Properties

Label 1008.4.bt.d.593.11
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 593.11
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.d.17.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.56246 + 2.70625i) q^{5} +(-17.1949 - 6.88015i) q^{7} +O(q^{10})\) \(q+(-1.56246 + 2.70625i) q^{5} +(-17.1949 - 6.88015i) q^{7} +(-33.2914 + 19.2208i) q^{11} -13.8046i q^{13} +(-47.5817 - 82.4140i) q^{17} +(-9.86718 - 5.69682i) q^{19} +(-23.9992 - 13.8559i) q^{23} +(57.6175 + 99.7964i) q^{25} +44.2317i q^{29} +(119.149 - 68.7907i) q^{31} +(45.4857 - 35.7837i) q^{35} +(70.6631 - 122.392i) q^{37} +337.946 q^{41} -417.510 q^{43} +(-145.043 + 251.222i) q^{47} +(248.327 + 236.607i) q^{49} +(-14.7904 + 8.53925i) q^{53} -120.127i q^{55} +(299.818 + 519.300i) q^{59} +(459.882 + 265.513i) q^{61} +(37.3586 + 21.5690i) q^{65} +(-325.105 - 563.098i) q^{67} +934.128i q^{71} +(787.145 - 454.458i) q^{73} +(704.683 - 101.449i) q^{77} +(397.516 - 688.517i) q^{79} -314.865 q^{83} +297.378 q^{85} +(179.521 - 310.940i) q^{89} +(-94.9775 + 237.368i) q^{91} +(30.8341 - 17.8021i) q^{95} -80.5572i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{7}+O(q^{10}) \) 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
\(5\) −1.56246 + 2.70625i −0.139750 + 0.242055i −0.927402 0.374066i \(-0.877963\pi\)
0.787652 + 0.616121i \(0.211297\pi\)
\(6\) 0 0
\(7\) −17.1949 6.88015i −0.928436 0.371493i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −33.2914 + 19.2208i −0.912521 + 0.526844i −0.881241 0.472667i \(-0.843291\pi\)
−0.0312793 + 0.999511i \(0.509958\pi\)
\(12\) 0 0
\(13\) 13.8046i 0.294515i −0.989098 0.147258i \(-0.952955\pi\)
0.989098 0.147258i \(-0.0470446\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −47.5817 82.4140i −0.678839 1.17578i −0.975331 0.220749i \(-0.929150\pi\)
0.296491 0.955036i \(-0.404183\pi\)
\(18\) 0 0
\(19\) −9.86718 5.69682i −0.119141 0.0687863i 0.439245 0.898367i \(-0.355246\pi\)
−0.558386 + 0.829581i \(0.688579\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −23.9992 13.8559i −0.217573 0.125616i 0.387253 0.921973i \(-0.373424\pi\)
−0.604826 + 0.796358i \(0.706757\pi\)
\(24\) 0 0
\(25\) 57.6175 + 99.7964i 0.460940 + 0.798371i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 44.2317i 0.283228i 0.989922 + 0.141614i \(0.0452293\pi\)
−0.989922 + 0.141614i \(0.954771\pi\)
\(30\) 0 0
\(31\) 119.149 68.7907i 0.690316 0.398554i −0.113414 0.993548i \(-0.536179\pi\)
0.803730 + 0.594994i \(0.202845\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 45.4857 35.7837i 0.219671 0.172816i
\(36\) 0 0
\(37\) 70.6631 122.392i 0.313972 0.543815i −0.665247 0.746624i \(-0.731674\pi\)
0.979218 + 0.202809i \(0.0650070\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 337.946 1.28728 0.643639 0.765330i \(-0.277424\pi\)
0.643639 + 0.765330i \(0.277424\pi\)
\(42\) 0 0
\(43\) −417.510 −1.48069 −0.740346 0.672226i \(-0.765338\pi\)
−0.740346 + 0.672226i \(0.765338\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −145.043 + 251.222i −0.450142 + 0.779670i −0.998394 0.0566436i \(-0.981960\pi\)
0.548252 + 0.836313i \(0.315293\pi\)
\(48\) 0 0
\(49\) 248.327 + 236.607i 0.723985 + 0.689815i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −14.7904 + 8.53925i −0.0383324 + 0.0221312i −0.519044 0.854748i \(-0.673712\pi\)
0.480711 + 0.876879i \(0.340379\pi\)
\(54\) 0 0
\(55\) 120.127i 0.294507i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 299.818 + 519.300i 0.661576 + 1.14588i 0.980201 + 0.198003i \(0.0634455\pi\)
−0.318625 + 0.947881i \(0.603221\pi\)
\(60\) 0 0
\(61\) 459.882 + 265.513i 0.965276 + 0.557302i 0.897793 0.440418i \(-0.145170\pi\)
0.0674831 + 0.997720i \(0.478503\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 37.3586 + 21.5690i 0.0712888 + 0.0411586i
\(66\) 0 0
\(67\) −325.105 563.098i −0.592804 1.02677i −0.993853 0.110710i \(-0.964687\pi\)
0.401048 0.916057i \(-0.368646\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 934.128i 1.56142i 0.624896 + 0.780708i \(0.285142\pi\)
−0.624896 + 0.780708i \(0.714858\pi\)
\(72\) 0 0
\(73\) 787.145 454.458i 1.26203 0.728634i 0.288564 0.957460i \(-0.406822\pi\)
0.973467 + 0.228826i \(0.0734887\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 704.683 101.449i 1.04294 0.150145i
\(78\) 0 0
\(79\) 397.516 688.517i 0.566127 0.980560i −0.430817 0.902439i \(-0.641775\pi\)
0.996944 0.0781211i \(-0.0248921\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −314.865 −0.416397 −0.208199 0.978087i \(-0.566760\pi\)
−0.208199 + 0.978087i \(0.566760\pi\)
\(84\) 0 0
\(85\) 297.378 0.379472
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 179.521 310.940i 0.213811 0.370332i −0.739093 0.673604i \(-0.764746\pi\)
