Properties

Label 588.4.k.e.521.6
Level $588$
Weight $4$
Character 588.521
Analytic conductor $34.693$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,4,Mod(509,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.509");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.k (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: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.6
Character \(\chi\) \(=\) 588.521
Dual form 588.4.k.e.509.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.41120 + 3.91966i) q^{3} +(6.50213 + 11.2620i) q^{5} +(-3.72746 - 26.7415i) q^{9} +O(q^{10})\) \(q+(-3.41120 + 3.91966i) q^{3} +(6.50213 + 11.2620i) q^{5} +(-3.72746 - 26.7415i) q^{9} +(-4.49726 - 2.59650i) q^{11} +72.6603i q^{13} +(-66.3233 - 12.9308i) q^{15} +(44.7733 - 77.5496i) q^{17} +(-113.080 + 65.2865i) q^{19} +(-108.141 + 62.4354i) q^{23} +(-22.0553 + 38.2010i) q^{25} +(117.533 + 76.6101i) q^{27} +63.1418i q^{29} +(91.6564 + 52.9179i) q^{31} +(25.5184 - 8.77058i) q^{33} +(46.9184 + 81.2651i) q^{37} +(-284.804 - 247.859i) q^{39} -320.640 q^{41} -351.830 q^{43} +(276.926 - 215.855i) q^{45} +(102.656 + 177.805i) q^{47} +(151.238 + 440.033i) q^{51} +(-68.9957 - 39.8347i) q^{53} -67.5310i q^{55} +(129.836 - 665.938i) q^{57} +(449.621 - 778.767i) q^{59} +(489.428 - 282.571i) q^{61} +(-818.302 + 472.447i) q^{65} +(41.1414 - 71.2591i) q^{67} +(124.166 - 636.856i) q^{69} -457.950i q^{71} +(-769.098 - 444.039i) q^{73} +(-74.4997 - 216.761i) q^{75} +(-247.926 - 429.421i) q^{79} +(-701.212 + 199.355i) q^{81} -1022.84 q^{83} +1164.49 q^{85} +(-247.494 - 215.389i) q^{87} +(65.5170 + 113.479i) q^{89} +(-520.078 + 178.749i) q^{93} +(-1470.51 - 849.002i) q^{95} +897.230i q^{97} +(-52.6707 + 129.942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −3.41120 + 3.91966i −0.656485 + 0.754339i
\(4\) 0 0
\(5\) 6.50213 + 11.2620i 0.581568 + 1.00731i 0.995294 + 0.0969038i \(0.0308939\pi\)
−0.413726 + 0.910402i \(0.635773\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −3.72746 26.7415i −0.138054 0.990425i
\(10\) 0 0
\(11\) −4.49726 2.59650i −0.123271 0.0711703i 0.437097 0.899414i \(-0.356007\pi\)
−0.560367 + 0.828244i \(0.689340\pi\)
\(12\) 0 0
\(13\) 72.6603i 1.55018i 0.631850 + 0.775090i \(0.282296\pi\)
−0.631850 + 0.775090i \(0.717704\pi\)
\(14\) 0 0
\(15\) −66.3233 12.9308i −1.14164 0.222582i
\(16\) 0 0
\(17\) 44.7733 77.5496i 0.638772 1.10639i −0.346931 0.937891i \(-0.612776\pi\)
0.985703 0.168495i \(-0.0538906\pi\)
\(18\) 0 0
\(19\) −113.080 + 65.2865i −1.36538 + 0.788302i −0.990334 0.138704i \(-0.955706\pi\)
−0.375046 + 0.927006i \(0.622373\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −108.141 + 62.4354i −0.980392 + 0.566029i −0.902388 0.430924i \(-0.858188\pi\)
−0.0780033 + 0.996953i \(0.524854\pi\)
\(24\) 0 0
\(25\) −22.0553 + 38.2010i −0.176443 + 0.305608i
\(26\) 0 0
\(27\) 117.533 + 76.6101i 0.837746 + 0.546060i
\(28\) 0 0
\(29\) 63.1418i 0.404315i 0.979353 + 0.202158i \(0.0647953\pi\)
−0.979353 + 0.202158i \(0.935205\pi\)
\(30\) 0 0
\(31\) 91.6564 + 52.9179i 0.531032 + 0.306591i 0.741436 0.671023i \(-0.234145\pi\)
−0.210405 + 0.977614i \(0.567478\pi\)
\(32\) 0 0
\(33\) 25.5184 8.77058i 0.134612 0.0462655i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 46.9184 + 81.2651i 0.208469 + 0.361078i 0.951232 0.308475i \(-0.0998187\pi\)
−0.742764 + 0.669554i \(0.766485\pi\)
\(38\) 0 0
\(39\) −284.804 247.859i −1.16936 1.01767i
\(40\) 0 0
\(41\) −320.640 −1.22136 −0.610678 0.791879i \(-0.709103\pi\)
−0.610678 + 0.791879i \(0.709103\pi\)
\(42\) 0 0
\(43\) −351.830 −1.24776 −0.623878 0.781522i \(-0.714444\pi\)
−0.623878 + 0.781522i \(0.714444\pi\)
\(44\) 0 0
\(45\) 276.926 215.855i 0.917372 0.715062i
\(46\) 0 0
\(47\) 102.656 + 177.805i 0.318593 + 0.551820i 0.980195 0.198036i \(-0.0634563\pi\)
−0.661602 + 0.749856i \(0.730123\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 151.238 + 440.033i 0.415245 + 1.20818i
\(52\) 0 0
\(53\) −68.9957 39.8347i −0.178817 0.103240i 0.407920 0.913018i \(-0.366254\pi\)
−0.586737 + 0.809778i \(0.699588\pi\)
\(54\) 0 0
\(55\) 67.5310i 0.165561i
\(56\) 0 0
\(57\) 129.836 665.938i 0.301705 1.54747i
\(58\) 0 0
\(59\) 449.621 778.767i 0.992130 1.71842i 0.387629 0.921815i \(-0.373294\pi\)
0.604501 0.796604i \(-0.293373\pi\)
\(60\) 0 0
\(61\) 489.428 282.571i 1.02729 0.593107i 0.111084 0.993811i \(-0.464568\pi\)
0.916208 + 0.400703i \(0.131234\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −818.302 + 472.447i −1.56151 + 0.901536i
\(66\) 0 0
\(67\) 41.1414 71.2591i 0.0750183 0.129936i −0.826076 0.563559i \(-0.809432\pi\)
0.901094 + 0.433623i \(0.142765\pi\)
\(68\) 0 0
\(69\) 124.166 636.856i 0.216635 1.11114i
\(70\) 0 0
\(71\) 457.950i 0.765474i −0.923857 0.382737i \(-0.874982\pi\)
0.923857 0.382737i \(-0.125018\pi\)
\(72\) 0 0
\(73\) −769.098 444.039i −1.23310 0.711929i −0.265423 0.964132i \(-0.585512\pi\)
−0.967674 + 0.252203i \(0.918845\pi\)
\(74\) 0 0
\(75\) −74.4997 216.761i −0.114700 0.333725i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −247.926 429.421i −0.353087 0.611565i 0.633701 0.773578i \(-0.281535\pi\)
