Properties

Label 1008.4.bt.d.593.7
Level $1008$
Weight $4$
Character 1008.593
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,4,Mod(17,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.17");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not 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: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 593.7
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.d.17.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.00025 + 8.66069i) q^{5} +(-1.56940 - 18.4536i) q^{7} +O(q^{10})\) \(q+(-5.00025 + 8.66069i) q^{5} +(-1.56940 - 18.4536i) q^{7} +(-8.94164 + 5.16246i) q^{11} +52.4866i q^{13} +(0.584477 + 1.01234i) q^{17} +(86.7124 + 50.0634i) q^{19} +(-90.1373 - 52.0408i) q^{23} +(12.4950 + 21.6419i) q^{25} -187.555i q^{29} +(107.524 - 62.0789i) q^{31} +(167.669 + 78.6808i) q^{35} +(16.0459 - 27.7922i) q^{37} -415.597 q^{41} +193.264 q^{43} +(-196.466 + 340.289i) q^{47} +(-338.074 + 57.9222i) q^{49} +(-74.7758 + 43.1718i) q^{53} -103.254i q^{55} +(102.286 + 177.165i) q^{59} +(-183.527 - 105.959i) q^{61} +(-454.570 - 262.446i) q^{65} +(-364.857 - 631.951i) q^{67} +315.022i q^{71} +(-899.220 + 519.165i) q^{73} +(109.299 + 156.904i) q^{77} +(607.787 - 1052.72i) q^{79} +333.797 q^{83} -11.6901 q^{85} +(-168.355 + 291.599i) q^{89} +(968.568 - 82.3723i) q^{91} +(-867.167 + 500.659i) q^{95} -893.179i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 24 q^{7} - 540 q^{19} - 924 q^{25} - 648 q^{31} - 132 q^{37} + 792 q^{43} + 672 q^{49} + 12 q^{67} + 2412 q^{73} - 1680 q^{79} + 480 q^{85} - 1404 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(5\) −5.00025 + 8.66069i −0.447236 + 0.774636i −0.998205 0.0598902i \(-0.980925\pi\)
0.550969 + 0.834526i \(0.314258\pi\)
\(6\) 0 0
\(7\) −1.56940 18.4536i −0.0847395 0.996403i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −8.94164 + 5.16246i −0.245092 + 0.141504i −0.617515 0.786559i \(-0.711860\pi\)
0.372423 + 0.928063i \(0.378527\pi\)
\(12\) 0 0
\(13\) 52.4866i 1.11978i 0.828567 + 0.559891i \(0.189157\pi\)
−0.828567 + 0.559891i \(0.810843\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.584477 + 1.01234i 0.00833862 + 0.0144429i 0.870165 0.492761i \(-0.164012\pi\)
−0.861826 + 0.507204i \(0.830679\pi\)
\(18\) 0 0
\(19\) 86.7124 + 50.0634i 1.04701 + 0.604491i 0.921811 0.387640i \(-0.126710\pi\)
0.125199 + 0.992132i \(0.460043\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −90.1373 52.0408i −0.817171 0.471794i 0.0322689 0.999479i \(-0.489727\pi\)
−0.849440 + 0.527685i \(0.823060\pi\)
\(24\) 0 0
\(25\) 12.4950 + 21.6419i 0.0999598 + 0.173135i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 187.555i 1.20097i −0.799636 0.600485i \(-0.794974\pi\)
0.799636 0.600485i \(-0.205026\pi\)
\(30\) 0 0
\(31\) 107.524 62.0789i 0.622963 0.359668i −0.155059 0.987905i \(-0.549557\pi\)
0.778022 + 0.628238i \(0.216223\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 167.669 + 78.6808i 0.809748 + 0.379985i
\(36\) 0 0
\(37\) 16.0459 27.7922i 0.0712952 0.123487i −0.828174 0.560471i \(-0.810620\pi\)
0.899469 + 0.436984i \(0.143953\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −415.597 −1.58306 −0.791528 0.611133i \(-0.790714\pi\)
−0.791528 + 0.611133i \(0.790714\pi\)
\(42\) 0 0
\(43\) 193.264 0.685407 0.342703 0.939444i \(-0.388657\pi\)
0.342703 + 0.939444i \(0.388657\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −196.466 + 340.289i −0.609735 + 1.05609i 0.381549 + 0.924348i \(0.375391\pi\)
−0.991284 + 0.131743i \(0.957943\pi\)
\(48\) 0 0
\(49\) −338.074 + 57.9222i −0.985638 + 0.168869i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −74.7758 + 43.1718i −0.193797 + 0.111889i −0.593759 0.804643i \(-0.702357\pi\)
0.399962 + 0.916532i \(0.369023\pi\)
\(54\) 0 0
\(55\) 103.254i 0.253142i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 102.286 + 177.165i 0.225704 + 0.390931i 0.956531 0.291632i \(-0.0941983\pi\)
−0.730826 + 0.682564i \(0.760865\pi\)
\(60\) 0 0
\(61\) −183.527 105.959i −0.385217 0.222405i 0.294869 0.955538i \(-0.404724\pi\)
−0.680086 + 0.733133i \(0.738057\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −454.570 262.446i −0.867422 0.500806i
\(66\) 0 0
\(67\) −364.857 631.951i −0.665290 1.15232i −0.979207 0.202865i \(-0.934975\pi\)
0.313917 0.949450i \(-0.398359\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 315.022i 0.526566i 0.964719 + 0.263283i \(0.0848053\pi\)
−0.964719 + 0.263283i \(0.915195\pi\)
\(72\) 0 0
\(73\) −899.220 + 519.165i −1.44172 + 0.832379i −0.997965 0.0637680i \(-0.979688\pi\)
−0.443758 + 0.896147i \(0.646355\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 109.299 + 156.904i 0.161764 + 0.232219i