0.952904 + 0.303271i \(0.0980789\pi\)
\(90\) 0 0
\(91\) −94.9775 + 237.368i −0.109410 + 0.273438i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 30.8341 17.8021i 0.0333001 0.0192258i
\(96\) 0 0
\(97\) 80.5572i 0.0843231i −0.999111 0.0421616i \(-0.986576\pi\)
0.999111 0.0421616i \(-0.0134244\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 434.184 + 752.028i 0.427752 + 0.740887i 0.996673 0.0815045i \(-0.0259725\pi\)
−0.568921 + 0.822392i \(0.692639\pi\)
\(102\) 0 0
\(103\) −104.861 60.5413i −0.100313 0.0579157i 0.449004 0.893530i \(-0.351779\pi\)
−0.549317 + 0.835614i \(0.685112\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 387.751 + 223.868i 0.350330 + 0.202263i 0.664830 0.746994i \(-0.268504\pi\)
−0.314501 + 0.949257i \(0.601837\pi\)
\(108\) 0 0
\(109\) 507.544 + 879.092i 0.445999 + 0.772493i 0.998121 0.0612702i \(-0.0195151\pi\)
−0.552122 + 0.833763i \(0.686182\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 889.812i 0.740765i 0.928879 + 0.370382i \(0.120773\pi\)
−0.928879 + 0.370382i \(0.879227\pi\)
\(114\) 0 0
\(115\) 74.9954 43.2986i 0.0608118 0.0351097i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 251.141 + 1744.47i 0.193463 + 1.34382i
\(120\) 0 0
\(121\) 73.3769 127.093i 0.0551292 0.0954865i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −750.713 −0.537167
\(126\) 0 0
\(127\) −279.668 −0.195406 −0.0977029 0.995216i \(-0.531149\pi\)
−0.0977029 + 0.995216i \(0.531149\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 81.4798 141.127i 0.0543429 0.0941247i −0.837574 0.546324i \(-0.816027\pi\)
0.891917 + 0.452199i \(0.149360\pi\)
\(132\) 0 0
\(133\) 130.470 + 165.844i 0.0850615 + 0.108124i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1004.98 580.224i 0.626723 0.361839i −0.152759 0.988263i \(-0.548816\pi\)
0.779482 + 0.626425i \(0.215482\pi\)
\(138\) 0 0
\(139\) 674.863i 0.411807i −0.978572 0.205903i \(-0.933987\pi\)
0.978572 0.205903i \(-0.0660133\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 265.334 + 459.573i 0.155163 + 0.268751i
\(144\) 0 0
\(145\) −119.702 69.1101i −0.0685568 0.0395813i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1230.83 + 710.619i 0.676734 + 0.390713i 0.798623 0.601831i \(-0.205562\pi\)
−0.121889 + 0.992544i \(0.538895\pi\)
\(150\) 0 0
\(151\) 1280.08 + 2217.16i 0.689875 + 1.19490i 0.971878 + 0.235485i \(0.0756678\pi\)
−0.282003 + 0.959413i \(0.590999\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 429.930i 0.222792i
\(156\) 0 0
\(157\) 1292.26 746.085i 0.656901 0.379262i −0.134194 0.990955i \(-0.542845\pi\)
0.791095 + 0.611693i \(0.209511\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 317.332 + 403.369i 0.155337 + 0.197453i
\(162\) 0 0
\(163\) 1068.87 1851.34i 0.513623 0.889622i −0.486252 0.873819i \(-0.661636\pi\)
0.999875 0.0158029i \(-0.00503043\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1154.81 0.535103 0.267552 0.963544i \(-0.413785\pi\)
0.267552 + 0.963544i \(0.413785\pi\)
\(168\) 0 0
\(169\) 2006.43 0.913261
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1881.14 + 3258.23i −0.826707 + 1.43190i 0.0739006 + 0.997266i \(0.476455\pi\)
−0.900608 + 0.434633i \(0.856878\pi\)
\(174\) 0 0
\(175\) −304.110 2112.40i −0.131363 0.912472i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 331.662 191.485i 0.138489 0.0799568i −0.429155 0.903231i \(-0.641188\pi\)
0.567644 + 0.823274i \(0.307855\pi\)
\(180\) 0 0
\(181\) 2689.85i 1.10461i −0.833641 0.552307i \(-0.813748\pi\)
0.833641 0.552307i \(-0.186252\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 220.816 + 382.465i 0.0877553 + 0.151997i
\(186\) 0 0
\(187\) 3168.12 + 1829.12i 1.23891 + 0.715285i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 634.579 + 366.374i 0.240401 + 0.138795i 0.615361 0.788246i \(-0.289010\pi\)
−0.374960 + 0.927041i \(0.622344\pi\)
\(192\) 0 0
\(193\) −2102.20 3641.11i −0.784039 1.35800i −0.929571 0.368642i \(-0.879823\pi\)
0.145532 0.989354i \(-0.453511\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2837.28i 1.02613i 0.858349 + 0.513066i \(0.171490\pi\)
−0.858349 + 0.513066i \(0.828510\pi\)
\(198\) 0 0
\(199\) 1256.70 725.558i 0.447665 0.258459i −0.259179 0.965829i \(-0.583452\pi\)
0.706843 + 0.707370i \(0.250119\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 304.321 760.559i 0.105217 0.262959i
\(204\) 0 0
\(205\) −528.027 + 914.569i −0.179897 + 0.311591i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 437.989 0.144959
\(210\) 0 0
\(211\) 5902.14 1.92569 0.962844 0.270058i \(-0.0870430\pi\)