−0.986789 + 0.162013i \(0.948201\pi\)
\(80\) 0 0
\(81\) −701.212 + 199.355i −0.961882 + 0.273464i
\(82\) 0 0
\(83\) −1022.84 −1.35267 −0.676336 0.736594i \(-0.736433\pi\)
−0.676336 + 0.736594i \(0.736433\pi\)
\(84\) 0 0
\(85\) 1164.49 1.48596
\(86\) 0 0
\(87\) −247.494 215.389i −0.304991 0.265427i
\(88\) 0 0
\(89\) 65.5170 + 113.479i 0.0780313 + 0.135154i 0.902400 0.430898i \(-0.141803\pi\)
−0.824369 + 0.566053i \(0.808470\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −520.078 + 178.749i −0.579888 + 0.199305i
\(94\) 0 0
\(95\) −1470.51 849.002i −1.58812 0.916903i
\(96\) 0 0
\(97\) 897.230i 0.939174i 0.882886 + 0.469587i \(0.155597\pi\)
−0.882886 + 0.469587i \(0.844403\pi\)
\(98\) 0 0
\(99\) −52.6707 + 129.942i −0.0534708 + 0.131915i
\(100\) 0 0
\(101\) 574.855 995.677i 0.566338 0.980927i −0.430585 0.902550i \(-0.641693\pi\)
0.996924 0.0783770i \(-0.0249738\pi\)
\(102\) 0 0
\(103\) −1425.92 + 823.254i −1.36408 + 0.787550i −0.990164 0.139914i \(-0.955318\pi\)
−0.373913 + 0.927464i \(0.621984\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1701.12 + 982.145i −1.53695 + 0.887360i −0.537938 + 0.842985i \(0.680796\pi\)
−0.999015 + 0.0443752i \(0.985870\pi\)
\(108\) 0 0
\(109\) −786.758 + 1362.70i −0.691355 + 1.19746i 0.280039 + 0.959989i \(0.409653\pi\)
−0.971394 + 0.237474i \(0.923681\pi\)
\(110\) 0 0
\(111\) −478.580 93.3071i −0.409232 0.0797866i
\(112\) 0 0
\(113\) 2002.30i 1.66691i −0.552590 0.833454i \(-0.686360\pi\)
0.552590 0.833454i \(-0.313640\pi\)
\(114\) 0 0
\(115\) −1406.30 811.926i −1.14033 0.658369i
\(116\) 0 0
\(117\) 1943.04 270.838i 1.53534 0.214009i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −652.016 1129.33i −0.489870 0.848479i
\(122\) 0 0
\(123\) 1093.77 1256.80i 0.801802 0.921316i
\(124\) 0 0
\(125\) 1051.91 0.752682
\(126\) 0 0
\(127\) −166.537 −0.116361 −0.0581803 0.998306i \(-0.518530\pi\)
−0.0581803 + 0.998306i \(0.518530\pi\)
\(128\) 0 0
\(129\) 1200.16 1379.05i 0.819134 0.941231i
\(130\) 0 0
\(131\) −157.967 273.606i −0.105356 0.182482i 0.808528 0.588458i \(-0.200265\pi\)
−0.913884 + 0.405976i \(0.866931\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −98.5721 + 1821.78i −0.0628425 + 1.16144i
\(136\) 0 0
\(137\) 345.158 + 199.277i 0.215247 + 0.124273i 0.603747 0.797176i \(-0.293674\pi\)
−0.388501 + 0.921448i \(0.627007\pi\)
\(138\) 0 0
\(139\) 228.245i 0.139277i 0.997572 + 0.0696384i \(0.0221845\pi\)
−0.997572 + 0.0696384i \(0.977815\pi\)
\(140\) 0 0
\(141\) −1047.11 204.152i −0.625411 0.121934i
\(142\) 0 0
\(143\) 188.662 326.773i 0.110327 0.191092i
\(144\) 0 0
\(145\) −711.104 + 410.556i −0.407269 + 0.235137i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3066.97 1770.71i 1.68628 0.973574i 0.728954 0.684563i \(-0.240007\pi\)
0.957326 0.289011i \(-0.0933263\pi\)
\(150\) 0 0
\(151\) 105.383 182.529i 0.0567945 0.0983710i −0.836230 0.548378i \(-0.815245\pi\)
0.893025 + 0.450007i \(0.148579\pi\)
\(152\) 0 0
\(153\) −2240.68 908.241i −1.18398 0.479914i
\(154\) 0 0
\(155\) 1376.31i 0.713215i
\(156\) 0 0
\(157\) 2462.26 + 1421.59i 1.25166 + 0.722644i 0.971438 0.237292i \(-0.0762599\pi\)
0.280218 + 0.959936i \(0.409593\pi\)
\(158\) 0 0
\(159\) 391.497 134.556i 0.195269 0.0671130i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 228.833 + 396.350i 0.109961 + 0.190457i 0.915754 0.401739i \(-0.131594\pi\)
−0.805794 + 0.592197i \(0.798261\pi\)
\(164\) 0 0
\(165\) 264.698 + 230.362i 0.124889 + 0.108689i
\(166\) 0 0
\(167\) 2108.64 0.977076 0.488538 0.872543i \(-0.337530\pi\)
0.488538 + 0.872543i \(0.337530\pi\)
\(168\) 0 0
\(169\) −3082.52 −1.40306
\(170\) 0 0
\(171\) 2167.36 + 2780.56i 0.969250 + 1.24348i
\(172\) 0 0
\(173\) 439.144 + 760.620i 0.192991 + 0.334271i 0.946240 0.323465i \(-0.104848\pi\)
−0.753249 + 0.657736i \(0.771514\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1518.75 + 4418.89i 0.644952 + 1.87652i
\(178\) 0 0
\(179\) −2742.00 1583.09i −1.14495 0.661039i −0.197301 0.980343i \(-0.563218\pi\)
−0.947652 + 0.319304i \(0.896551\pi\)
\(180\) 0 0
\(181\) 4000.19i 1.64272i 0.570413 + 0.821358i \(0.306783\pi\)
−0.570413 + 0.821358i \(0.693217\pi\)
\(182\) 0 0
\(183\) −561.952 + 2882.30i −0.226998 + 1.16429i
\(184\) 0 0
\(185\) −610.139 + 1056.79i −0.242478 + 0.419983i
\(186\) 0 0
\(187\) −402.715 + 232.507i −0.157483 + 0.0909231i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −861.175 + 497.200i −0.326243 + 0.188357i −0.654172 0.756346i \(-0.726983\pi\)
0.327929 + 0.944702i \(0.393649\pi\)
\(192\) 0 0
\(193\) 1030.58 1785.02i 0.384367 0.665743i −0.607314 0.794462i \(-0.707753\pi\)
0.991681 + 0.128719i \(0.0410864\pi\)
\(194\) 0 0
\(195\) 939.559 4819.07i 0.345042 1.76975i
\(196\) 0 0
\(197\) 399.812i 0.144596i 0.997383 + 0.0722980i \(0.0230333\pi\)
−0.997383 + 0.0722980i \(0.976967\pi\)
\(198\) 0 0
\(199\) −2516.96 1453.17i −0.896597 0.517650i −0.0205024 0.999790i \(-0.506527\pi\)
−0.876095 + 0.482139i \(0.839860\pi\)
\(200\) 0 0
\(201\) 138.970 + 404.339i 0.0487670 + 0.141890i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2084.84 3611.06i −0.710301 1.23028i
\(206\) 0 0