\(78\) 0 0
\(79\) 607.787 1052.72i 0.865587 1.49924i −0.000876764 1.00000i \(-0.500279\pi\)
0.866463 0.499241i \(-0.166388\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 333.797 0.441434 0.220717 0.975338i \(-0.429160\pi\)
0.220717 + 0.975338i \(0.429160\pi\)
\(84\) 0 0
\(85\) −11.6901 −0.0149173
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −168.355 + 291.599i −0.200512 + 0.347297i −0.948693 0.316197i \(-0.897594\pi\)
0.748182 + 0.663494i \(0.230927\pi\)
\(90\) 0 0
\(91\) 968.568 82.3723i 1.11575 0.0948897i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −867.167 + 500.659i −0.936521 + 0.540701i
\(96\) 0 0
\(97\) 893.179i 0.934934i −0.884011 0.467467i \(-0.845167\pi\)
0.884011 0.467467i \(-0.154833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −463.543 802.881i −0.456676 0.790986i 0.542107 0.840310i \(-0.317627\pi\)
−0.998783 + 0.0493234i \(0.984293\pi\)
\(102\) 0 0
\(103\) −487.361 281.378i −0.466224 0.269175i 0.248434 0.968649i \(-0.420084\pi\)
−0.714658 + 0.699474i \(0.753418\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1290.34 744.979i −1.16581 0.673082i −0.213123 0.977025i \(-0.568363\pi\)
−0.952690 + 0.303943i \(0.901697\pi\)
\(108\) 0 0
\(109\) −726.305 1258.00i −0.638233 1.10545i −0.985820 0.167804i \(-0.946332\pi\)
0.347587 0.937648i \(-0.387001\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1761.48i 1.46642i −0.680001 0.733211i \(-0.738021\pi\)
0.680001 0.733211i \(-0.261979\pi\)
\(114\) 0 0
\(115\) 901.419 520.434i 0.730937 0.422007i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 17.7642 12.3745i 0.0136844 0.00953251i
\(120\) 0 0
\(121\) −612.198 + 1060.36i −0.459953 + 0.796663i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1499.97 −1.07329
\(126\) 0 0
\(127\) −68.3256 −0.0477395 −0.0238697 0.999715i \(-0.507599\pi\)
−0.0238697 + 0.999715i \(0.507599\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 242.249 419.588i 0.161568 0.279844i −0.773863 0.633353i \(-0.781678\pi\)
0.935431 + 0.353509i \(0.115012\pi\)
\(132\) 0 0
\(133\) 787.766 1678.73i 0.513594 1.09447i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1247.91 + 720.479i −0.778217 + 0.449304i −0.835798 0.549037i \(-0.814995\pi\)
0.0575809 + 0.998341i \(0.481661\pi\)
\(138\) 0 0
\(139\) 1445.47i 0.882035i −0.897499 0.441017i \(-0.854618\pi\)
0.897499 0.441017i \(-0.145382\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −270.960 469.316i −0.158453 0.274449i
\(144\) 0 0
\(145\) 1624.36 + 937.824i 0.930314 + 0.537117i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −846.151 488.526i −0.465231 0.268601i 0.249010 0.968501i \(-0.419895\pi\)
−0.714241 + 0.699900i \(0.753228\pi\)
\(150\) 0 0
\(151\) −667.146 1155.53i −0.359547 0.622753i 0.628338 0.777940i \(-0.283735\pi\)
−0.987885 + 0.155187i \(0.950402\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1241.64i 0.643425i
\(156\) 0 0
\(157\) 1296.09 748.295i 0.658846 0.380385i −0.132991 0.991117i \(-0.542458\pi\)
0.791837 + 0.610732i \(0.209125\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −818.881 + 1745.04i −0.400850 + 0.854211i
\(162\) 0 0
\(163\) −1894.73 + 3281.76i −0.910469 + 1.57698i −0.0970652 + 0.995278i \(0.530946\pi\)
−0.813403 + 0.581700i \(0.802388\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1202.66 −0.557273 −0.278637 0.960397i \(-0.589883\pi\)
−0.278637 + 0.960397i \(0.589883\pi\)
\(168\) 0 0
\(169\) −557.839 −0.253910
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −765.529 + 1325.94i −0.336428 + 0.582711i −0.983758 0.179499i \(-0.942552\pi\)
0.647330 + 0.762210i \(0.275886\pi\)
\(174\) 0 0
\(175\) 379.763 264.543i 0.164042 0.114272i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1595.31 + 921.053i −0.666141 + 0.384596i −0.794613 0.607117i \(-0.792326\pi\)
0.128472 + 0.991713i \(0.458993\pi\)
\(180\) 0 0
\(181\) 325.049i 0.133485i −0.997770 0.0667423i \(-0.978739\pi\)
0.997770 0.0667423i \(-0.0212605\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 160.467 + 277.936i 0.0637716 + 0.110456i
\(186\) 0 0
\(187\) −10.4524 6.03468i −0.00408745 0.00235989i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3045.91 1758.56i −1.15390 0.666203i −0.204063 0.978958i \(-0.565415\pi\)
−0.949834 + 0.312755i \(0.898748\pi\)
\(192\) 0 0
\(193\) −502.491 870.339i −0.187410 0.324603i 0.756976 0.653442i \(-0.226676\pi\)
−0.944386 + 0.328839i \(0.893343\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2808.91i 1.01587i 0.861395 + 0.507935i \(0.169591\pi\)
−0.861395 + 0.507935i \(0.830409\pi\)
\(198\) 0 0
\(199\) 210.249 121.387i 0.0748954 0.0432409i −0.462085 0.886836i \(-0.652898\pi\)
0.536980 + 0.843595i \(0.319565\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3461.08 + 294.349i −1.19665 + 0.101770i