0.962844 + 0.270058i \(0.0870430\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 652.342 1129.89i 0.206927 0.358408i
\(216\) 0 0
\(217\) −2522.04 + 363.084i −0.788974 + 0.113584i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1137.69 + 656.845i −0.346286 + 0.199928i
\(222\) 0 0
\(223\) 1445.01i 0.433925i 0.976180 + 0.216962i \(0.0696149\pi\)
−0.976180 + 0.216962i \(0.930385\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2754.73 + 4771.33i 0.805453 + 1.39509i 0.915985 + 0.401213i \(0.131411\pi\)
−0.110532 + 0.993873i \(0.535255\pi\)
\(228\) 0 0
\(229\) −4147.74 2394.70i −1.19690 0.691032i −0.237039 0.971500i \(-0.576177\pi\)
−0.959863 + 0.280468i \(0.909510\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3268.04 + 1886.80i 0.918868 + 0.530509i 0.883274 0.468857i \(-0.155334\pi\)
0.0355944 + 0.999366i \(0.488668\pi\)
\(234\) 0 0
\(235\) −453.247 785.046i −0.125815 0.217918i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1246.09i 0.337250i −0.985680 0.168625i \(-0.946067\pi\)
0.985680 0.168625i \(-0.0539326\pi\)
\(240\) 0 0
\(241\) 821.731 474.426i 0.219636 0.126807i −0.386146 0.922438i \(-0.626194\pi\)
0.605782 + 0.795631i \(0.292860\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1028.32 + 302.348i −0.268150 + 0.0788421i
\(246\) 0 0
\(247\) −78.6421 + 136.212i −0.0202586 + 0.0350889i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1494.83 0.375908 0.187954 0.982178i \(-0.439814\pi\)
0.187954 + 0.982178i \(0.439814\pi\)
\(252\) 0 0
\(253\) 1065.29 0.264720
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1762.12 + 3052.09i −0.427697 + 0.740794i −0.996668 0.0815642i \(-0.974008\pi\)
0.568971 + 0.822358i \(0.307342\pi\)
\(258\) 0 0
\(259\) −2057.12 + 1618.34i −0.493526 + 0.388259i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5514.20 3183.62i 1.29285 0.746428i 0.313693 0.949524i \(-0.398434\pi\)
0.979159 + 0.203096i \(0.0651004\pi\)
\(264\) 0 0
\(265\) 53.3688i 0.0123714i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1738.97 + 3011.98i 0.394152 + 0.682690i 0.992992 0.118178i \(-0.0377052\pi\)
−0.598841 + 0.800868i \(0.704372\pi\)
\(270\) 0 0
\(271\) 4121.15 + 2379.35i 0.923772 + 0.533340i 0.884836 0.465902i \(-0.154270\pi\)
0.0389354 + 0.999242i \(0.487603\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3836.33 2214.91i −0.841234 0.485687i
\(276\) 0 0
\(277\) 1117.86 + 1936.19i 0.242476 + 0.419980i 0.961419 0.275089i \(-0.0887073\pi\)
−0.718943 + 0.695069i \(0.755374\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8109.09i 1.72152i −0.509008 0.860762i \(-0.669988\pi\)
0.509008 0.860762i \(-0.330012\pi\)
\(282\) 0 0
\(283\) −2858.65 + 1650.44i −0.600456 + 0.346673i −0.769221 0.638983i \(-0.779355\pi\)
0.168765 + 0.985656i \(0.446022\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5810.94 2325.12i −1.19515 0.478215i
\(288\) 0 0
\(289\) −2071.55 + 3588.02i −0.421646 + 0.730312i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3129.58 −0.624001 −0.312001 0.950082i \(-0.600999\pi\)
−0.312001 + 0.950082i \(0.600999\pi\)
\(294\) 0 0
\(295\) −1873.81 −0.369822
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −191.275 + 331.298i −0.0369958 + 0.0640785i
\(300\) 0 0
\(301\) 7179.04 + 2872.54i 1.37473 + 0.550067i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1437.09 + 829.705i −0.269795 + 0.155766i
\(306\) 0 0
\(307\) 9190.88i 1.70864i 0.519751 + 0.854318i \(0.326025\pi\)
−0.519751 + 0.854318i \(0.673975\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −953.133 1650.88i −0.173785 0.301005i 0.765955 0.642894i \(-0.222267\pi\)
−0.939740 + 0.341889i \(0.888933\pi\)
\(312\) 0 0
\(313\) −8295.18 4789.22i −1.49799 0.864866i −0.497994 0.867181i \(-0.665930\pi\)
−0.999997 + 0.00231512i \(0.999263\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2310.11 1333.74i −0.409301 0.236310i 0.281188 0.959653i \(-0.409271\pi\)
−0.690489 + 0.723342i \(0.742605\pi\)
\(318\) 0 0
\(319\) −850.168 1472.53i −0.149217 0.258452i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1084.26i 0.186779i
\(324\) 0 0
\(325\) 1377.64 795.384i 0.235132 0.135754i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4222.44 3321.81i 0.707570 0.556648i
\(330\) 0 0
\(331\) 3959.19 6857.53i 0.657453 1.13874i −0.323819 0.946119i \(-0.604967\pi\)
0.981273 0.192624i \(-0.0616996\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2031.85 0.331379
\(336\) 0 0
\(337\) −5173.45 −0.836248 −0.418124 0.908390i \(-0.637312\pi\)
−0.418124 + 0.908390i \(0.637312\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2644.42 + 4580.28i −0.419952 + 0.727378i
\(342\) 0 0