\(207\) 2072.71 + 2659.13i 0.695957 + 0.892861i
\(208\) 0 0
\(209\) 678.064 0.224415
\(210\) 0 0
\(211\) 2947.20 0.961582 0.480791 0.876835i \(-0.340350\pi\)
0.480791 + 0.876835i \(0.340350\pi\)
\(212\) 0 0
\(213\) 1795.01 + 1562.16i 0.577426 + 0.502522i
\(214\) 0 0
\(215\) −2287.64 3962.31i −0.725655 1.25687i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4364.03 1499.90i 1.34655 0.462802i
\(220\) 0 0
\(221\) 5634.78 + 3253.24i 1.71510 + 0.990212i
\(222\) 0 0
\(223\) 3481.59i 1.04549i 0.852489 + 0.522745i \(0.175092\pi\)
−0.852489 + 0.522745i \(0.824908\pi\)
\(224\) 0 0
\(225\) 1103.76 + 447.400i 0.327040 + 0.132563i
\(226\) 0 0
\(227\) −1937.00 + 3354.98i −0.566357 + 0.980959i 0.430565 + 0.902560i \(0.358314\pi\)
−0.996922 + 0.0783996i \(0.975019\pi\)
\(228\) 0 0
\(229\) −3472.34 + 2004.76i −1.00200 + 0.578507i −0.908841 0.417144i \(-0.863031\pi\)
−0.0931632 + 0.995651i \(0.529698\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4398.07 2539.23i 1.23660 0.713949i 0.268200 0.963363i \(-0.413571\pi\)
0.968397 + 0.249414i \(0.0802380\pi\)
\(234\) 0 0
\(235\) −1334.96 + 2312.22i −0.370567 + 0.641841i
\(236\) 0 0
\(237\) 2528.91 + 493.053i 0.693124 + 0.135136i
\(238\) 0 0
\(239\) 1081.25i 0.292636i 0.989238 + 0.146318i \(0.0467423\pi\)
−0.989238 + 0.146318i \(0.953258\pi\)
\(240\) 0 0
\(241\) −2854.95 1648.31i −0.763086 0.440568i 0.0673168 0.997732i \(-0.478556\pi\)
−0.830403 + 0.557164i \(0.811890\pi\)
\(242\) 0 0
\(243\) 1610.57 3428.55i 0.425177 0.905110i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4743.74 8216.40i −1.22201 2.11659i
\(248\) 0 0
\(249\) 3489.12 4009.20i 0.888009 1.02037i
\(250\) 0 0
\(251\) −690.705 −0.173693 −0.0868464 0.996222i \(-0.527679\pi\)
−0.0868464 + 0.996222i \(0.527679\pi\)
\(252\) 0 0
\(253\) 648.453 0.161138
\(254\) 0 0
\(255\) −3972.30 + 4564.39i −0.975509 + 1.12092i
\(256\) 0 0
\(257\) 3948.33 + 6838.71i 0.958327 + 1.65987i 0.726563 + 0.687100i \(0.241117\pi\)
0.231764 + 0.972772i \(0.425550\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1688.50 235.359i 0.400444 0.0558173i
\(262\) 0 0
\(263\) 2595.62 + 1498.58i 0.608567 + 0.351356i 0.772404 0.635131i \(-0.219054\pi\)
−0.163838 + 0.986487i \(0.552387\pi\)
\(264\) 0 0
\(265\) 1036.04i 0.240164i
\(266\) 0 0
\(267\) −668.289 130.294i −0.153178 0.0298647i
\(268\) 0 0
\(269\) −4041.71 + 7000.45i −0.916087 + 1.58671i −0.110785 + 0.993844i \(0.535337\pi\)
−0.805302 + 0.592865i \(0.797997\pi\)
\(270\) 0 0
\(271\) −2865.50 + 1654.40i −0.642313 + 0.370840i −0.785505 0.618855i \(-0.787597\pi\)
0.143192 + 0.989695i \(0.454263\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 198.377 114.533i 0.0435004 0.0251150i
\(276\) 0 0
\(277\) −2497.77 + 4326.26i −0.541792 + 0.938411i 0.457009 + 0.889462i \(0.348921\pi\)
−0.998801 + 0.0489494i \(0.984413\pi\)
\(278\) 0 0
\(279\) 1073.46 2648.28i 0.230344 0.568273i
\(280\) 0 0
\(281\) 4123.67i 0.875436i 0.899112 + 0.437718i \(0.144213\pi\)
−0.899112 + 0.437718i \(0.855787\pi\)
\(282\) 0 0
\(283\) −1586.09 915.727i −0.333155 0.192347i 0.324086 0.946028i \(-0.394943\pi\)
−0.657241 + 0.753680i \(0.728277\pi\)
\(284\) 0 0
\(285\) 8344.02 2867.80i 1.73423 0.596049i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1552.80 2689.52i −0.316059 0.547430i
\(290\) 0 0
\(291\) −3516.84 3060.63i −0.708456 0.616554i
\(292\) 0 0
\(293\) −2676.36 −0.533634 −0.266817 0.963747i \(-0.585972\pi\)
−0.266817 + 0.963747i \(0.585972\pi\)
\(294\) 0 0
\(295\) 11694.0 2.30796
\(296\) 0 0
\(297\) −329.657 649.708i −0.0644062 0.126936i
\(298\) 0 0
\(299\) −4536.58 7857.58i −0.877448 1.51978i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1941.77 + 5649.69i 0.368158 + 1.07118i
\(304\) 0 0
\(305\) 6364.65 + 3674.63i 1.19488 + 0.689865i
\(306\) 0 0
\(307\) 384.925i 0.0715597i −0.999360 0.0357798i \(-0.988608\pi\)
0.999360 0.0357798i \(-0.0113915\pi\)
\(308\) 0 0
\(309\) 1637.21 8397.40i 0.301417 1.54599i
\(310\) 0 0
\(311\) −1220.95 + 2114.75i −0.222617 + 0.385584i −0.955602 0.294661i \(-0.904793\pi\)
0.732985 + 0.680245i \(0.238127\pi\)
\(312\) 0 0
\(313\) −3573.75 + 2063.30i −0.645368 + 0.372603i −0.786679 0.617362i \(-0.788201\pi\)
0.141312 + 0.989965i \(0.454868\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5833.28 3367.85i 1.03353 0.596710i 0.115538 0.993303i \(-0.463141\pi\)
0.917995 + 0.396593i \(0.129808\pi\)
\(318\) 0 0
\(319\) 163.947 283.965i 0.0287752 0.0498401i
\(320\) 0 0
\(321\) 1953.20 10018.1i 0.339617 1.74192i
\(322\) 0 0
\(323\) 11692.4i 2.01418i
\(324\) 0 0
\(325\) −2775.70 1602.55i −0.473747 0.273518i
\(326\) 0 0
\(327\) −2657.55 7732.28i −0.449428 1.30763i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2059.35 + 3566.90i 0.341970 + 0.592310i 0.984799 0.173700i \(-0.0555724\pi\)
−0.642828 + 0.766010i \(0.722239\pi\)
\(332\) 0 0
\(333\) 1998.26 1557.58i 0.328841 0.256321i
\(334\) 0 0
\(335\) 1070.03 0.174513
\(336\) 0 0
\(337\) −4453.87 −0.719934 −0.359967 0.932965i \(-0.617212\pi\)
−0.359967 + 0.932965i \(0.617212\pi\)
\(338\) 0 0
\(339\) 7848.33 + 6830.24i 1.25741 + 1.09430i
\(340\) 0 0