\(204\) 0 0
\(205\) 2078.09 3599.35i 0.707999 1.22629i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1033.80 −0.342151
\(210\) 0 0
\(211\) −2238.46 −0.730342 −0.365171 0.930940i \(-0.618989\pi\)
−0.365171 + 0.930940i \(0.618989\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −966.369 + 1673.80i −0.306539 + 0.530941i
\(216\) 0 0
\(217\) −1314.33 1886.78i −0.411164 0.590244i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −53.1345 + 30.6772i −0.0161729 + 0.00933743i
\(222\) 0 0
\(223\) 724.158i 0.217458i 0.994071 + 0.108729i \(0.0346781\pi\)
−0.994071 + 0.108729i \(0.965322\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1234.34 2137.94i −0.360908 0.625111i 0.627202 0.778856i \(-0.284200\pi\)
−0.988111 + 0.153745i \(0.950867\pi\)
\(228\) 0 0
\(229\) 3595.98 + 2076.14i 1.03768 + 0.599106i 0.919176 0.393847i \(-0.128856\pi\)
0.118507 + 0.992953i \(0.462189\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5140.63 + 2967.94i 1.44538 + 0.834492i 0.998201 0.0599522i \(-0.0190948\pi\)
0.447180 + 0.894444i \(0.352428\pi\)
\(234\) 0 0
\(235\) −1964.76 3403.06i −0.545391 0.944644i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4306.49i 1.16554i −0.812638 0.582769i \(-0.801969\pi\)
0.812638 0.582769i \(-0.198031\pi\)
\(240\) 0 0
\(241\) 674.728 389.554i 0.180345 0.104122i −0.407110 0.913379i \(-0.633463\pi\)
0.587455 + 0.809257i \(0.300130\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1188.81 3217.58i 0.310001 0.839035i
\(246\) 0 0
\(247\) −2627.66 + 4551.23i −0.676898 + 1.17242i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −804.927 −0.202416 −0.101208 0.994865i \(-0.532271\pi\)
−0.101208 + 0.994865i \(0.532271\pi\)
\(252\) 0 0
\(253\) 1074.63 0.267042
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2967.92 + 5140.59i −0.720365 + 1.24771i 0.240489 + 0.970652i \(0.422692\pi\)
−0.960854 + 0.277057i \(0.910641\pi\)
\(258\) 0 0
\(259\) −538.050 252.487i −0.129084 0.0605745i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6468.89 3734.82i 1.51669 0.875660i 0.516880 0.856058i \(-0.327093\pi\)
0.999808 0.0196026i \(-0.00624010\pi\)
\(264\) 0 0
\(265\) 863.480i 0.200163i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3714.97 6434.52i −0.842029 1.45844i −0.888176 0.459503i \(-0.848028\pi\)
0.0461472 0.998935i \(-0.485306\pi\)
\(270\) 0 0
\(271\) −1076.21 621.349i −0.241236 0.139278i 0.374509 0.927223i \(-0.377811\pi\)
−0.615745 + 0.787946i \(0.711145\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −223.451 129.010i −0.0489986 0.0282894i
\(276\) 0 0
\(277\) −339.471 587.980i −0.0736347 0.127539i 0.826857 0.562412i \(-0.190127\pi\)
−0.900492 + 0.434873i \(0.856793\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2157.54i 0.458036i 0.973422 + 0.229018i \(0.0735515\pi\)
−0.973422 + 0.229018i \(0.926449\pi\)
\(282\) 0 0
\(283\) 843.962 487.262i 0.177273 0.102349i −0.408738 0.912652i \(-0.634031\pi\)
0.586011 + 0.810303i \(0.300698\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 652.236 + 7669.27i 0.134147 + 1.57736i
\(288\) 0 0
\(289\) 2455.82 4253.60i 0.499861 0.865785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6457.16 1.28748 0.643740 0.765245i \(-0.277382\pi\)
0.643740 + 0.765245i \(0.277382\pi\)
\(294\) 0 0
\(295\) −2045.83 −0.403773
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2731.44 4731.00i 0.528306 0.915053i
\(300\) 0 0
\(301\) −303.308 3566.43i −0.0580810 0.682942i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1835.36 1059.65i 0.344566 0.198935i
\(306\) 0 0
\(307\) 4133.66i 0.768471i −0.923235 0.384235i \(-0.874465\pi\)
0.923235 0.384235i \(-0.125535\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1222.12 2116.77i −0.222829 0.385952i 0.732837 0.680405i \(-0.238196\pi\)
−0.955666 + 0.294453i \(0.904863\pi\)
\(312\) 0 0
\(313\) 3072.40 + 1773.85i 0.554831 + 0.320332i 0.751068 0.660225i \(-0.229539\pi\)
−0.196237 + 0.980556i \(0.562872\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6357.24 3670.36i −1.12637 0.650308i −0.183348 0.983048i \(-0.558694\pi\)
−0.943019 + 0.332740i \(0.892027\pi\)
\(318\) 0 0
\(319\) 968.247 + 1677.05i 0.169942 + 0.294348i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 117.044i 0.0201625i
\(324\) 0 0
\(325\) −1135.91 + 655.818i −0.193874 + 0.111933i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6587.91 + 3091.47i 1.10396 + 0.518049i
\(330\) 0 0
\(331\) −2815.66 + 4876.87i −0.467561 + 0.809840i −0.999313 0.0370602i \(-0.988201\pi\)
0.531752 + 0.846900i \(0.321534\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7297.51 1.19017
\(336\) 0 0
\(337\) −9281.97 −1.50036 −0.750180 0.661234i \(-0.770033\pi\)
