Properties

Label 980.2.e.f.589.2
Level $980$
Weight $2$
Character 980.589
Analytic conductor $7.825$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [980,2,Mod(589,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.589");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.e (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.2
Root \(-1.63746 + 1.52274i\) of defining polynomial
Character \(\chi\) \(=\) 980.589
Dual form 980.2.e.f.589.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.73205i q^{3} +(2.13746 + 0.656712i) q^{5} +O(q^{10})\) \(q-1.73205i q^{3} +(2.13746 + 0.656712i) q^{5} +2.27492 q^{11} +6.09095i q^{13} +(1.13746 - 3.70219i) q^{15} +4.77753i q^{17} +4.27492 q^{19} -0.894797i q^{23} +(4.13746 + 2.80739i) q^{25} -5.19615i q^{27} +3.27492 q^{29} -4.27492 q^{31} -3.94027i q^{33} -5.61478i q^{37} +10.5498 q^{39} -11.2749 q^{41} +6.50958i q^{43} +2.15068i q^{47} +8.27492 q^{51} -7.40437i q^{53} +(4.86254 + 1.49397i) q^{55} -7.40437i q^{57} -4.27492 q^{59} +1.54983 q^{61} +(-4.00000 + 13.0192i) q^{65} -13.9140i q^{67} -1.54983 q^{69} +10.5498 q^{71} -2.15068i q^{73} +(4.86254 - 7.16629i) q^{75} +0.274917 q^{79} -9.00000 q^{81} -5.67232i q^{83} +(-3.13746 + 10.2118i) q^{85} -5.67232i q^{87} +7.00000 q^{89} +7.40437i q^{93} +(9.13746 + 2.80739i) q^{95} -6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{5} - 6 q^{11} - 3 q^{15} + 2 q^{19} + 9 q^{25} - 2 q^{29} - 2 q^{31} + 12 q^{39} - 30 q^{41} + 18 q^{51} + 27 q^{55} - 2 q^{59} - 24 q^{61} - 16 q^{65} + 24 q^{69} + 12 q^{71} + 27 q^{75} - 14 q^{79} - 36 q^{81} - 5 q^{85} + 28 q^{89} + 29 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 1.73205i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) 0 0
\(5\) 2.13746 + 0.656712i 0.955901 + 0.293691i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.27492 0.685913 0.342957 0.939351i \(-0.388572\pi\)
0.342957 + 0.939351i \(0.388572\pi\)
\(12\) 0 0
\(13\) 6.09095i 1.68933i 0.535299 + 0.844663i \(0.320199\pi\)
−0.535299 + 0.844663i \(0.679801\pi\)
\(14\) 0 0
\(15\) 1.13746 3.70219i 0.293691 0.955901i
\(16\) 0 0
\(17\) 4.77753i 1.15872i 0.815072 + 0.579360i \(0.196697\pi\)
−0.815072 + 0.579360i \(0.803303\pi\)
\(18\) 0 0
\(19\) 4.27492 0.980733 0.490367 0.871516i \(-0.336863\pi\)
0.490367 + 0.871516i \(0.336863\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.894797i 0.186578i −0.995639 0.0932891i \(-0.970262\pi\)
0.995639 0.0932891i \(-0.0297381\pi\)
\(24\) 0 0
\(25\) 4.13746 + 2.80739i 0.827492 + 0.561478i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 3.27492 0.608137 0.304068 0.952650i \(-0.401655\pi\)
0.304068 + 0.952650i \(0.401655\pi\)
\(30\) 0 0
\(31\) −4.27492 −0.767798 −0.383899 0.923375i \(-0.625419\pi\)
−0.383899 + 0.923375i \(0.625419\pi\)
\(32\) 0 0
\(33\) 3.94027i 0.685913i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.61478i 0.923064i −0.887124 0.461532i \(-0.847300\pi\)
0.887124 0.461532i \(-0.152700\pi\)
\(38\) 0 0
\(39\) 10.5498 1.68933
\(40\) 0 0
\(41\) −11.2749 −1.76085 −0.880423 0.474189i \(-0.842741\pi\)
−0.880423 + 0.474189i \(0.842741\pi\)
\(42\) 0 0
\(43\) 6.50958i 0.992701i 0.868122 + 0.496351i \(0.165327\pi\)
−0.868122 + 0.496351i \(0.834673\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.15068i 0.313709i 0.987622 + 0.156854i \(0.0501353\pi\)