\(341\) −274.802 475.971i −0.0436404 0.0755873i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 7979.63 2742.56i 1.24524 0.427985i
\(346\) 0 0
\(347\) 4468.22 + 2579.73i 0.691258 + 0.399098i 0.804083 0.594517i \(-0.202657\pi\)
−0.112825 + 0.993615i \(0.535990\pi\)
\(348\) 0 0
\(349\) 2662.35i 0.408345i 0.978935 + 0.204173i \(0.0654504\pi\)
−0.978935 + 0.204173i \(0.934550\pi\)
\(350\) 0 0
\(351\) −5566.51 + 8539.95i −0.846491 + 1.29866i
\(352\) 0 0
\(353\) 294.789 510.590i 0.0444477 0.0769857i −0.842946 0.537999i \(-0.819181\pi\)
0.887393 + 0.461013i \(0.152514\pi\)
\(354\) 0 0
\(355\) 5157.44 2977.65i 0.771066 0.445175i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7391.47 + 4267.47i −1.08665 + 0.627377i −0.932682 0.360699i \(-0.882538\pi\)
−0.153967 + 0.988076i \(0.549205\pi\)
\(360\) 0 0
\(361\) 5095.15 8825.06i 0.742841 1.28664i
\(362\) 0 0
\(363\) 6650.73 + 1296.67i 0.961633 + 0.187486i
\(364\) 0 0
\(365\) 11548.8i 1.65614i
\(366\) 0 0
\(367\) 6753.50 + 3899.13i 0.960571 + 0.554586i 0.896349 0.443350i \(-0.146210\pi\)
0.0642224 + 0.997936i \(0.479543\pi\)
\(368\) 0 0
\(369\) 1195.17 + 8574.39i 0.168613 + 1.20966i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −602.802 1044.08i −0.0836780 0.144934i 0.821149 0.570714i \(-0.193333\pi\)
−0.904827 + 0.425779i \(0.860000\pi\)
\(374\) 0 0
\(375\) −3588.26 + 4123.11i −0.494125 + 0.567777i
\(376\) 0 0
\(377\) −4587.90 −0.626762
\(378\) 0 0
\(379\) −8527.67 −1.15577 −0.577885 0.816118i \(-0.696122\pi\)
−0.577885 + 0.816118i \(0.696122\pi\)
\(380\) 0 0
\(381\) 568.091 652.769i 0.0763890 0.0877753i
\(382\) 0 0
\(383\) 4723.71 + 8181.71i 0.630210 + 1.09156i 0.987509 + 0.157566i \(0.0503645\pi\)
−0.357299 + 0.933990i \(0.616302\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1311.43 + 9408.44i 0.172258 + 1.23581i
\(388\) 0 0
\(389\) −8117.13 4686.42i −1.05798 0.610826i −0.133108 0.991102i \(-0.542496\pi\)
−0.924873 + 0.380276i \(0.875829\pi\)
\(390\) 0 0
\(391\) 11181.8i 1.44625i
\(392\) 0 0
\(393\) 1611.30 + 314.150i 0.206818 + 0.0403225i
\(394\) 0 0
\(395\) 3224.10 5584.30i 0.410688 0.711333i
\(396\) 0 0
\(397\) −1236.96 + 714.160i −0.156376 + 0.0902837i −0.576146 0.817347i \(-0.695444\pi\)
0.419770 + 0.907630i \(0.362111\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2535.87 1464.08i 0.315799 0.182326i −0.333720 0.942672i \(-0.608304\pi\)
0.649518 + 0.760346i \(0.274971\pi\)
\(402\) 0 0
\(403\) −3845.03 + 6659.79i −0.475272 + 0.823195i
\(404\) 0 0
\(405\) −6804.52 6600.83i −0.834862 0.809871i
\(406\) 0 0
\(407\) 487.294i 0.0593471i
\(408\) 0 0
\(409\) −7106.97 4103.21i −0.859210 0.496065i 0.00453767 0.999990i \(-0.498556\pi\)
−0.863748 + 0.503925i \(0.831889\pi\)
\(410\) 0 0
\(411\) −1958.50 + 673.128i −0.235050 + 0.0807857i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −6650.66 11519.3i −0.786670 1.36255i
\(416\) 0 0
\(417\) −894.642 778.588i −0.105062 0.0914332i
\(418\) 0 0
\(419\) 191.679 0.0223487 0.0111744 0.999938i \(-0.496443\pi\)
0.0111744 + 0.999938i \(0.496443\pi\)
\(420\) 0 0
\(421\) −5722.17 −0.662427 −0.331213 0.943556i \(-0.607458\pi\)
−0.331213 + 0.943556i \(0.607458\pi\)
\(422\) 0 0
\(423\) 4372.12 3407.93i 0.502553 0.391723i
\(424\) 0 0
\(425\) 1974.98 + 3420.77i 0.225413 + 0.390427i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 637.273 + 1854.18i 0.0717199 + 0.208673i
\(430\) 0 0
\(431\) −11254.2 6497.61i −1.25776 0.726169i −0.285122 0.958491i \(-0.592034\pi\)
−0.972639 + 0.232323i \(0.925368\pi\)
\(432\) 0 0
\(433\) 7022.02i 0.779346i 0.920953 + 0.389673i \(0.127412\pi\)
−0.920953 + 0.389673i \(0.872588\pi\)
\(434\) 0 0
\(435\) 816.476 4187.77i 0.0899932 0.461582i
\(436\) 0 0
\(437\) 8152.37 14120.3i 0.892405 1.54569i
\(438\) 0 0
\(439\) −10337.2 + 5968.16i −1.12384 + 0.648849i −0.942378 0.334549i \(-0.891416\pi\)
−0.181461 + 0.983398i \(0.558083\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6650.98 + 3839.94i −0.713313 + 0.411831i −0.812286 0.583259i \(-0.801777\pi\)
0.0989738 + 0.995090i \(0.468444\pi\)
\(444\) 0 0
\(445\) −851.999 + 1475.71i −0.0907610 + 0.157203i
\(446\) 0 0
\(447\) −3521.43 + 18061.7i −0.372613 + 1.91116i
\(448\) 0 0
\(449\) 1268.09i 0.133285i −0.997777 0.0666425i \(-0.978771\pi\)
0.997777 0.0666425i \(-0.0212287\pi\)
\(450\) 0 0
\(451\) 1442.00 + 832.541i 0.150557 + 0.0869242i
\(452\) 0 0
\(453\) 355.969 + 1035.71i 0.0369203 + 0.107421i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1900.21 3291.25i −0.194503 0.336889i 0.752234 0.658896i \(-0.228976\pi\)
−0.946738 + 0.322006i \(0.895643\pi\)
\(458\) 0 0
\(459\) 11203.4 5684.52i 1.13928 0.578063i
\(460\) 0 0
\(461\) 11736.5 1.18573 0.592866 0.805301i \(-0.297996\pi\)
0.592866 + 0.805301i \(0.297996\pi\)
\(462\) 0 0
\(463\) −5696.66 −0.571806 −0.285903 0.958259i \(-0.592294\pi\)
−0.285903 + 0.958259i \(0.592294\pi\)
\(464\) 0 0
\(465\) −5394.68 4694.88i −0.538005 0.468215i
\(466\) 0 0
\(467\) −8339.06 14443.7i −0.826307 1.43121i −0.900916 0.433993i \(-0.857104\pi\)
0.0746089 0.997213i \(-0.476229\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −13971.4 + 4801.92i −1.36681 + 0.469768i