−0.750180 + 0.661234i \(0.770033\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −640.960 + 1110.17i −0.101789 + 0.176303i
\(342\) 0 0
\(343\) 1599.45 + 6147.79i 0.251784 + 0.967783i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4441.01 + 2564.02i −0.687049 + 0.396668i −0.802506 0.596644i \(-0.796500\pi\)
0.115456 + 0.993313i \(0.463167\pi\)
\(348\) 0 0
\(349\) 11096.5i 1.70196i 0.525199 + 0.850980i \(0.323991\pi\)
−0.525199 + 0.850980i \(0.676009\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −401.521 695.454i −0.0605405 0.104859i 0.834167 0.551512i \(-0.185949\pi\)
−0.894707 + 0.446653i \(0.852616\pi\)
\(354\) 0 0
\(355\) −2728.30 1575.19i −0.407897 0.235499i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1596.45 921.712i −0.234701 0.135504i 0.378038 0.925790i \(-0.376599\pi\)
−0.612739 + 0.790286i \(0.709932\pi\)
\(360\) 0 0
\(361\) 1583.19 + 2742.16i 0.230819 + 0.399791i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10383.8i 1.48908i
\(366\) 0 0
\(367\) 10118.6 5841.98i 1.43920 0.830924i 0.441408 0.897307i \(-0.354479\pi\)
0.997794 + 0.0663827i \(0.0211458\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 914.030 + 1312.13i 0.127909 + 0.183619i
\(372\) 0 0
\(373\) 541.327 937.606i 0.0751444 0.130154i −0.826005 0.563663i \(-0.809392\pi\)
0.901149 + 0.433509i \(0.142725\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9844.13 1.34482
\(378\) 0 0
\(379\) 13929.3 1.88786 0.943929 0.330148i \(-0.107099\pi\)
0.943929 + 0.330148i \(0.107099\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1693.36 2932.98i 0.225918 0.391301i −0.730677 0.682724i \(-0.760795\pi\)
0.956594 + 0.291423i \(0.0941286\pi\)
\(384\) 0 0
\(385\) −1905.42 + 162.047i −0.252232 + 0.0214511i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6652.61 + 3840.89i −0.867097 + 0.500619i −0.866382 0.499381i \(-0.833561\pi\)
−0.000714618 1.00000i \(0.500227\pi\)
\(390\) 0 0
\(391\) 121.667i 0.0157364i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6078.17 + 10527.7i 0.774243 + 1.34103i
\(396\) 0 0
\(397\) 8528.01 + 4923.65i 1.07811 + 0.622446i 0.930385 0.366583i \(-0.119472\pi\)
0.147722 + 0.989029i \(0.452806\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11009.5 + 6356.33i 1.37104 + 0.791571i 0.991059 0.133423i \(-0.0425969\pi\)
0.379982 + 0.924994i \(0.375930\pi\)
\(402\) 0 0
\(403\) 3258.31 + 5643.55i 0.402749 + 0.697582i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 331.344i 0.0403541i
\(408\) 0 0
\(409\) −13544.0 + 7819.64i −1.63743 + 0.945370i −0.655715 + 0.755009i \(0.727633\pi\)
−0.981714 + 0.190362i \(0.939034\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3108.82 2165.60i 0.370399 0.258020i
\(414\) 0 0
\(415\) −1669.07 + 2890.91i −0.197425 + 0.341950i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10568.3 1.23221 0.616105 0.787664i \(-0.288710\pi\)
0.616105 + 0.787664i \(0.288710\pi\)
\(420\) 0 0
\(421\) −3890.36 −0.450367 −0.225184 0.974316i \(-0.572298\pi\)
−0.225184 + 0.974316i \(0.572298\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −14.6061 + 25.2984i −0.00166705 + 0.00288742i
\(426\) 0 0
\(427\) −1667.31 + 3553.04i −0.188962 + 0.402678i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2554.42 + 1474.79i −0.285480 + 0.164822i −0.635902 0.771770i \(-0.719372\pi\)
0.350422 + 0.936592i \(0.386038\pi\)
\(432\) 0 0
\(433\) 14292.9i 1.58632i 0.609017 + 0.793158i \(0.291564\pi\)
−0.609017 + 0.793158i \(0.708436\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5210.68 9025.17i −0.570391 0.987946i
\(438\) 0 0
\(439\) −10289.2 5940.50i −1.11863 0.645842i −0.177580 0.984106i \(-0.556827\pi\)
−0.941051 + 0.338265i \(0.890160\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8000.43 + 4619.05i 0.858040 + 0.495390i 0.863356 0.504596i \(-0.168359\pi\)
−0.00531517 + 0.999986i \(0.501692\pi\)
\(444\) 0 0
\(445\) −1683.63 2916.14i −0.179352 0.310647i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5478.22i 0.575798i 0.957661 + 0.287899i \(0.0929568\pi\)
−0.957661 + 0.287899i \(0.907043\pi\)
\(450\) 0 0
\(451\) 3716.12 2145.50i 0.387994 0.224008i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4129.68 + 8800.35i −0.425500 + 0.906740i
\(456\) 0 0
\(457\) −4423.49 + 7661.71i −0.452784 + 0.784244i −0.998558 0.0536880i \(-0.982902\pi\)
0.545774 + 0.837932i \(0.316236\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −15927.8 −1.60917 −0.804587 0.593834i \(-0.797614\pi\)
−0.804587 + 0.593834i \(0.797614\pi\)
\(462\) 0 0
\(463\) 10491.3 1.05307 0.526535 0.850153i \(-0.323491\pi\)
0.526535 + 0.850153i \(0.323491\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7862.95 13619.0i 0.779130 1.34949i −0.153313 0.988178i \(-0.548994\pi\)