\(343\) −2642.06 5776.95i −0.415912 0.909405i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −346.881 + 200.272i −0.0536644 + 0.0309831i −0.526592 0.850118i \(-0.676530\pi\)
0.472928 + 0.881101i \(0.343197\pi\)
\(348\) 0 0
\(349\) 6360.10i 0.975496i 0.872984 + 0.487748i \(0.162182\pi\)
−0.872984 + 0.487748i \(0.837818\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6154.02 10659.1i −0.927891 1.60715i −0.786844 0.617152i \(-0.788286\pi\)
−0.141047 0.990003i \(-0.545047\pi\)
\(354\) 0 0
\(355\) −2527.99 1459.53i −0.377948 0.218209i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7649.34 4416.35i −1.12456 0.649264i −0.181998 0.983299i \(-0.558256\pi\)
−0.942561 + 0.334035i \(0.891590\pi\)
\(360\) 0 0
\(361\) −3364.59 5827.65i −0.490537 0.849635i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2840.28i 0.407308i
\(366\) 0 0
\(367\) −3655.01 + 2110.22i −0.519864 + 0.300144i −0.736879 0.676025i \(-0.763701\pi\)
0.217015 + 0.976168i \(0.430368\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 313.070 45.0709i 0.0438108 0.00630718i
\(372\) 0 0
\(373\) −2165.80 + 3751.28i −0.300646 + 0.520734i −0.976282 0.216501i \(-0.930536\pi\)
0.675637 + 0.737235i \(0.263869\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 610.599 0.0834150
\(378\) 0 0
\(379\) −9160.86 −1.24159 −0.620794 0.783974i \(-0.713190\pi\)
−0.620794 + 0.783974i \(0.713190\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 382.423 662.376i 0.0510206 0.0883703i −0.839387 0.543534i \(-0.817086\pi\)
0.890408 + 0.455164i \(0.150419\pi\)
\(384\) 0 0
\(385\) −826.489 + 2065.56i −0.109407 + 0.273430i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5806.30 3352.27i 0.756789 0.436932i −0.0713526 0.997451i \(-0.522732\pi\)
0.828142 + 0.560519i \(0.189398\pi\)
\(390\) 0 0
\(391\) 2637.16i 0.341092i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1242.20 + 2151.56i 0.158233 + 0.274067i
\(396\) 0 0
\(397\) 4026.96 + 2324.97i 0.509087 + 0.293921i 0.732458 0.680812i \(-0.238373\pi\)
−0.223371 + 0.974733i \(0.571706\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3072.03 + 1773.64i 0.382568 + 0.220876i 0.678935 0.734198i \(-0.262442\pi\)
−0.296367 + 0.955074i \(0.595775\pi\)
\(402\) 0 0
\(403\) −949.626 1644.80i −0.117380 0.203309i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5432.80i 0.661656i
\(408\) 0 0
\(409\) 11353.0 6554.64i 1.37254 0.792436i 0.381292 0.924455i \(-0.375479\pi\)
0.991247 + 0.132019i \(0.0421460\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1582.47 10992.1i −0.188543 1.30965i
\(414\) 0 0
\(415\) 491.963 852.106i 0.0581916 0.100791i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5937.56 −0.692288 −0.346144 0.938181i \(-0.612509\pi\)
−0.346144 + 0.938181i \(0.612509\pi\)
\(420\) 0 0
\(421\) 12210.2 1.41351 0.706757 0.707456i \(-0.250157\pi\)
0.706757 + 0.707456i \(0.250157\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5483.08 9496.97i 0.625808 1.08393i
\(426\) 0 0
\(427\) −6080.84 7729.52i −0.689162 0.876013i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2782.80 + 1606.65i −0.311004 + 0.179558i −0.647376 0.762171i \(-0.724134\pi\)
0.336372 + 0.941729i \(0.390800\pi\)
\(432\) 0 0
\(433\) 6616.31i 0.734318i 0.930158 + 0.367159i \(0.119669\pi\)
−0.930158 + 0.367159i \(0.880331\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 157.870 + 273.438i 0.0172813 + 0.0299321i
\(438\) 0 0
\(439\) 2084.48 + 1203.48i 0.226622 + 0.130840i 0.609013 0.793161i \(-0.291566\pi\)
−0.382391 + 0.924001i \(0.624899\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9059.31 5230.40i −0.971605 0.560956i −0.0718798 0.997413i \(-0.522900\pi\)
−0.899725 + 0.436457i \(0.856233\pi\)
\(444\) 0 0
\(445\) 560.988 + 971.660i 0.0597604 + 0.103508i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7633.63i 0.802346i −0.916002 0.401173i \(-0.868603\pi\)
0.916002 0.401173i \(-0.131397\pi\)
\(450\) 0 0
\(451\) −11250.7 + 6495.59i −1.17467 + 0.678194i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −493.979 627.910i −0.0508969 0.0646964i
\(456\) 0 0
\(457\) −7723.99 + 13378.3i −0.790620 + 1.36939i 0.134964 + 0.990850i \(0.456908\pi\)
−0.925584 + 0.378543i \(0.876425\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −19428.0 −1.96280 −0.981401 0.191970i \(-0.938512\pi\)
−0.981401 + 0.191970i \(0.938512\pi\)
\(462\) 0 0
\(463\) −8196.41 −0.822720 −0.411360 0.911473i \(-0.634946\pi\)
−0.411360 + 0.911473i \(0.634946\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7344.66 12721.3i 0.727774 1.26054i −0.230048 0.973179i \(-0.573888\pi\)
0.957822 0.287362i \(-0.0927784\pi\)
\(468\) 0 0
\(469\) 1715.93 + 11919.2i 0.168943 + 1.17351i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 13899.5 8024.88i 1.35116 0.780093i