\(472\) 0 0
\(473\) 1582.27 + 913.524i 0.153812 + 0.0888032i
\(474\) 0 0
\(475\) 5759.66i 0.556361i
\(476\) 0 0
\(477\) −808.060 + 1993.53i −0.0775650 + 0.191357i
\(478\) 0 0
\(479\) −528.256 + 914.966i −0.0503896 + 0.0872774i −0.890120 0.455726i \(-0.849380\pi\)
0.839730 + 0.543004i \(0.182713\pi\)
\(480\) 0 0
\(481\) −5904.75 + 3409.11i −0.559737 + 0.323164i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10104.6 + 5833.90i −0.946035 + 0.546194i
\(486\) 0 0
\(487\) −4919.83 + 8521.40i −0.457780 + 0.792898i −0.998843 0.0480836i \(-0.984689\pi\)
0.541063 + 0.840982i \(0.318022\pi\)
\(488\) 0 0
\(489\) −2334.15 455.082i −0.215857 0.0420849i
\(490\) 0 0
\(491\) 5838.19i 0.536606i −0.963335 0.268303i \(-0.913537\pi\)
0.963335 0.268303i \(-0.0864629\pi\)
\(492\) 0 0
\(493\) 4896.62 + 2827.07i 0.447328 + 0.258265i
\(494\) 0 0
\(495\) −1805.88 + 251.719i −0.163976 + 0.0228564i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 9197.15 + 15929.9i 0.825092 + 1.42910i 0.901849 + 0.432052i \(0.142210\pi\)
−0.0767565 + 0.997050i \(0.524456\pi\)
\(500\) 0 0
\(501\) −7193.00 + 8265.16i −0.641436 + 0.737047i
\(502\) 0 0
\(503\) 5908.41 0.523743 0.261872 0.965103i \(-0.415660\pi\)
0.261872 + 0.965103i \(0.415660\pi\)
\(504\) 0 0
\(505\) 14951.1 1.31746
\(506\) 0 0
\(507\) 10515.1 12082.4i 0.921089 1.05838i
\(508\) 0 0
\(509\) 8348.77 + 14460.5i 0.727019 + 1.25923i 0.958138 + 0.286308i \(0.0924282\pi\)
−0.231118 + 0.972926i \(0.574238\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −18292.1 989.741i −1.57430 0.0851816i
\(514\) 0 0
\(515\) −18543.0 10705.8i −1.58661 0.916028i
\(516\) 0 0
\(517\) 1066.18i 0.0906974i
\(518\) 0 0
\(519\) −4479.38 873.330i −0.378850 0.0738631i
\(520\) 0 0
\(521\) 3648.66 6319.67i 0.306815 0.531420i −0.670849 0.741594i \(-0.734070\pi\)
0.977664 + 0.210175i \(0.0674033\pi\)
\(522\) 0 0
\(523\) 5470.78 3158.56i 0.457401 0.264080i −0.253550 0.967322i \(-0.581598\pi\)
0.710951 + 0.703242i \(0.248265\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8207.52 4738.61i 0.678416 0.391684i
\(528\) 0 0
\(529\) 1712.85 2966.75i 0.140779 0.243836i
\(530\) 0 0
\(531\) −22501.3 9120.71i −1.83893 0.745395i
\(532\) 0 0
\(533\) 23297.8i 1.89332i
\(534\) 0 0
\(535\) −22121.9 12772.1i −1.78768 1.03212i
\(536\) 0 0
\(537\) 15558.7 5347.46i 1.25029 0.429720i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 6292.24 + 10898.5i 0.500045 + 0.866104i 1.00000 5.25096e-5i \(1.67143e-5\pi\)
−0.499955 + 0.866052i \(0.666650\pi\)
\(542\) 0 0
\(543\) −15679.4 13645.4i −1.23916 1.07842i
\(544\) 0 0
\(545\) −20462.4 −1.60828
\(546\) 0 0
\(547\) 15886.3 1.24177 0.620887 0.783900i \(-0.286773\pi\)
0.620887 + 0.783900i \(0.286773\pi\)
\(548\) 0 0
\(549\) −9380.70 12034.7i −0.729250 0.935575i
\(550\) 0 0
\(551\) −4122.31 7140.04i −0.318723 0.552044i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2060.96 5996.47i −0.157627 0.458623i
\(556\) 0 0
\(557\) −10421.1 6016.60i −0.792737 0.457687i 0.0481881 0.998838i \(-0.484655\pi\)
−0.840925 + 0.541151i \(0.817989\pi\)
\(558\) 0 0
\(559\) 25564.1i 1.93425i
\(560\) 0 0
\(561\) 462.389 2371.63i 0.0347987 0.178486i
\(562\) 0 0
\(563\) 1019.73 1766.23i 0.0763351 0.132216i −0.825331 0.564649i \(-0.809011\pi\)
0.901666 + 0.432433i \(0.142345\pi\)
\(564\) 0 0
\(565\) 22549.9 13019.2i 1.67908 0.969420i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11615.0 + 6705.91i −0.855756 + 0.494071i −0.862589 0.505906i \(-0.831158\pi\)
0.00683300 + 0.999977i \(0.497825\pi\)
\(570\) 0 0
\(571\) 2317.42 4013.88i 0.169844 0.294178i −0.768521 0.639825i \(-0.779007\pi\)
0.938365 + 0.345646i \(0.112340\pi\)
\(572\) 0 0
\(573\) 988.786 5071.56i 0.0720892 0.369751i
\(574\) 0 0
\(575\) 5508.13i 0.399487i
\(576\) 0 0
\(577\) 18977.8 + 10956.9i 1.36925 + 0.790538i 0.990832 0.135097i \(-0.0431346\pi\)
0.378419 + 0.925634i \(0.376468\pi\)
\(578\) 0 0
\(579\) 3481.15 + 10128.6i 0.249865 + 0.726993i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 206.861 + 358.294i 0.0146952 + 0.0254529i
\(584\) 0 0
\(585\) 15684.1 + 20121.6i 1.10848 + 1.42209i
\(586\) 0 0
\(587\) −3112.06 −0.218822 −0.109411 0.993997i \(-0.534896\pi\)
−0.109411 + 0.993997i \(0.534896\pi\)
\(588\) 0 0
\(589\) −13819.3 −0.966746
\(590\) 0 0
\(591\) −1567.13 1363.84i −0.109074 0.0949252i
\(592\) 0 0
\(593\) −610.968 1058.23i −0.0423094 0.0732820i 0.844095 0.536193i \(-0.180138\pi\)
−0.886405 + 0.462911i \(0.846805\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14281.8 4908.59i 0.979087 0.336508i
\(598\) 0 0
\(599\) 7696.43 + 4443.53i 0.524987 + 0.303102i 0.738973 0.673735i \(-0.235311\pi\)
−0.213985 + 0.976837i \(0.568645\pi\)
\(600\) 0 0
\(601\) 6820.42i 0.462913i 0.972845 + 0.231457i \(0.0743491\pi\)
−0.972845 + 0.231457i \(0.925651\pi\)
\(602\) 0 0
\(603\) −2058.92 834.567i −0.139048 0.0563619i
\(604\) 0 0
\(605\) 8478.99 14686.0i 0.569785 0.986897i
\(606\) 0 0
\(607\) 11643.9 6722.61i 0.778602 0.449526i −0.0573326 0.998355i \(-0.518260\pi\)
0.835935 + 0.548829i \(0.184926\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12919.4 + 7459.00i −0.855420 + 0.493877i
