −33.6119 −0.0385901
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1610.97i 1.84111i
\(876\) 0 0
\(877\) −343.774 −0.391989 −0.195994 0.980605i \(-0.562793\pi\)
−0.195994 + 0.980605i \(0.562793\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1109.44i 1.25930i 0.776881 + 0.629648i \(0.216801\pi\)
−0.776881 + 0.629648i \(0.783199\pi\)
\(882\) 0 0
\(883\) 888.121 1.00580 0.502900 0.864345i \(-0.332266\pi\)
0.502900 + 0.864345i \(0.332266\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 304.043i − 0.342777i −0.985204 0.171388i \(-0.945175\pi\)
0.985204 0.171388i \(-0.0548253\pi\)
\(888\) 0 0
\(889\) −2377.26 −2.67408
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 352.581i 0.394827i
\(894\) 0 0
\(895\) 596.149 0.666088
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1439.38i 1.60109i
\(900\) 0 0
\(901\) −713.083 −0.791435
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 11.4916i − 0.0126979i
\(906\) 0 0
\(907\) −576.702 −0.635834 −0.317917 0.948119i \(-0.602983\pi\)
−0.317917 + 0.948119i \(0.602983\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 400.564i 0.439697i 0.975534 + 0.219849i \(0.0705564\pi\)
−0.975534 + 0.219849i \(0.929444\pi\)
\(912\) 0 0
\(913\) 1827.86 2.00204
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 1278.38i − 1.39409i
\(918\) 0 0
\(919\) 356.293 0.387696 0.193848 0.981032i \(-0.437903\pi\)
0.193848 + 0.981032i \(0.437903\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 80.0244i 0.0867004i
\(924\) 0 0
\(925\) −497.296 −0.537618
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 256.863i − 0.276495i −0.990398 0.138247i \(-0.955853\pi\)
0.990398 0.138247i \(-0.0441469\pi\)
\(930\) 0 0
\(931\) −345.631 −0.371247
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 692.626i 0.740777i
\(936\) 0 0
\(937\) −1569.56 −1.67509 −0.837547 0.546365i \(-0.816011\pi\)
−0.837547 + 0.546365i \(0.816011\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 1310.13i − 1.39227i −0.717909 0.696137i \(-0.754901\pi\)
0.717909 0.696137i \(-0.245099\pi\)
\(942\) 0 0
\(943\) 136.704 0.144967
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 452.283i − 0.477595i −0.971069 0.238798i \(-0.923247\pi\)
0.971069 0.238798i \(-0.0767532\pi\)
\(948\) 0 0
\(949\) −100.524 −0.105926
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 1670.70i − 1.75310i −0.481310 0.876550i \(-0.659839\pi\)
0.481310 0.876550i \(-0.340161\pi\)
\(954\) 0 0
\(955\) −157.988 −0.165433
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) − 1027.37i − 1.07129i
\(960\) 0 0
\(961\) 256.767 0.267187
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 518.873i 0.537692i
\(966\) 0 0
\(967\) −1202.12 −1.24314 −0.621572 0.783357i \(-0.713506\pi\)
−0.621572 + 0.783357i \(0.713506\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 482.574i 0.496987i 0.968634 + 0.248493i \(0.0799354\pi\)
−0.968634 + 0.248493i \(0.920065\pi\)
\(972\) 0 0
\(973\) −725.840 −0.745982
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 592.682i 0.606635i 0.952890 + 0.303318i \(0.0980943\pi\)
−0.952890 + 0.303318i \(0.901906\pi\)
\(978\) 0 0
\(979\) 248.811 0.254148
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1711.14i 1.74073i 0.492408 + 0.870365i \(0.336117\pi\)
−0.492408 + 0.870365i \(0.663883\pi\)
\(984\) 0 0
\(985\) 242.894 0.246593
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 1246.38i − 1.26024i
\(990\) 0 0
\(991\) 513.628 0.518293 0.259146 0.965838i \(-0.416559\pi\)
0.259146 + 0.965838i \(0.416559\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 1305.32i − 1.31188i
\(996\) 0 0
\(997\) 1681.33 1.68638 0.843192 0.537612i \(-0.180674\pi\)
0.843192 + 0.537612i \(0.180674\pi\)
\(998\) 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 2916.3.c.b.1457.10 36
3.2 odd 2 inner 2916.3.c.b.1457.27 36
27.5 odd 18 324.3.k.a.89.5 36
27.11 odd 18 108.3.k.a.41.1 yes 36
27.16 even 9 324.3.k.a.233.5 36
27.22 even 9 108.3.k.a.29.1 36
108.11 even 18 432.3.bc.b.257.6 36
108.103 odd 18 432.3.bc.b.353.6 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.k.a.29.1 36 27.22 even 9
108.3.k.a.41.1 yes 36 27.11 odd 18
324.3.k.a.89.5 36 27.5 odd 18
324.3.k.a.233.5 36 27.16 even 9
432.3.bc.b.257.6 36 108.11 even 18
432.3.bc.b.353.6 36 108.103 odd 18
2916.3.c.b.1457.10 36 1.1 even 1 trivial
2916.3.c.b.1457.27 36 3.2 odd 2 inner