\(474\) 0 0
\(475\) 1312.95i 0.126825i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8549.24 + 14807.7i 0.815500 + 1.41249i 0.908968 + 0.416866i \(0.136871\pi\)
−0.0934678 + 0.995622i \(0.529795\pi\)
\(480\) 0 0
\(481\) −1689.57 975.473i −0.160162 0.0924693i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 218.008 + 125.867i 0.0204108 + 0.0117842i
\(486\) 0 0
\(487\) −2428.25 4205.85i −0.225944 0.391346i 0.730659 0.682743i \(-0.239213\pi\)
−0.956602 + 0.291397i \(0.905880\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3844.24i 0.353336i −0.984270 0.176668i \(-0.943468\pi\)
0.984270 0.176668i \(-0.0565320\pi\)
\(492\) 0 0
\(493\) 3645.31 2104.62i 0.333016 0.192267i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6426.94 16062.2i 0.580056 1.44967i
\(498\) 0 0
\(499\) 2307.84 3997.30i 0.207041 0.358605i −0.743740 0.668469i \(-0.766950\pi\)
0.950781 + 0.309864i \(0.100283\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11692.2 −1.03644 −0.518219 0.855248i \(-0.673405\pi\)
−0.518219 + 0.855248i \(0.673405\pi\)
\(504\) 0 0
\(505\) −2713.57 −0.239114
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10752.4 + 18623.7i −0.936327 + 1.62177i −0.164077 + 0.986447i \(0.552465\pi\)
−0.772250 + 0.635319i \(0.780869\pi\)
\(510\) 0 0
\(511\) −16661.6 + 2398.67i −1.44240 + 0.207654i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 327.680 189.186i 0.0280375 0.0161875i
\(516\) 0 0
\(517\) 11151.4i 0.948619i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −184.719 319.942i −0.0155330 0.0269039i 0.858154 0.513392i \(-0.171611\pi\)
−0.873687 + 0.486488i \(0.838278\pi\)
\(522\) 0 0
\(523\) 13219.0 + 7631.98i 1.10521 + 0.638094i 0.937585 0.347757i \(-0.113057\pi\)
0.167626 + 0.985851i \(0.446390\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11338.6 6546.37i −0.937228 0.541109i
\(528\) 0 0
\(529\) −5699.53 9871.87i −0.468441 0.811364i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4665.20i 0.379122i
\(534\) 0 0
\(535\) −1211.69 + 699.568i −0.0979173 + 0.0565326i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −12814.9 3103.92i −1.02408 0.248043i
\(540\) 0 0
\(541\) −8163.08 + 14138.9i −0.648721 + 1.12362i 0.334707 + 0.942322i \(0.391363\pi\)
−0.983429 + 0.181296i \(0.941971\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3172.06 −0.249314
\(546\) 0 0
\(547\) −13065.7 −1.02130 −0.510649 0.859789i \(-0.670595\pi\)
−0.510649 + 0.859789i \(0.670595\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 251.980 436.442i 0.0194822 0.0337442i
\(552\) 0 0
\(553\) −11572.3 + 9104.00i −0.889884 + 0.700075i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9145.80 + 5280.33i −0.695727 + 0.401678i −0.805754 0.592250i \(-0.798240\pi\)
0.110027 + 0.993929i \(0.464906\pi\)
\(558\) 0 0
\(559\) 5763.55i 0.436086i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6474.13 11213.5i −0.484640 0.839420i 0.515205 0.857067i \(-0.327716\pi\)
−0.999844 + 0.0176468i \(0.994383\pi\)
\(564\) 0 0
\(565\) −2408.06 1390.29i −0.179306 0.103522i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12555.1 7248.69i −0.925021 0.534061i −0.0397876 0.999208i \(-0.512668\pi\)
−0.885233 + 0.465147i \(0.846001\pi\)
\(570\) 0 0
\(571\) −1966.46 3406.00i −0.144122 0.249626i 0.784923 0.619593i \(-0.212702\pi\)
−0.929045 + 0.369967i \(0.879369\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3193.38i 0.231605i
\(576\) 0 0
\(577\) 7970.48 4601.76i 0.575070 0.332017i −0.184101 0.982907i \(-0.558938\pi\)
0.759172 + 0.650890i \(0.225604\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5414.07 + 2166.32i 0.386598 + 0.154689i
\(582\) 0 0
\(583\) 328.262 568.566i 0.0233194 0.0403904i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4778.34 0.335985 0.167992 0.985788i \(-0.446272\pi\)
0.167992 + 0.985788i \(0.446272\pi\)
\(588\) 0 0
\(589\) −1567.55 −0.109660
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7388.21 12796.8i 0.511631 0.886172i −0.488278 0.872688i \(-0.662375\pi\)
0.999909 0.0134834i \(-0.00429202\pi\)
\(594\) 0 0
\(595\) −5113.37 2046.00i −0.352315 0.140971i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20384.4 11769.0i 1.39046 0.802783i 0.397094 0.917778i \(-0.370019\pi\)
0.993366 + 0.114995i \(0.0366852\pi\)
\(600\) 0 0
\(601\) 13020.6i 0.883727i −0.897082 0.441864i \(-0.854318\pi\)
0.897082 0.441864i \(-0.145682\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 229.296 + 397.153i 0.0154086 + 0.0266885i
\(606\) 0 0
\(607\) 15450.9 + 8920.59i 1.03317 + 0.596500i 0.917891 0.396833i \(-0.129891\pi\)
0.115278 + 0.993333i \(0.463224\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3468.01 + 2002.25i 0.229624 + 0.132574i