\(612\) 0 0
\(613\) 5472.47 9478.60i 0.360573 0.624530i −0.627482 0.778631i \(-0.715915\pi\)
0.988055 + 0.154100i \(0.0492479\pi\)
\(614\) 0 0
\(615\) 21265.9 + 4146.15i 1.39435 + 0.271852i
\(616\) 0 0
\(617\) 14042.9i 0.916283i −0.888879 0.458141i \(-0.848515\pi\)
0.888879 0.458141i \(-0.151485\pi\)
\(618\) 0 0
\(619\) −4108.96 2372.31i −0.266806 0.154041i 0.360629 0.932709i \(-0.382562\pi\)
−0.627435 + 0.778669i \(0.715895\pi\)
\(620\) 0 0
\(621\) −17493.3 946.519i −1.13041 0.0611634i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9596.54 + 16621.7i 0.614179 + 1.06379i
\(626\) 0 0
\(627\) −2313.01 + 2657.78i −0.147325 + 0.169285i
\(628\) 0 0
\(629\) 8402.77 0.532656
\(630\) 0 0
\(631\) 10939.3 0.690151 0.345075 0.938575i \(-0.387853\pi\)
0.345075 + 0.938575i \(0.387853\pi\)
\(632\) 0 0
\(633\) −10053.5 + 11552.0i −0.631264 + 0.725358i
\(634\) 0 0
\(635\) −1082.85 1875.54i −0.0676716 0.117211i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −12246.2 + 1706.99i −0.758144 + 0.105677i
\(640\) 0 0
\(641\) 3499.79 + 2020.61i 0.215653 + 0.124507i 0.603936 0.797033i \(-0.293598\pi\)
−0.388283 + 0.921540i \(0.626932\pi\)
\(642\) 0 0
\(643\) 25370.2i 1.55599i −0.628268 0.777997i \(-0.716236\pi\)
0.628268 0.777997i \(-0.283764\pi\)
\(644\) 0 0
\(645\) 23334.5 + 4549.45i 1.42449 + 0.277728i
\(646\) 0 0
\(647\) −1094.96 + 1896.53i −0.0665339 + 0.115240i −0.897373 0.441272i \(-0.854527\pi\)
0.830839 + 0.556512i \(0.187861\pi\)
\(648\) 0 0
\(649\) −4044.13 + 2334.88i −0.244601 + 0.141220i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8980.82 5185.08i 0.538203 0.310732i −0.206147 0.978521i \(-0.566093\pi\)
0.744350 + 0.667789i \(0.232759\pi\)
\(654\) 0 0
\(655\) 2054.24 3558.05i 0.122543 0.212251i
\(656\) 0 0
\(657\) −9007.47 + 22221.9i −0.534878 + 1.31957i
\(658\) 0 0
\(659\) 26192.1i 1.54825i 0.633032 + 0.774126i \(0.281810\pi\)
−0.633032 + 0.774126i \(0.718190\pi\)
\(660\) 0 0
\(661\) 7399.81 + 4272.28i 0.435430 + 0.251396i 0.701657 0.712515i \(-0.252444\pi\)
−0.266227 + 0.963910i \(0.585777\pi\)
\(662\) 0 0
\(663\) −31973.0 + 10989.0i −1.87289 + 0.643705i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3942.28 6828.23i −0.228854 0.396387i
\(668\) 0 0
\(669\) −13646.6 11876.4i −0.788654 0.686349i
\(670\) 0 0
\(671\) −2934.78 −0.168846
\(672\) 0 0
\(673\) −32802.3 −1.87881 −0.939404 0.342813i \(-0.888620\pi\)
−0.939404 + 0.342813i \(0.888620\pi\)
\(674\) 0 0
\(675\) −5518.80 + 2800.20i −0.314694 + 0.159674i
\(676\) 0 0
\(677\) −968.152 1676.89i −0.0549617 0.0951965i 0.837236 0.546842i \(-0.184170\pi\)
−0.892197 + 0.451646i \(0.850837\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −6542.89 19036.9i −0.368171 1.07121i
\(682\) 0 0
\(683\) 1697.40 + 979.995i 0.0950940 + 0.0549026i 0.546793 0.837268i \(-0.315849\pi\)
−0.451699 + 0.892170i \(0.649182\pi\)
\(684\) 0 0
\(685\) 5182.89i 0.289092i
\(686\) 0 0
\(687\) 3986.88 20449.0i 0.221410 1.13563i
\(688\) 0 0
\(689\) 2894.40 5013.25i 0.160041 0.277198i
\(690\) 0 0
\(691\) 17263.4 9967.05i 0.950408 0.548718i 0.0572002 0.998363i \(-0.481783\pi\)
0.893208 + 0.449645i \(0.148449\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2570.50 + 1484.08i −0.140294 + 0.0809989i
\(696\) 0 0
\(697\) −14356.1 + 24865.5i −0.780168 + 1.35129i
\(698\) 0 0
\(699\) −5049.78 + 25900.7i −0.273248 + 1.40151i
\(700\) 0 0
\(701\) 26738.5i 1.44065i 0.693635 + 0.720327i \(0.256008\pi\)
−0.693635 + 0.720327i \(0.743992\pi\)
\(702\) 0 0
\(703\) −10611.0 6126.28i −0.569278 0.328673i
\(704\) 0 0
\(705\) −4509.30 13120.0i −0.240894 0.700893i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −6441.45 11156.9i −0.341204 0.590983i 0.643452 0.765486i \(-0.277501\pi\)
−0.984657 + 0.174503i \(0.944168\pi\)
\(710\) 0 0
\(711\) −10559.2 + 8230.56i −0.556964 + 0.434135i
\(712\) 0 0
\(713\) −13215.8 −0.694159
\(714\) 0 0
\(715\) 4906.82 0.256650
\(716\) 0 0
\(717\) −4238.12 3688.34i −0.220747 0.192111i
\(718\) 0 0
\(719\) 13721.5 + 23766.3i 0.711717 + 1.23273i 0.964212 + 0.265131i \(0.0854153\pi\)
−0.252496 + 0.967598i \(0.581251\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 16199.6 5567.74i 0.833292 0.286399i
\(724\) 0 0
\(725\) −2412.08 1392.61i −0.123562 0.0713385i
\(726\) 0 0
\(727\) 10869.4i 0.554501i 0.960798 + 0.277250i \(0.0894231\pi\)
−0.960798 + 0.277250i \(0.910577\pi\)
\(728\) 0 0
\(729\) 7944.80 + 18008.4i 0.403638 + 0.914919i
\(730\) 0 0
\(731\) −15752.6 + 27284.3i −0.797032 + 1.38050i
\(732\) 0 0
\(733\) −28893.2 + 16681.5i −1.45593 + 0.840580i −0.998807 0.0488247i \(-0.984452\pi\)
−0.457120 + 0.889405i \(0.651119\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −370.048 + 213.647i −0.0184951 + 0.0106781i
\(738\) 0 0
\(739\) 18226.4 31569.0i 0.907265 1.57143i 0.0894168 0.995994i \(-0.471500\pi\)
0.817848 0.575434i \(-0.195167\pi\)
\(740\) 0 0
\(741\) 48387.3 + 9433.91i 2.39886 + 0.467697i
\(742\) 0 0
\(743\) 139.301i 0.00687814i 0.999994 + 0.00343907i \(0.00109469\pi\)
−0.999994 + 0.00343907i \(0.998905\pi\)
\(744\) 0 0
\(745\) 39883.6 + 23026.8i 1.96137 + 1.13240i
\(746\) 0 0