0.932444 0.361316i \(-0.117672\pi\)
\(468\) 0 0
\(469\) −11089.2 + 7724.73i −1.09179 + 0.760543i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1728.10 + 997.718i −0.167987 + 0.0969876i
\(474\) 0 0
\(475\) 2502.16i 0.241699i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8758.87 + 15170.8i 0.835496 + 1.44712i 0.893626 + 0.448813i \(0.148153\pi\)
−0.0581291 + 0.998309i \(0.518513\pi\)
\(480\) 0 0
\(481\) 1458.72 + 842.192i 0.138278 + 0.0798350i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7735.54 + 4466.12i 0.724233 + 0.418136i
\(486\) 0 0
\(487\) −7026.77 12170.7i −0.653826 1.13246i −0.982187 0.187908i \(-0.939829\pi\)
0.328360 0.944553i \(-0.393504\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9854.09i 0.905720i 0.891582 + 0.452860i \(0.149596\pi\)
−0.891582 + 0.452860i \(0.850404\pi\)
\(492\) 0 0
\(493\) 189.871 109.622i 0.0173455 0.0100144i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5813.30 494.394i 0.524672 0.0446209i
\(498\) 0 0
\(499\) −6290.14 + 10894.8i −0.564300 + 0.977396i 0.432815 + 0.901483i \(0.357520\pi\)
−0.997114 + 0.0759128i \(0.975813\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2545.29 0.225624 0.112812 0.993616i \(-0.464014\pi\)
0.112812 + 0.993616i \(0.464014\pi\)
\(504\) 0 0
\(505\) 9271.33 0.816968
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7388.51 12797.3i 0.643399 1.11440i −0.341270 0.939965i \(-0.610857\pi\)
0.984669 0.174434i \(-0.0558097\pi\)
\(510\) 0 0
\(511\) 10991.7 + 15779.1i 0.951556 + 1.36600i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4873.85 2813.92i 0.417025 0.240769i
\(516\) 0 0
\(517\) 4056.99i 0.345119i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 25.4037 + 44.0005i 0.00213619 + 0.00369999i 0.867092 0.498149i \(-0.165987\pi\)
−0.864955 + 0.501849i \(0.832653\pi\)
\(522\) 0 0
\(523\) 12714.2 + 7340.56i 1.06301 + 0.613729i 0.926263 0.376877i \(-0.123002\pi\)
0.136746 + 0.990606i \(0.456335\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 125.690 + 72.5674i 0.0103893 + 0.00599827i
\(528\) 0 0
\(529\) −667.006 1155.29i −0.0548209 0.0949526i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 21813.2i 1.77268i
\(534\) 0 0
\(535\) 12904.1 7450.16i 1.04279 0.602053i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2723.92 2263.21i 0.217676 0.180860i
\(540\) 0 0
\(541\) 8294.42 14366.4i 0.659159 1.14170i −0.321675 0.946850i \(-0.604246\pi\)
0.980834 0.194846i \(-0.0624208\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14526.8 1.14176
\(546\) 0 0
\(547\) −2029.96 −0.158674 −0.0793371 0.996848i \(-0.525280\pi\)
−0.0793371 + 0.996848i \(0.525280\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9389.66 16263.4i 0.725976 1.25743i
\(552\) 0 0
\(553\) −20380.3 9563.75i −1.56720 0.735428i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2597.94 + 1499.92i −0.197627 + 0.114100i −0.595548 0.803320i \(-0.703065\pi\)
0.397921 + 0.917420i \(0.369732\pi\)
\(558\) 0 0
\(559\) 10143.8i 0.767506i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8333.02 14433.2i −0.623792 1.08044i −0.988773 0.149424i \(-0.952258\pi\)
0.364981 0.931015i \(-0.381075\pi\)
\(564\) 0 0
\(565\) 15255.6 + 8807.82i 1.13594 + 0.655837i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16427.3 + 9484.30i 1.21031 + 0.698774i 0.962827 0.270118i \(-0.0870627\pi\)
0.247485 + 0.968892i \(0.420396\pi\)
\(570\) 0 0
\(571\) −7667.11 13279.8i −0.561924 0.973281i −0.997329 0.0730460i \(-0.976728\pi\)
0.435405 0.900235i \(-0.356605\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2601.00i 0.188642i
\(576\) 0 0
\(577\) −10576.2 + 6106.20i −0.763076 + 0.440562i −0.830399 0.557169i \(-0.811887\pi\)
0.0673231 + 0.997731i \(0.478554\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −523.861 6159.78i −0.0374069 0.439846i
\(582\) 0 0
\(583\) 445.746 772.054i 0.0316653 0.0548460i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23173.7 1.62944 0.814718 0.579857i \(-0.196892\pi\)
0.814718 + 0.579857i \(0.196892\pi\)
\(588\) 0 0
\(589\) 12431.5 0.869664
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1894.64 3281.61i 0.131203 0.227251i −0.792937 0.609303i \(-0.791449\pi\)
0.924141 + 0.382052i \(0.124783\pi\)
\(594\) 0 0
\(595\) 18.3465 + 215.726i 0.00126409 + 0.0148637i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13663.6 + 7888.67i −0.932018 + 0.538101i −0.887449 0.460906i \(-0.847525\pi\)
−0.0445687 + 0.999006i \(0.514191\pi\)
\(600\) 0 0
\(601\) 23750.2i 1.61197i 0.591939 + 0.805983i \(0.298362\pi\)
−0.591939 + 0.805983i \(0.701638\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6122.29 10604.1i −0.411416 0.712593i
\(606\) 0 0