−0.987622 + 0.156854i \(0.949865\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 8.27492 1.15872
\(52\) 0 0
\(53\) 7.40437i 1.01707i −0.861042 0.508534i \(-0.830187\pi\)
0.861042 0.508534i \(-0.169813\pi\)
\(54\) 0 0
\(55\) 4.86254 + 1.49397i 0.655665 + 0.201446i
\(56\) 0 0
\(57\) 7.40437i 0.980733i
\(58\) 0 0
\(59\) −4.27492 −0.556547 −0.278273 0.960502i \(-0.589762\pi\)
−0.278273 + 0.960502i \(0.589762\pi\)
\(60\) 0 0
\(61\) 1.54983 0.198436 0.0992180 0.995066i \(-0.468366\pi\)
0.0992180 + 0.995066i \(0.468366\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.00000 + 13.0192i −0.496139 + 1.61483i
\(66\) 0 0
\(67\) 13.9140i 1.69986i −0.526896 0.849930i \(-0.676644\pi\)
0.526896 0.849930i \(-0.323356\pi\)
\(68\) 0 0
\(69\) −1.54983 −0.186578
\(70\) 0 0
\(71\) 10.5498 1.25204 0.626018 0.779809i \(-0.284684\pi\)
0.626018 + 0.779809i \(0.284684\pi\)
\(72\) 0 0
\(73\) 2.15068i 0.251718i −0.992048 0.125859i \(-0.959831\pi\)
0.992048 0.125859i \(-0.0401687\pi\)
\(74\) 0 0
\(75\) 4.86254 7.16629i 0.561478 0.827492i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.274917 0.0309306 0.0154653 0.999880i \(-0.495077\pi\)
0.0154653 + 0.999880i \(0.495077\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) 5.67232i 0.622618i −0.950309 0.311309i \(-0.899233\pi\)
0.950309 0.311309i \(-0.100767\pi\)
\(84\) 0 0
\(85\) −3.13746 + 10.2118i −0.340305 + 1.10762i
\(86\) 0 0
\(87\) 5.67232i 0.608137i
\(88\) 0 0
\(89\) 7.00000 0.741999 0.370999 0.928633i \(-0.379015\pi\)
0.370999 + 0.928633i \(0.379015\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 7.40437i 0.767798i
\(94\) 0 0
\(95\) 9.13746 + 2.80739i 0.937483 + 0.288032i
\(96\) 0 0
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.54983 0.154214 0.0771071 0.997023i \(-0.475432\pi\)
0.0771071 + 0.997023i \(0.475432\pi\)
\(102\) 0 0
\(103\) 2.56930i 0.253161i −0.991956 0.126581i \(-0.959600\pi\)
0.991956 0.126581i \(-0.0404002\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.9140i 1.34511i −0.740046 0.672556i \(-0.765196\pi\)
0.740046 0.672556i \(-0.234804\pi\)
\(108\) 0 0
\(109\) −3.54983 −0.340012 −0.170006 0.985443i \(-0.554379\pi\)
−0.170006 + 0.985443i \(0.554379\pi\)
\(110\) 0 0
\(111\) −9.72508 −0.923064
\(112\) 0 0
\(113\) 13.0192i 1.22474i −0.790572 0.612369i \(-0.790217\pi\)
0.790572 0.612369i \(-0.209783\pi\)
\(114\) 0 0
\(115\) 0.587624 1.91259i 0.0547962 0.178350i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −5.82475 −0.529523
\(122\) 0 0
\(123\) 19.5287i 1.76085i
\(124\) 0 0
\(125\) 7.00000 + 8.71780i 0.626099 + 0.779744i
\(126\) 0 0
\(127\) 1.78959i 0.158801i 0.996843 + 0.0794004i \(0.0253006\pi\)
−0.996843 + 0.0794004i \(0.974699\pi\)
\(128\) 0 0
\(129\) 11.2749 0.992701
\(130\) 0 0
\(131\) −18.2749 −1.59669 −0.798343 0.602202i \(-0.794290\pi\)
−0.798343 + 0.602202i \(0.794290\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 3.41238 11.1066i 0.293691 0.955901i
\(136\) 0 0
\(137\) 9.19397i 0.785494i 0.919647 + 0.392747i \(0.128475\pi\)
−0.919647 + 0.392747i \(0.871525\pi\)
\(138\) 0 0
\(139\) 17.0997 1.45037 0.725187 0.688551i \(-0.241753\pi\)
0.725187 + 0.688551i \(0.241753\pi\)
\(140\) 0 0
\(141\) 3.72508 0.313709
\(142\) 0 0