\(747\) 3812.61 + 27352.4i 0.186742 + 1.33972i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8485.28 + 14696.9i 0.412293 + 0.714113i 0.995140 0.0984692i \(-0.0313946\pi\)
−0.582847 + 0.812582i \(0.698061\pi\)
\(752\) 0 0
\(753\) 2356.13 2707.33i 0.114027 0.131023i
\(754\) 0 0
\(755\) 2740.86 0.132120
\(756\) 0 0
\(757\) −29233.1 −1.40356 −0.701781 0.712393i \(-0.747611\pi\)
−0.701781 + 0.712393i \(0.747611\pi\)
\(758\) 0 0
\(759\) −2212.00 + 2541.71i −0.105785 + 0.121553i
\(760\) 0 0
\(761\) −5497.11 9521.27i −0.261853 0.453542i 0.704882 0.709325i \(-0.251000\pi\)
−0.966734 + 0.255783i \(0.917667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −4340.58 31140.1i −0.205142 1.47173i
\(766\) 0 0
\(767\) 56585.4 + 32669.6i 2.66386 + 1.53798i
\(768\) 0 0
\(769\) 1694.37i 0.0794547i 0.999211 + 0.0397273i \(0.0126489\pi\)
−0.999211 + 0.0397273i \(0.987351\pi\)
\(770\) 0 0
\(771\) −40274.0 7852.08i −1.88123 0.366778i
\(772\) 0 0
\(773\) −16225.5 + 28103.4i −0.754969 + 1.30764i 0.190421 + 0.981702i \(0.439015\pi\)
−0.945390 + 0.325942i \(0.894319\pi\)
\(774\) 0 0
\(775\) −4043.03 + 2334.24i −0.187393 + 0.108192i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 36257.8 20933.5i 1.66761 0.962798i
\(780\) 0 0
\(781\) −1189.06 + 2059.52i −0.0544790 + 0.0943603i
\(782\) 0 0
\(783\) −4837.30 + 7421.22i −0.220780 + 0.338713i
\(784\) 0 0
\(785\) 36973.4i 1.68107i
\(786\) 0 0
\(787\) 18152.9 + 10480.6i 0.822212 + 0.474704i 0.851179 0.524876i \(-0.175888\pi\)
−0.0289667 + 0.999580i \(0.509222\pi\)
\(788\) 0 0
\(789\) −14728.1 + 5061.99i −0.664557 + 0.228405i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 20531.7 + 35562.0i 0.919424 + 1.59249i
\(794\) 0 0
\(795\) 4060.93 + 3534.14i 0.181165 + 0.157664i
\(796\) 0 0
\(797\) 30873.3 1.37213 0.686066 0.727540i \(-0.259336\pi\)
0.686066 + 0.727540i \(0.259336\pi\)
\(798\) 0 0
\(799\) 18384.9 0.814033
\(800\) 0 0
\(801\) 2790.38 2175.01i 0.123087 0.0959427i
\(802\) 0 0
\(803\) 2305.89 + 3993.92i 0.101336 + 0.175520i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −13652.3 39722.0i −0.595519 1.73269i
\(808\) 0 0
\(809\) 23921.2 + 13810.9i 1.03958 + 0.600204i 0.919716 0.392585i \(-0.128419\pi\)
0.119869 + 0.992790i \(0.461753\pi\)
\(810\) 0 0
\(811\) 20022.9i 0.866954i −0.901165 0.433477i \(-0.857287\pi\)
0.901165 0.433477i \(-0.142713\pi\)
\(812\) 0 0
\(813\) 3290.11 16875.3i 0.141930 0.727972i
\(814\) 0 0
\(815\) −2975.80 + 5154.24i −0.127899 + 0.221528i
\(816\) 0 0
\(817\) 39784.7 22969.7i 1.70366 0.983609i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 6115.05 3530.52i 0.259947 0.150081i −0.364363 0.931257i \(-0.618713\pi\)
0.624310 + 0.781176i \(0.285380\pi\)
\(822\) 0 0
\(823\) 18834.7 32622.6i 0.797734 1.38172i −0.123354 0.992363i \(-0.539365\pi\)
0.921089 0.389353i \(-0.127301\pi\)
\(824\) 0 0
\(825\) −227.773 + 1168.27i −0.00961217 + 0.0493016i
\(826\) 0 0
\(827\) 5566.45i 0.234056i −0.993129 0.117028i \(-0.962663\pi\)
0.993129 0.117028i \(-0.0373368\pi\)
\(828\) 0 0
\(829\) 9558.42 + 5518.56i 0.400455 + 0.231203i 0.686680 0.726959i \(-0.259067\pi\)
−0.286225 + 0.958162i \(0.592400\pi\)
\(830\) 0 0
\(831\) −8437.09 24548.1i −0.352202 1.02475i
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 13710.7 + 23747.6i 0.568236 + 0.984214i
\(836\) 0 0
\(837\) 6718.57 + 13241.4i 0.277453 + 0.546821i
\(838\) 0 0
\(839\) −28936.3 −1.19069 −0.595347 0.803469i \(-0.702986\pi\)
−0.595347 + 0.803469i \(0.702986\pi\)
\(840\) 0 0
\(841\) 20402.1 0.836529
\(842\) 0 0
\(843\) −16163.4 14066.7i −0.660375 0.574711i
\(844\) 0 0
\(845\) −20043.0 34715.4i −0.815975 1.41331i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 8999.79 3093.19i 0.363807 0.125039i
\(850\) 0 0
\(851\) −10147.6 5858.74i −0.408762 0.235999i
\(852\) 0 0
\(853\) 25646.9i 1.02946i −0.857351 0.514732i \(-0.827891\pi\)
0.857351 0.514732i \(-0.172109\pi\)
\(854\) 0 0
\(855\) −17222.3 + 42488.3i −0.688877 + 1.69950i
\(856\) 0 0
\(857\) −2745.33 + 4755.06i −0.109427 + 0.189533i −0.915538 0.402231i \(-0.868235\pi\)
0.806111 + 0.591764i \(0.201568\pi\)
\(858\) 0 0
\(859\) 7955.53 4593.13i 0.315994 0.182439i −0.333611 0.942711i \(-0.608267\pi\)
0.649606 + 0.760271i \(0.274934\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 38541.3 22251.9i 1.52023 0.877708i 0.520520 0.853850i \(-0.325738\pi\)
0.999715 0.0238583i \(-0.00759505\pi\)
\(864\) 0 0
\(865\) −5710.74 + 9891.30i −0.224475 + 0.388803i
\(866\) 0 0
\(867\) 15838.9 + 3088.06i 0.620436 + 0.120964i
\(868\) 0 0
\(869\) 2574.96i 0.100517i
\(870\) 0 0
\(871\) 5177.71 + 2989.35i 0.201424 + 0.116292i
\(872\) 0 0
\(873\) 23993.2 3344.39i 0.930181 0.129657i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 9236.70 + 15998.4i 0.355645 + 0.615996i 0.987228 0.159312i \(-0.0509277\pi\)
−0.631583 + 0.775308i \(0.717594\pi\)
\(878\) 0 0
\(879\) 9129.60 10490.4i 0.350323 0.402541i
\(880\) 0 0
\(881\) −9245.06 −0.353546 −0.176773 0.984252i \(-0.556566\pi\)
−0.176773 + 0.984252i \(0.556566\pi\)
\(882\) 0 0
\(883\) 14216.8 0.541827 0.270913 0.962604i \(-0.412674\pi\)
0.270913 + 0.962604i \(0.412674\pi\)
\(884\) 0 0