\(612\) 0 0
\(613\) 8589.91 + 14878.2i 0.565976 + 0.980299i 0.996958 + 0.0779389i \(0.0248339\pi\)
−0.430982 + 0.902361i \(0.641833\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7147.22i 0.466347i −0.972435 0.233174i \(-0.925089\pi\)
0.972435 0.233174i \(-0.0749111\pi\)
\(618\) 0 0
\(619\) 5170.09 2984.95i 0.335708 0.193821i −0.322664 0.946514i \(-0.604578\pi\)
0.658373 + 0.752692i \(0.271245\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5226.16 + 4111.44i −0.336086 + 0.264400i
\(624\) 0 0
\(625\) −6029.23 + 10442.9i −0.385870 + 0.668347i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −13449.1 −0.852545
\(630\) 0 0
\(631\) 15148.2 0.955693 0.477846 0.878443i \(-0.341418\pi\)
0.477846 + 0.878443i \(0.341418\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 436.969 756.853i 0.0273080 0.0472989i
\(636\) 0 0
\(637\) 3266.25 3428.04i 0.203161 0.213225i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4316.39 2492.07i 0.265971 0.153558i −0.361085 0.932533i \(-0.617593\pi\)
0.627055 + 0.778975i \(0.284260\pi\)
\(642\) 0 0
\(643\) 6255.66i 0.383669i 0.981427 + 0.191834i \(0.0614436\pi\)
−0.981427 + 0.191834i \(0.938556\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12254.3 + 21225.1i 0.744618 + 1.28972i 0.950373 + 0.311112i \(0.100702\pi\)
−0.205755 + 0.978603i \(0.565965\pi\)
\(648\) 0 0
\(649\) −19962.7 11525.5i −1.20740 0.697095i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26910.6 + 15536.8i 1.61270 + 0.931093i 0.988741 + 0.149636i \(0.0478101\pi\)
0.623959 + 0.781457i \(0.285523\pi\)
\(654\) 0 0
\(655\) 254.617 + 441.010i 0.0151889 + 0.0263079i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13489.0i 0.797357i 0.917091 + 0.398678i \(0.130531\pi\)
−0.917091 + 0.398678i \(0.869469\pi\)
\(660\) 0 0
\(661\) 16896.0 9754.92i 0.994219 0.574013i 0.0876864 0.996148i \(-0.472053\pi\)
0.906533 + 0.422135i \(0.138719\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −652.669 + 93.9609i −0.0380593 + 0.00547917i
\(666\) 0 0
\(667\) 612.872 1061.53i 0.0355780 0.0616229i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −20413.5 −1.17445
\(672\) 0 0
\(673\) −7967.95 −0.456377 −0.228189 0.973617i \(-0.573280\pi\)
−0.228189 + 0.973617i \(0.573280\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13315.2 + 23062.5i −0.755898 + 1.30925i 0.189028 + 0.981972i \(0.439466\pi\)
−0.944926 + 0.327283i \(0.893867\pi\)
\(678\) 0 0
\(679\) −554.246 + 1385.17i −0.0313255 + 0.0782886i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26596.3 15355.4i 1.49001 0.860259i 0.490078 0.871679i \(-0.336968\pi\)
0.999935 + 0.0114194i \(0.00363498\pi\)
\(684\) 0 0
\(685\) 3626.30i 0.202268i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 117.881 + 204.175i 0.00651798 + 0.0112895i
\(690\) 0 0
\(691\) 25217.6 + 14559.4i 1.38831 + 0.801541i 0.993125 0.117061i \(-0.0373471\pi\)
0.395185 + 0.918602i \(0.370680\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1826.35 + 1054.44i 0.0996798 + 0.0575502i
\(696\) 0 0
\(697\) −16080.1 27851.5i −0.873854 1.51356i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30038.9i 1.61848i 0.587480 + 0.809239i \(0.300120\pi\)
−0.587480 + 0.809239i \(0.699880\pi\)
\(702\) 0 0
\(703\) −1394.49 + 805.110i −0.0748140 + 0.0431939i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2291.66 15918.3i −0.121905 0.846773i
\(708\) 0 0
\(709\) −4914.07 + 8511.42i −0.260299 + 0.450851i −0.966321 0.257339i \(-0.917154\pi\)
0.706023 + 0.708189i \(0.250488\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3812.64 −0.200259
\(714\) 0 0
\(715\) −1658.29 −0.0867366
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12838.1 22236.2i 0.665897 1.15337i −0.313144 0.949706i \(-0.601382\pi\)
0.979041 0.203662i \(-0.0652843\pi\)
\(720\) 0 0
\(721\) 1386.53 + 1762.46i 0.0716188 + 0.0910366i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4414.17 + 2548.52i −0.226121 + 0.130551i
\(726\) 0 0
\(727\) 9770.68i 0.498452i 0.968445 + 0.249226i \(0.0801761\pi\)
−0.968445 + 0.249226i \(0.919824\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 19865.9 + 34408.7i 1.00515 + 1.74097i
\(732\) 0 0
\(733\) 1265.95 + 730.896i 0.0637912 + 0.0368298i 0.531556 0.847023i \(-0.321607\pi\)
−0.467765 + 0.883853i \(0.654941\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21646.4 + 12497.5i 1.08189 + 0.624631i
\(738\) 0 0
\(739\) 6722.13 + 11643.1i 0.334611 + 0.579563i 0.983410 0.181397i \(-0.0580618\pi\)
−0.648799 + 0.760960i \(0.724728\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13757.2i 0.679278i −0.940556 0.339639i \(-0.889695\pi\)