\(607\) −21418.8 12366.1i −1.43223 0.826897i −0.434937 0.900461i \(-0.643229\pi\)
−0.997290 + 0.0735641i \(0.976563\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17860.6 10311.8i −1.18259 0.682769i
\(612\) 0 0
\(613\) 4659.04 + 8069.69i 0.306977 + 0.531700i 0.977700 0.210009i \(-0.0673492\pi\)
−0.670723 + 0.741708i \(0.734016\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16544.3i 1.07949i 0.841828 + 0.539746i \(0.181480\pi\)
−0.841828 + 0.539746i \(0.818520\pi\)
\(618\) 0 0
\(619\) 8835.49 5101.18i 0.573713 0.331234i −0.184918 0.982754i \(-0.559202\pi\)
0.758631 + 0.651520i \(0.225869\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5645.28 + 2649.12i 0.363039 + 0.170361i
\(624\) 0 0
\(625\) 5938.38 10285.6i 0.380056 0.658277i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 37.5137 0.00237801
\(630\) 0 0
\(631\) −14729.3 −0.929259 −0.464630 0.885505i \(-0.653813\pi\)
−0.464630 + 0.885505i \(0.653813\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 341.645 591.746i 0.0213508 0.0369807i
\(636\) 0 0
\(637\) −3040.14 17744.3i −0.189097 1.10370i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −25503.6 + 14724.5i −1.57150 + 0.907304i −0.575511 + 0.817794i \(0.695197\pi\)
−0.995986 + 0.0895107i \(0.971470\pi\)
\(642\) 0 0
\(643\) 4194.07i 0.257228i −0.991695 0.128614i \(-0.958947\pi\)
0.991695 0.128614i \(-0.0410529\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10732.4 18589.0i −0.652137 1.12953i −0.982603 0.185717i \(-0.940539\pi\)
0.330466 0.943818i \(-0.392794\pi\)
\(648\) 0 0
\(649\) −1829.22 1056.10i −0.110636 0.0638760i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 28232.5 + 16300.1i 1.69192 + 0.976832i 0.952966 + 0.303078i \(0.0980143\pi\)
0.738956 + 0.673753i \(0.235319\pi\)
\(654\) 0 0
\(655\) 2422.61 + 4196.09i 0.144518 + 0.250313i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5931.69i 0.350631i 0.984512 + 0.175315i \(0.0560945\pi\)
−0.984512 + 0.175315i \(0.943905\pi\)
\(660\) 0 0
\(661\) 16409.5 9474.01i 0.965589 0.557483i 0.0677004 0.997706i \(-0.478434\pi\)
0.897889 + 0.440223i \(0.145100\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10599.9 + 15216.7i 0.618116 + 0.887334i
\(666\) 0 0
\(667\) −9760.53 + 16905.7i −0.566611 + 0.981398i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2188.05 0.125885
\(672\) 0 0
\(673\) −19463.2 −1.11479 −0.557394 0.830248i \(-0.688199\pi\)
−0.557394 + 0.830248i \(0.688199\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7010.82 + 12143.1i −0.398003 + 0.689361i −0.993479 0.114012i \(-0.963630\pi\)
0.595477 + 0.803373i \(0.296963\pi\)
\(678\) 0 0
\(679\) −16482.4 + 1401.75i −0.931571 + 0.0792258i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24229.0 + 13988.6i −1.35739 + 0.783688i −0.989271 0.146091i \(-0.953331\pi\)
−0.368117 + 0.929780i \(0.619997\pi\)
\(684\) 0 0
\(685\) 14410.3i 0.803780i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2265.94 3924.72i −0.125291 0.217010i
\(690\) 0 0
\(691\) −22352.5 12905.2i −1.23058 0.710475i −0.263429 0.964679i \(-0.584853\pi\)
−0.967151 + 0.254203i \(0.918187\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12518.7 + 7227.69i 0.683255 + 0.394478i
\(696\) 0 0
\(697\) −242.907 420.727i −0.0132005 0.0228639i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15653.8i 0.843420i −0.906731 0.421710i \(-0.861430\pi\)
0.906731 0.421710i \(-0.138570\pi\)
\(702\) 0 0
\(703\) 2782.75 1606.62i 0.149293 0.0861946i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −14088.6 + 9814.10i −0.749443 + 0.522061i
\(708\) 0 0
\(709\) 16769.6 29045.8i 0.888286 1.53856i 0.0463856 0.998924i \(-0.485230\pi\)
0.841900 0.539633i \(-0.181437\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −12922.5 −0.678756
\(714\) 0 0
\(715\) 5419.47 0.283464
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6620.60 11467.2i 0.343403 0.594791i −0.641659 0.766990i \(-0.721754\pi\)
0.985062 + 0.172198i \(0.0550870\pi\)
\(720\) 0 0
\(721\) −4427.58 + 9435.18i −0.228699 + 0.487357i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4059.06 2343.50i 0.207931 0.120049i
\(726\) 0 0
\(727\) 33618.0i 1.71502i 0.514464 + 0.857512i \(0.327991\pi\)
−0.514464 + 0.857512i \(0.672009\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 112.958 + 195.650i 0.00571535 + 0.00989927i
\(732\) 0 0
\(733\) 3921.55 + 2264.11i 0.197607 + 0.114088i 0.595539 0.803327i \(-0.296939\pi\)
−0.397932 + 0.917415i \(0.630272\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6524.85 + 3767.12i 0.326114 + 0.188282i
\(738\) 0 0
\(739\) 8723.03 + 15108.7i 0.434211 + 0.752075i 0.997231 0.0743682i \(-0.0236940\pi\)