\(143\) 13.8564i 1.15873i
\(144\) 0 0
\(145\) 7.00000 + 2.15068i 0.581318 + 0.178604i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.54983 −0.618507 −0.309253 0.950980i \(-0.600079\pi\)
−0.309253 + 0.950980i \(0.600079\pi\)
\(150\) 0 0
\(151\) −20.2749 −1.64995 −0.824975 0.565170i \(-0.808811\pi\)
−0.824975 + 0.565170i \(0.808811\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.13746 2.80739i −0.733938 0.225495i
\(156\) 0 0
\(157\) 10.8685i 0.867399i 0.901058 + 0.433699i \(0.142792\pi\)
−0.901058 + 0.433699i \(0.857208\pi\)
\(158\) 0 0
\(159\) −12.8248 −1.01707
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 7.40437i 0.579955i 0.957033 + 0.289978i \(0.0936479\pi\)
−0.957033 + 0.289978i \(0.906352\pi\)
\(164\) 0 0
\(165\) 2.58762 8.42217i 0.201446 0.655665i
\(166\) 0 0
\(167\) 12.6005i 0.975058i 0.873107 + 0.487529i \(0.162102\pi\)
−0.873107 + 0.487529i \(0.837898\pi\)
\(168\) 0 0
\(169\) −24.0997 −1.85382
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 18.7490i 1.42546i 0.701438 + 0.712731i \(0.252542\pi\)
−0.701438 + 0.712731i \(0.747458\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 7.40437i 0.556547i
\(178\) 0 0
\(179\) −0.274917 −0.0205483 −0.0102741 0.999947i \(-0.503270\pi\)
−0.0102741 + 0.999947i \(0.503270\pi\)
\(180\) 0 0
\(181\) −16.7251 −1.24317 −0.621583 0.783348i \(-0.713510\pi\)
−0.621583 + 0.783348i \(0.713510\pi\)
\(182\) 0 0
\(183\) 2.68439i 0.198436i
\(184\) 0 0
\(185\) 3.68729 12.0014i 0.271095 0.882357i
\(186\) 0 0
\(187\) 10.8685i 0.794782i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.8248 1.65154 0.825771 0.564006i \(-0.190741\pi\)
0.825771 + 0.564006i \(0.190741\pi\)
\(192\) 0 0
\(193\) 9.19397i 0.661796i 0.943666 + 0.330898i \(0.107352\pi\)
−0.943666 + 0.330898i \(0.892648\pi\)
\(194\) 0 0
\(195\) 22.5498 + 6.92820i 1.61483 + 0.496139i
\(196\) 0 0
\(197\) 26.0383i 1.85515i 0.373634 + 0.927576i \(0.378112\pi\)
−0.373634 + 0.927576i \(0.621888\pi\)
\(198\) 0 0
\(199\) −9.72508 −0.689393 −0.344696 0.938714i \(-0.612018\pi\)
−0.344696 + 0.938714i \(0.612018\pi\)
\(200\) 0 0
\(201\) −24.0997 −1.69986
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −24.0997 7.40437i −1.68319 0.517144i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 9.72508 0.672698
\(210\) 0 0
\(211\) −19.6495 −1.35273 −0.676364 0.736568i \(-0.736445\pi\)
−0.676364 + 0.736568i \(0.736445\pi\)
\(212\) 0 0
\(213\) 18.2728i 1.25204i
\(214\) 0 0
\(215\) −4.27492 + 13.9140i −0.291547 + 0.948924i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3.72508 −0.251718
\(220\) 0 0
\(221\) −29.0997 −1.95746
\(222\) 0 0
\(223\) 8.71780i 0.583787i −0.956451 0.291893i \(-0.905715\pi\)
0.956451 0.291893i \(-0.0942853\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.45203i 0.428236i −0.976808 0.214118i \(-0.931312\pi\)
0.976808 0.214118i \(-0.0686878\pi\)
\(228\) 0 0
\(229\) 4.27492 0.282494 0.141247 0.989974i \(-0.454889\pi\)
0.141247 + 0.989974i \(0.454889\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.6339i 1.22075i −0.792113 0.610375i \(-0.791019\pi\)
0.792113 0.610375i \(-0.208981\pi\)
\(234\) 0 0
\(235\) −1.41238 + 4.59698i −0.0921332 + 0.299874i
\(236\) 0 0
\(237\) 0.476171i 0.0309306i
\(238\) 0 0
\(239\) 14.5498 0.941151 0.470575 0.882360i \(-0.344046\pi\)