0.940556 0.339639i \(-0.110305\pi\)
\(744\) 0 0
\(745\) −3846.23 + 2220.62i −0.189148 + 0.109204i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5127.07 6517.16i −0.250119 0.317933i
\(750\) 0 0
\(751\) 14594.6 25278.6i 0.709142 1.22827i −0.256034 0.966668i \(-0.582416\pi\)
0.965176 0.261602i \(-0.0842508\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8000.25 −0.385641
\(756\) 0 0
\(757\) 8236.25 0.395445 0.197722 0.980258i \(-0.436646\pi\)
0.197722 + 0.980258i \(0.436646\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −16521.8 + 28616.6i −0.787011 + 1.36314i 0.140779 + 0.990041i \(0.455039\pi\)
−0.927790 + 0.373102i \(0.878294\pi\)
\(762\) 0 0
\(763\) −2678.86 18607.9i −0.127105 0.882896i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7168.71 4138.86i 0.337480 0.194844i
\(768\) 0 0
\(769\) 23591.7i 1.10629i −0.833084 0.553146i \(-0.813427\pi\)
0.833084 0.553146i \(-0.186573\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 15883.6 + 27511.2i 0.739060 + 1.28009i 0.952919 + 0.303225i \(0.0980635\pi\)
−0.213858 + 0.976865i \(0.568603\pi\)
\(774\) 0 0
\(775\) 13730.1 + 7927.10i 0.636388 + 0.367419i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3334.58 1925.22i −0.153368 0.0885471i
\(780\) 0 0
\(781\) −17954.7 31098.4i −0.822623 1.42482i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4662.90i 0.212008i
\(786\) 0 0
\(787\) 34978.6 20194.9i 1.58431 0.914702i 0.590092 0.807336i \(-0.299092\pi\)
0.994220 0.107366i \(-0.0342417\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6122.04 15300.2i 0.275189 0.687752i
\(792\) 0 0
\(793\) 3665.29 6348.46i 0.164134 0.284288i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14289.7 −0.635092 −0.317546 0.948243i \(-0.602859\pi\)
−0.317546 + 0.948243i \(0.602859\pi\)
\(798\) 0 0
\(799\) 27605.6 1.22230
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −17470.1 + 30259.1i −0.767753 + 1.32979i
\(804\) 0 0
\(805\) −1587.44 + 228.534i −0.0695029 + 0.0100059i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 28576.0 16498.3i 1.24188 0.716997i 0.272400 0.962184i \(-0.412183\pi\)
0.969476 + 0.245187i \(0.0788493\pi\)
\(810\) 0 0
\(811\) 36278.0i 1.57077i 0.619008 + 0.785384i \(0.287535\pi\)
−0.619008 + 0.785384i \(0.712465\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3340.14 + 5785.28i 0.143558 + 0.248650i
\(816\) 0 0
\(817\) 4119.65 + 2378.48i 0.176412 + 0.101851i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33219.3 19179.2i −1.41213 0.815296i −0.416545 0.909115i \(-0.636759\pi\)
−0.995589 + 0.0938191i \(0.970092\pi\)
\(822\) 0 0
\(823\) −18987.0 32886.5i −0.804186 1.39289i −0.916839 0.399257i \(-0.869268\pi\)
0.112652 0.993634i \(-0.464065\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 21864.0i 0.919331i 0.888092 + 0.459666i \(0.152031\pi\)
−0.888092 + 0.459666i \(0.847969\pi\)
\(828\) 0 0
\(829\) 16368.9 9450.57i 0.685783 0.395937i −0.116247 0.993220i \(-0.537087\pi\)
0.802030 + 0.597283i \(0.203753\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 7683.87 31723.8i 0.319604 1.31952i
\(834\) 0 0
\(835\) −1804.35 + 3125.22i −0.0747809 + 0.129524i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 26571.8 1.09340 0.546699 0.837329i \(-0.315884\pi\)
0.546699 + 0.837329i \(0.315884\pi\)
\(840\) 0 0
\(841\) 22432.6 0.919782
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3134.97 + 5429.92i −0.127629 + 0.221059i
\(846\) 0 0
\(847\) −2136.12 + 1680.49i −0.0866565 + 0.0681729i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3391.72 + 1958.21i −0.136623 + 0.0788796i
\(852\) 0 0
\(853\) 43958.5i 1.76449i 0.470789 + 0.882246i \(0.343969\pi\)
−0.470789 + 0.882246i \(0.656031\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3199.70 + 5542.04i 0.127537 + 0.220901i 0.922722 0.385466i \(-0.125959\pi\)
−0.795185 + 0.606367i \(0.792626\pi\)
\(858\) 0 0
\(859\) −6804.26 3928.44i −0.270266 0.156038i 0.358743 0.933437i \(-0.383206\pi\)
−0.629009 + 0.777398i \(0.716539\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −27014.2 15596.7i −1.06556 0.615199i −0.138592 0.990349i \(-0.544258\pi\)
−0.926964 + 0.375150i \(0.877591\pi\)
\(864\) 0 0
\(865\) −5878.39 10181.7i −0.231065 0.400217i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 30562.3i 1.19304i
\(870\) 0 0
\(871\) −7773.32 + 4487.93i −0.302398 + 0.174590i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 12908.4 + 5165.02i 0.498725 + 0.199554i
\(876\) 0 0
\(877\) 5510.34 9544.19i 0.212168 0.367485i −0.740225 0.672359i \(-0.765281\pi\)
0.952393 + 0.304874i \(0.0986144\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 751.266 0.0287296 0.0143648 0.999897i \(-0.495427\pi\)