−0.563020 + 0.826443i \(0.690361\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5516.23i 0.272370i 0.990683 + 0.136185i \(0.0434842\pi\)
−0.990683 + 0.136185i \(0.956516\pi\)
\(744\) 0 0
\(745\) 8461.94 4885.50i 0.416136 0.240256i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −11722.5 + 24980.7i −0.571871 + 1.21866i
\(750\) 0 0
\(751\) 1743.07 3019.09i 0.0846947 0.146695i −0.820566 0.571551i \(-0.806342\pi\)
0.905261 + 0.424856i \(0.139675\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 13343.6 0.643209
\(756\) 0 0
\(757\) 28650.9 1.37561 0.687805 0.725896i \(-0.258575\pi\)
0.687805 + 0.725896i \(0.258575\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9804.44 + 16981.8i −0.467031 + 0.808922i −0.999291 0.0376594i \(-0.988010\pi\)
0.532259 + 0.846581i \(0.321343\pi\)
\(762\) 0 0
\(763\) −22074.8 + 15377.3i −1.04739 + 0.729613i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9298.80 + 5368.66i −0.437758 + 0.252739i
\(768\) 0 0
\(769\) 6180.49i 0.289823i 0.989445 + 0.144912i \(0.0462898\pi\)
−0.989445 + 0.144912i \(0.953710\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18600.6 32217.2i −0.865483 1.49906i −0.866567 0.499060i \(-0.833679\pi\)
0.00108453 0.999999i \(-0.499655\pi\)
\(774\) 0 0
\(775\) 2687.01 + 1551.35i 0.124542 + 0.0719046i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −36037.4 20806.2i −1.65747 0.956943i
\(780\) 0 0
\(781\) −1626.29 2816.81i −0.0745110 0.129057i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14966.7i 0.680488i
\(786\) 0 0
\(787\) 4876.40 2815.39i 0.220870 0.127519i −0.385483 0.922715i \(-0.625965\pi\)
0.606353 + 0.795196i \(0.292632\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −32505.6 + 2764.45i −1.46115 + 0.124264i
\(792\) 0 0
\(793\) 5561.45 9632.71i 0.249045 0.431359i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −482.766 −0.0214560 −0.0107280 0.999942i \(-0.503415\pi\)
−0.0107280 + 0.999942i \(0.503415\pi\)
\(798\) 0 0
\(799\) −459.320 −0.0203374
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5360.34 9284.38i 0.235569 0.408018i
\(804\) 0 0
\(805\) −11018.6 15817.7i −0.482428 0.692547i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6666.35 + 3848.82i −0.289711 + 0.167265i −0.637812 0.770192i \(-0.720160\pi\)
0.348100 + 0.937457i \(0.386827\pi\)
\(810\) 0 0
\(811\) 17872.8i 0.773858i −0.922110 0.386929i \(-0.873536\pi\)
0.922110 0.386929i \(-0.126464\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −18948.2 32819.3i −0.814389 1.41056i
\(816\) 0 0
\(817\) 16758.4 + 9675.46i 0.717628 + 0.414322i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −30510.4 17615.2i −1.29698 0.748811i −0.317097 0.948393i \(-0.602708\pi\)
−0.979881 + 0.199582i \(0.936042\pi\)
\(822\) 0 0
\(823\) −10049.0 17405.3i −0.425619 0.737194i 0.570859 0.821048i \(-0.306610\pi\)
−0.996478 + 0.0838543i \(0.973277\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 4666.09i 0.196198i 0.995177 + 0.0980990i \(0.0312762\pi\)
−0.995177 + 0.0980990i \(0.968724\pi\)
\(828\) 0 0
\(829\) 25975.9 14997.2i 1.08828 0.628317i 0.155159 0.987889i \(-0.450411\pi\)
0.933117 + 0.359573i \(0.117078\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −256.234 308.393i −0.0106578 0.0128274i
\(834\) 0 0
\(835\) 6013.60 10415.9i 0.249233 0.431684i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −13935.9 −0.573446 −0.286723 0.958014i \(-0.592566\pi\)
−0.286723 + 0.958014i \(0.592566\pi\)
\(840\) 0 0
\(841\) −10788.0 −0.442330
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2789.34 4831.27i 0.113558 0.196687i
\(846\) 0 0
\(847\) 20528.3 + 9633.16i 0.832773 + 0.390790i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2892.66 + 1670.08i −0.116521 + 0.0672733i
\(852\) 0 0
\(853\) 1372.58i 0.0550952i 0.999620 + 0.0275476i \(0.00876979\pi\)
−0.999620 + 0.0275476i \(0.991230\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −5619.68 9733.57i −0.223996 0.387973i 0.732022 0.681281i \(-0.238577\pi\)
−0.956018 + 0.293309i \(0.905244\pi\)
\(858\) 0 0
\(859\) −37877.1 21868.4i −1.50448 0.868613i −0.999986 0.00519912i \(-0.998345\pi\)
−0.504496 0.863414i \(-0.668322\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 17076.7 + 9859.22i 0.673577 + 0.388890i 0.797430 0.603411i \(-0.206192\pi\)
−0.123854 + 0.992300i \(0.539525\pi\)
\(864\) 0 0
\(865\) −7655.68 13260.0i −0.300926 0.521219i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 12550.7i 0.489935i
\(870\) 0 0
\(871\) 33168.9 19150.1i 1.29034 0.744979i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2354.06 + 27680.0i 0.0909504 + 1.06943i
\(876\) 0 0
\(877\) −11293.8 + 19561.4i −0.434850 + 0.753183i −0.997283 0.0736598i \(-0.976532\pi\)
0.562433 + 0.826843i \(0.309865\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 39105.2 1.49545 0.747723 0.664011i \(-0.231147\pi\)