0.470575 + 0.882360i \(0.344046\pi\)
\(240\) 0 0
\(241\) −12.8248 −0.826115 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 26.0383i 1.65678i
\(248\) 0 0
\(249\) −9.82475 −0.622618
\(250\) 0 0
\(251\) −5.45017 −0.344011 −0.172006 0.985096i \(-0.555025\pi\)
−0.172006 + 0.985096i \(0.555025\pi\)
\(252\) 0 0
\(253\) 2.03559i 0.127976i
\(254\) 0 0
\(255\) 17.6873 + 5.43424i 1.10762 + 0.340305i
\(256\) 0 0
\(257\) 24.7249i 1.54230i −0.636656 0.771148i \(-0.719683\pi\)
0.636656 0.771148i \(-0.280317\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 26.9331i 1.66077i −0.557193 0.830383i \(-0.688122\pi\)
0.557193 0.830383i \(-0.311878\pi\)
\(264\) 0 0
\(265\) 4.86254 15.8265i 0.298704 0.972217i
\(266\) 0 0
\(267\) 12.1244i 0.741999i
\(268\) 0 0
\(269\) 29.5498 1.80169 0.900843 0.434146i \(-0.142950\pi\)
0.900843 + 0.434146i \(0.142950\pi\)
\(270\) 0 0
\(271\) −12.8248 −0.779048 −0.389524 0.921016i \(-0.627361\pi\)
−0.389524 + 0.921016i \(0.627361\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.41238 + 6.38658i 0.567588 + 0.385125i
\(276\) 0 0
\(277\) 18.6339i 1.11960i 0.828626 + 0.559802i \(0.189123\pi\)
−0.828626 + 0.559802i \(0.810877\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 19.5863i 1.16428i 0.813087 + 0.582142i \(0.197785\pi\)
−0.813087 + 0.582142i \(0.802215\pi\)
\(284\) 0 0
\(285\) 4.86254 15.8265i 0.288032 0.937483i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −5.82475 −0.342632
\(290\) 0 0
\(291\) −12.0000 −0.703452
\(292\) 0 0
\(293\) 6.92820i 0.404750i −0.979308 0.202375i \(-0.935134\pi\)
0.979308 0.202375i \(-0.0648660\pi\)
\(294\) 0 0
\(295\) −9.13746 2.80739i −0.532003 0.163453i
\(296\) 0 0
\(297\) 11.8208i 0.685913i
\(298\) 0 0
\(299\) 5.45017 0.315191
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 2.68439i 0.154214i
\(304\) 0 0
\(305\) 3.31271 + 1.01779i 0.189685 + 0.0582788i
\(306\) 0 0
\(307\) 3.99782i 0.228167i −0.993471 0.114084i \(-0.963607\pi\)
0.993471 0.114084i \(-0.0363932\pi\)
\(308\) 0 0
\(309\) −4.45017 −0.253161
\(310\) 0 0
\(311\) 12.8248 0.727225 0.363612 0.931550i \(-0.381543\pi\)
0.363612 + 0.931550i \(0.381543\pi\)
\(312\) 0 0
\(313\) 14.4477i 0.816630i −0.912841 0.408315i \(-0.866116\pi\)
0.912841 0.408315i \(-0.133884\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.82518i 0.214844i 0.994214 + 0.107422i \(0.0342596\pi\)
−0.994214 + 0.107422i \(0.965740\pi\)
\(318\) 0 0
\(319\) 7.45017 0.417129
\(320\) 0 0
\(321\) −24.0997 −1.34511
\(322\) 0 0
\(323\) 20.4235i 1.13640i
\(324\) 0 0
\(325\) −17.0997 + 25.2011i −0.948519 + 1.39790i
\(326\) 0 0
\(327\) 6.14849i 0.340012i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −4.82475 −0.265192 −0.132596 0.991170i \(-0.542331\pi\)
−0.132596 + 0.991170i \(0.542331\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.13746 29.7405i 0.499233 1.62490i
\(336\) 0 0
\(337\) 13.0192i 0.709198i −0.935018 0.354599i \(-0.884617\pi\)
0.935018 0.354599i \(-0.115383\pi\)
\(338\) 0 0
\(339\) −22.5498 −1.22474
\(340\) 0 0
\(341\) −9.72508 −0.526643
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3.31271 1.01779i −0.178350 0.0547962i
\(346\) 0 0
\(347\) 12.1244i 0.650870i 0.945564 + 0.325435i \(0.105511\pi\)
−0.945564 + 0.325435i \(0.894489\pi\)