0.0143648 + 0.999897i \(0.495427\pi\)
\(882\) 0 0
\(883\) 1345.17 0.0512669 0.0256334 0.999671i \(-0.491840\pi\)
0.0256334 + 0.999671i \(0.491840\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −845.523 + 1464.49i −0.0320066 + 0.0554371i −0.881585 0.472025i \(-0.843523\pi\)
0.849578 + 0.527462i \(0.176856\pi\)
\(888\) 0 0
\(889\) 4808.86 + 1924.16i 0.181422 + 0.0725920i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2862.33 1652.57i 0.107261 0.0619273i
\(894\) 0 0
\(895\) 1196.75i 0.0446960i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3042.73 + 5270.17i 0.112882 + 0.195517i
\(900\) 0 0
\(901\) 1407.51 + 812.624i 0.0520431 + 0.0300471i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7279.43 + 4202.78i 0.267377 + 0.154370i
\(906\) 0 0
\(907\) −5003.83 8666.89i −0.183186 0.317287i 0.759778 0.650183i \(-0.225308\pi\)
−0.942964 + 0.332896i \(0.891974\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 35217.1i 1.28078i 0.768048 + 0.640392i \(0.221228\pi\)
−0.768048 + 0.640392i \(0.778772\pi\)
\(912\) 0 0
\(913\) 10482.3 6051.96i 0.379971 0.219376i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2372.01 + 1866.07i −0.0854206 + 0.0672007i
\(918\) 0 0
\(919\) −8680.34 + 15034.8i −0.311576 + 0.539665i −0.978704 0.205278i \(-0.934190\pi\)
0.667128 + 0.744943i \(0.267523\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 12895.2 0.459861
\(924\) 0 0
\(925\) 16285.7 0.578888
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 931.872 1614.05i 0.0329104 0.0570024i −0.849101 0.528230i \(-0.822856\pi\)
0.882011 + 0.471228i \(0.156189\pi\)
\(930\) 0 0
\(931\) −1102.38 3749.32i −0.0388068 0.131986i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9900.11 + 5715.83i −0.346276 + 0.199923i
\(936\) 0 0
\(937\) 44596.5i 1.55486i 0.628970 + 0.777429i \(0.283477\pi\)
−0.628970 + 0.777429i \(0.716523\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 23617.3 + 40906.4i 0.818175 + 1.41712i 0.907026 + 0.421075i \(0.138347\pi\)
−0.0888512 + 0.996045i \(0.528320\pi\)
\(942\) 0 0
\(943\) −8110.44 4682.57i −0.280077 0.161702i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8008.25 + 4623.57i 0.274797 + 0.158654i 0.631066 0.775729i \(-0.282618\pi\)
−0.356268 + 0.934384i \(0.615951\pi\)
\(948\) 0 0
\(949\) −6273.59 10866.2i −0.214594 0.371687i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1138.35i 0.0386932i −0.999813 0.0193466i \(-0.993841\pi\)
0.999813 0.0193466i \(-0.00615860\pi\)
\(954\) 0 0
\(955\) −1983.00 + 1144.89i −0.0671921 + 0.0387934i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −21272.5 + 3062.48i −0.716293 + 0.103120i
\(960\) 0 0
\(961\) −5431.17 + 9407.06i −0.182309 + 0.315769i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 13138.4 0.438279
\(966\) 0 0
\(967\) −5284.04 −0.175722 −0.0878610 0.996133i \(-0.528003\pi\)
−0.0878610 + 0.996133i \(0.528003\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −11258.4 + 19500.1i −0.372089 + 0.644478i −0.989887 0.141860i \(-0.954692\pi\)
0.617797 + 0.786337i \(0.288025\pi\)
\(972\) 0 0
\(973\) −4643.16 + 11604.2i −0.152984 + 0.382336i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32273.4 18633.1i 1.05683 0.610158i 0.132273 0.991213i \(-0.457773\pi\)
0.924552 + 0.381055i \(0.124439\pi\)
\(978\) 0 0
\(979\) 13802.2i 0.450581i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 20156.0 + 34911.3i 0.653995 + 1.13275i 0.982145 + 0.188127i \(0.0602418\pi\)
−0.328149 + 0.944626i \(0.606425\pi\)
\(984\) 0 0
\(985\) −7678.40 4433.13i −0.248380 0.143402i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 10019.9 + 5785.00i 0.322159 + 0.185998i
\(990\) 0 0
\(991\) 2601.46 + 4505.86i 0.0833885 + 0.144433i 0.904703 0.426042i \(-0.140092\pi\)
−0.821315 + 0.570475i \(0.806759\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4534.61i 0.144479i
\(996\) 0 0
\(997\) 54015.6 31185.9i 1.71584 0.990640i 0.789670 0.613532i \(-0.210252\pi\)
0.926169 0.377108i \(-0.123082\pi\)
\(998\) 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.593.11 48
3.2 odd 2 inner 1008.4.bt.d.593.14 48
4.3 odd 2 504.4.bl.a.89.11 yes 48
7.3 odd 6 inner 1008.4.bt.d.17.14 48
12.11 even 2 504.4.bl.a.89.14 yes 48
21.17 even 6 inner 1008.4.bt.d.17.11 48
28.3 even 6 504.4.bl.a.17.14 yes 48
84.59 odd 6 504.4.bl.a.17.11 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.4.bl.a.17.11 48 84.59 odd 6
504.4.bl.a.17.14 yes 48 28.3 even 6
504.4.bl.a.89.11 yes 48 4.3 odd 2
504.4.bl.a.89.14 yes 48 12.11 even 2
1008.4.bt.d.17.11 48 21.17 even 6 inner
1008.4.bt.d.17.14 48 7.3 odd 6 inner
1008.4.bt.d.593.11 48 1.1 even 1 trivial
1008.4.bt.d.593.14 48 3.2 odd 2 inner