0.747723 + 0.664011i \(0.231147\pi\)
\(882\) 0 0
\(883\) 37839.6 1.44213 0.721066 0.692866i \(-0.243652\pi\)
0.721066 + 0.692866i \(0.243652\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8185.69 + 14178.0i −0.309863 + 0.536698i −0.978332 0.207041i \(-0.933616\pi\)
0.668469 + 0.743740i \(0.266950\pi\)
\(888\) 0 0
\(889\) 107.230 + 1260.86i 0.00404542 + 0.0475678i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −34072.1 + 19671.5i −1.27680 + 0.737158i
\(894\) 0 0
\(895\) 18422.0i 0.688022i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −11643.2 20166.7i −0.431950 0.748160i
\(900\) 0 0
\(901\) −87.4095 50.4659i −0.00323200 0.00186600i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2815.15 + 1625.33i 0.103402 + 0.0596991i
\(906\) 0 0
\(907\) −13419.7 23243.6i −0.491283 0.850927i 0.508667 0.860964i \(-0.330139\pi\)
−0.999950 + 0.0100365i \(0.996805\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 45173.3i 1.64287i −0.570300 0.821437i \(-0.693173\pi\)
0.570300 0.821437i \(-0.306827\pi\)
\(912\) 0 0
\(913\) −2984.70 + 1723.22i −0.108192 + 0.0624645i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8123.11 3811.88i −0.292529 0.137273i
\(918\) 0 0
\(919\) −10893.7 + 18868.4i −0.391022 + 0.677270i −0.992585 0.121556i \(-0.961212\pi\)
0.601563 + 0.798826i \(0.294545\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −16534.4 −0.589639
\(924\) 0 0
\(925\) 801.970 0.0285066
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −5860.89 + 10151.4i −0.206985 + 0.358509i −0.950763 0.309917i \(-0.899699\pi\)
0.743778 + 0.668427i \(0.233032\pi\)
\(930\) 0 0
\(931\) −32215.0 11902.6i −1.13405 0.419002i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 104.529 60.3499i 0.00365611 0.00211086i
\(936\) 0 0
\(937\) 9781.37i 0.341028i 0.985355 + 0.170514i \(0.0545429\pi\)
−0.985355 + 0.170514i \(0.945457\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14914.6 25832.9i −0.516687 0.894928i −0.999812 0.0193766i \(-0.993832\pi\)
0.483125 0.875551i \(-0.339501\pi\)
\(942\) 0 0
\(943\) 37460.8 + 21628.0i 1.29363 + 0.746876i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1073.64 + 619.868i 0.0368413 + 0.0212703i 0.518308 0.855194i \(-0.326562\pi\)
−0.481466 + 0.876465i \(0.659896\pi\)
\(948\) 0 0
\(949\) −27249.2 47197.0i −0.932082 1.61441i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 35161.2i 1.19516i −0.801810 0.597578i \(-0.796130\pi\)
0.801810 0.597578i \(-0.203870\pi\)
\(954\) 0 0
\(955\) 30460.6 17586.5i 1.03213 0.595900i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 15253.9 + 21897.7i 0.513634 + 0.737344i
\(960\) 0 0
\(961\) −7187.92 + 12449.8i −0.241278 + 0.417906i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10050.3 0.335265
\(966\) 0 0
\(967\) −38907.9 −1.29389 −0.646946 0.762536i \(-0.723954\pi\)
−0.646946 + 0.762536i \(0.723954\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2540.26 + 4399.87i −0.0839557 + 0.145415i −0.904946 0.425527i \(-0.860089\pi\)
0.820990 + 0.570942i \(0.193422\pi\)
\(972\) 0 0
\(973\) −26674.1 + 2268.51i −0.878862 + 0.0747432i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −13364.5 + 7715.98i −0.437633 + 0.252667i −0.702593 0.711592i \(-0.747974\pi\)
0.264960 + 0.964259i \(0.414641\pi\)
\(978\) 0 0
\(979\) 3476.50i 0.113493i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 16878.9 + 29235.2i 0.547665 + 0.948584i 0.998434 + 0.0559429i \(0.0178165\pi\)
−0.450769 + 0.892641i \(0.648850\pi\)
\(984\) 0 0
\(985\) −24327.1 14045.2i −0.786929 0.454334i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −17420.3 10057.6i −0.560095 0.323371i
\(990\) 0 0
\(991\) −26259.7 45483.2i −0.841743 1.45794i −0.888420 0.459032i \(-0.848196\pi\)
0.0466765 0.998910i \(-0.485137\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2427.87i 0.0773555i
\(996\) 0 0
\(997\) 3156.68 1822.51i 0.100274 0.0578931i −0.449025 0.893519i \(-0.648228\pi\)
0.549298 + 0.835626i \(0.314895\pi\)
\(998\) 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 1008.4.bt.d.593.7 48
3.2 odd 2 inner 1008.4.bt.d.593.18 48
4.3 odd 2 504.4.bl.a.89.7 yes 48
7.3 odd 6 inner 1008.4.bt.d.17.18 48
12.11 even 2 504.4.bl.a.89.18 yes 48
21.17 even 6 inner 1008.4.bt.d.17.7 48
28.3 even 6 504.4.bl.a.17.18 yes 48
84.59 odd 6 504.4.bl.a.17.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.4.bl.a.17.7 48 84.59 odd 6
504.4.bl.a.17.18 yes 48 28.3 even 6
504.4.bl.a.89.7 yes 48 4.3 odd 2
504.4.bl.a.89.18 yes 48 12.11 even 2
1008.4.bt.d.17.7 48 21.17 even 6 inner
1008.4.bt.d.17.18 48 7.3 odd 6 inner
1008.4.bt.d.593.7 48 1.1 even 1 trivial
1008.4.bt.d.593.18 48 3.2 odd 2 inner