\(885\) −39890.5 + 45836.4i −1.51514 + 1.74099i
\(886\) 0 0
\(887\) 15492.2 + 26833.3i 0.586445 + 1.01575i 0.994694 + 0.102882i \(0.0328065\pi\)
−0.408248 + 0.912871i \(0.633860\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 3671.16 + 924.140i 0.138034 + 0.0347473i
\(892\) 0 0
\(893\) −23216.5 13404.1i −0.870001 0.502296i
\(894\) 0 0
\(895\) 41173.9i 1.53776i
\(896\) 0 0
\(897\) 46274.2 + 9021.93i 1.72246 + 0.335823i
\(898\) 0 0
\(899\) −3341.33 + 5787.35i −0.123959 + 0.214704i
\(900\) 0 0
\(901\) −6178.33 + 3567.06i −0.228446 + 0.131894i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −45050.2 + 26009.7i −1.65472 + 0.955351i
\(906\) 0 0
\(907\) −22640.9 + 39215.3i −0.828865 + 1.43564i 0.0700650 + 0.997542i \(0.477679\pi\)
−0.898930 + 0.438093i \(0.855654\pi\)
\(908\) 0 0
\(909\) −28768.6 11661.1i −1.04972 0.425495i
\(910\) 0 0
\(911\) 1202.70i 0.0437402i −0.999761 0.0218701i \(-0.993038\pi\)
0.999761 0.0218701i \(-0.00696202\pi\)
\(912\) 0 0
\(913\) 4600.00 + 2655.81i 0.166744 + 0.0962700i
\(914\) 0 0
\(915\) −36114.4 + 12412.4i −1.30481 + 0.448459i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 5398.13 + 9349.83i 0.193763 + 0.335607i 0.946494 0.322721i \(-0.104598\pi\)
−0.752732 + 0.658328i \(0.771264\pi\)
\(920\) 0 0
\(921\) 1508.77 + 1313.05i 0.0539802 + 0.0469779i
\(922\) 0 0
\(923\) 33274.8 1.18662
\(924\) 0 0
\(925\) −4139.21 −0.147131
\(926\) 0 0
\(927\) 27330.1 + 35062.5i 0.968325 + 1.24229i
\(928\) 0 0
\(929\) −4138.39 7167.89i −0.146153 0.253144i 0.783650 0.621203i \(-0.213356\pi\)
−0.929802 + 0.368059i \(0.880022\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −4124.20 11999.6i −0.144716 0.421059i
\(934\) 0 0
\(935\) −5237.00 3023.59i −0.183175 0.105756i
\(936\) 0 0
\(937\) 13731.8i 0.478760i −0.970926 0.239380i \(-0.923056\pi\)
0.970926 0.239380i \(-0.0769441\pi\)
\(938\) 0 0
\(939\) 4103.31 21046.2i 0.142605 0.731434i
\(940\) 0 0
\(941\) −24731.9 + 42837.0i −0.856789 + 1.48400i 0.0181872 + 0.999835i \(0.494211\pi\)
−0.874976 + 0.484167i \(0.839123\pi\)
\(942\) 0 0
\(943\) 34674.4 20019.3i 1.19741 0.691323i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 16333.6 9430.23i 0.560477 0.323592i −0.192860 0.981226i \(-0.561776\pi\)
0.753337 + 0.657635i \(0.228443\pi\)
\(948\) 0 0
\(949\) 32264.0 55882.9i 1.10362 1.91152i
\(950\) 0 0
\(951\) −6697.67 + 34352.9i −0.228377 + 1.17136i
\(952\) 0 0
\(953\) 26144.6i 0.888674i 0.895860 + 0.444337i \(0.146561\pi\)
−0.895860 + 0.444337i \(0.853439\pi\)
\(954\) 0 0
\(955\) −11198.9 6465.72i −0.379465 0.219084i
\(956\) 0 0
\(957\) 553.790 + 1611.28i 0.0187058 + 0.0544256i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −9294.90 16099.2i −0.312004 0.540406i
\(962\) 0 0
\(963\) 32604.9 + 41829.7i 1.09105 + 1.39973i
\(964\) 0 0
\(965\) 26803.9 0.894142
\(966\) 0 0
\(967\) −12791.3 −0.425377 −0.212688 0.977120i \(-0.568222\pi\)
−0.212688 + 0.977120i \(0.568222\pi\)
\(968\) 0 0
\(969\) −45830.1 39885.0i −1.51938 1.32228i
\(970\) 0 0
\(971\) −7487.53 12968.8i −0.247463 0.428618i 0.715359 0.698758i \(-0.246263\pi\)
−0.962821 + 0.270140i \(0.912930\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 15749.9 5413.17i 0.517334 0.177805i
\(976\) 0 0
\(977\) 26012.8 + 15018.5i 0.851815 + 0.491796i 0.861263 0.508160i \(-0.169674\pi\)
−0.00944779 + 0.999955i \(0.503007\pi\)
\(978\) 0 0
\(979\) 680.458i 0.0222140i
\(980\) 0 0
\(981\) 39373.3 + 15959.6i 1.28144 + 0.519421i
\(982\) 0 0
\(983\) 8226.35 14248.5i 0.266918 0.462315i −0.701147 0.713017i \(-0.747328\pi\)
0.968064 + 0.250702i \(0.0806615\pi\)
\(984\) 0 0
\(985\) −4502.69 + 2599.63i −0.145652 + 0.0840924i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 38047.3 21966.6i 1.22329 0.706267i
\(990\) 0 0
\(991\) −12196.1 + 21124.3i −0.390941 + 0.677130i −0.992574 0.121643i \(-0.961184\pi\)
0.601633 + 0.798773i \(0.294517\pi\)
\(992\) 0 0
\(993\) −21005.9 4095.45i −0.671301 0.130881i
\(994\) 0 0
\(995\) 37794.8i 1.20420i
\(996\) 0 0
\(997\) −15826.1 9137.19i −0.502725 0.290249i 0.227113 0.973868i \(-0.427071\pi\)
−0.729838 + 0.683620i \(0.760405\pi\)
\(998\) 0 0
\(999\) −711.282 + 13145.7i −0.0225265 + 0.416329i
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 588.4.k.e.521.6 48
3.2 odd 2 inner 588.4.k.e.521.13 48
7.2 even 3 inner 588.4.k.e.509.12 48
7.3 odd 6 588.4.f.d.293.3 24
7.4 even 3 588.4.f.d.293.22 yes 24
7.5 odd 6 inner 588.4.k.e.509.13 48
7.6 odd 2 inner 588.4.k.e.521.19 48
21.2 odd 6 inner 588.4.k.e.509.19 48
21.5 even 6 inner 588.4.k.e.509.6 48
21.11 odd 6 588.4.f.d.293.4 yes 24
21.17 even 6 588.4.f.d.293.21 yes 24
21.20 even 2 inner 588.4.k.e.521.12 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.4.f.d.293.3 24 7.3 odd 6
588.4.f.d.293.4 yes 24 21.11 odd 6
588.4.f.d.293.21 yes 24 21.17 even 6
588.4.f.d.293.22 yes 24 7.4 even 3
588.4.k.e.509.6 48 21.5 even 6 inner
588.4.k.e.509.12 48 7.2 even 3 inner
588.4.k.e.509.13 48 7.5 odd 6 inner
588.4.k.e.509.19 48 21.2 odd 6 inner
588.4.k.e.521.6 48 1.1 even 1 trivial
588.4.k.e.521.12 48 21.20 even 2 inner
588.4.k.e.521.13 48 3.2 odd 2 inner
588.4.k.e.521.19 48 7.6 odd 2 inner