\(348\) 0 0
\(349\) 11.2749 0.603532 0.301766 0.953382i \(-0.402424\pi\)
0.301766 + 0.953382i \(0.402424\pi\)
\(350\) 0 0
\(351\) 31.6495 1.68933
\(352\) 0 0
\(353\) 21.2608i 1.13160i −0.824543 0.565799i \(-0.808568\pi\)
0.824543 0.565799i \(-0.191432\pi\)
\(354\) 0 0
\(355\) 22.5498 + 6.92820i 1.19682 + 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.37459 0.0725479 0.0362739 0.999342i \(-0.488451\pi\)
0.0362739 + 0.999342i \(0.488451\pi\)
\(360\) 0 0
\(361\) −0.725083 −0.0381623
\(362\) 0 0
\(363\) 10.0888i 0.529523i
\(364\) 0 0
\(365\) 1.41238 4.59698i 0.0739271 0.240617i
\(366\) 0 0
\(367\) 14.7512i 0.770007i −0.922915 0.385003i \(-0.874200\pi\)
0.922915 0.385003i \(-0.125800\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5.61478i 0.290722i −0.989379 0.145361i \(-0.953566\pi\)
0.989379 0.145361i \(-0.0464344\pi\)
\(374\) 0 0
\(375\) 15.0997 12.1244i 0.779744 0.626099i
\(376\) 0 0
\(377\) 19.9474i 1.02734i
\(378\) 0 0
\(379\) −23.6495 −1.21479 −0.607397 0.794399i \(-0.707786\pi\)
−0.607397 + 0.794399i \(0.707786\pi\)
\(380\) 0 0
\(381\) 3.09967 0.158801
\(382\) 0 0
\(383\) 20.0049i 1.02220i −0.859520 0.511101i \(-0.829238\pi\)
0.859520 0.511101i \(-0.170762\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.37459 0.272502 0.136251 0.990674i \(-0.456495\pi\)
0.136251 + 0.990674i \(0.456495\pi\)
\(390\) 0 0
\(391\) 4.27492 0.216192
\(392\) 0 0
\(393\) 31.6531i 1.59669i
\(394\) 0 0
\(395\) 0.587624 + 0.180541i 0.0295666 + 0.00908403i
\(396\) 0 0
\(397\) 15.1698i 0.761352i 0.924708 + 0.380676i \(0.124309\pi\)
−0.924708 + 0.380676i \(0.875691\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 0 0
\(403\) 26.0383i 1.29706i
\(404\) 0 0
\(405\) −19.2371 5.91041i −0.955901 0.293691i
\(406\) 0 0
\(407\) 12.7732i 0.633142i
\(408\) 0 0
\(409\) −10.0997 −0.499396 −0.249698 0.968324i \(-0.580331\pi\)
−0.249698 + 0.968324i \(0.580331\pi\)
\(410\) 0 0
\(411\) 15.9244 0.785494
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 3.72508 12.1244i 0.182857 0.595161i
\(416\) 0 0
\(417\) 29.6175i 1.45037i
\(418\) 0 0
\(419\) −17.0997 −0.835373 −0.417687 0.908591i \(-0.637159\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(420\) 0 0
\(421\) 3.27492 0.159610 0.0798048 0.996811i \(-0.474570\pi\)
0.0798048 + 0.996811i \(0.474570\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −13.4124 + 19.7668i −0.650596 + 0.958831i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 24.0000 1.15873
\(430\) 0 0
\(431\) 19.3746 0.933241 0.466620 0.884458i \(-0.345471\pi\)
0.466620 + 0.884458i \(0.345471\pi\)
\(432\) 0 0
\(433\) 26.8756i 1.29156i 0.763525 + 0.645778i \(0.223467\pi\)
−0.763525 + 0.645778i \(0.776533\pi\)
\(434\) 0 0
\(435\) 3.72508 12.1244i 0.178604 0.581318i
\(436\) 0 0
\(437\) 3.82518i 0.182983i
\(438\) 0 0
\(439\) −1.17525 −0.0560915 −0.0280458 0.999607i \(-0.508928\pi\)
−0.0280458 + 0.999607i \(0.508928\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.1244i 0.576046i 0.957624 + 0.288023i \(0.0929979\pi\)
−0.957624 + 0.288023i \(0.907002\pi\)
\(444\) 0 0
\(445\) 14.9622 + 4.59698i 0.709277 + 0.217918i
\(446\) 0 0
\(447\) 13.0767i 0.618507i
\(448\) 0 0
\(449\) 25.8248 1.21875 0.609373 0.792884i \(-0.291421\pi\)
0.609373 + 0.792884i \(0.291421\pi\)
\(450\) 0 0
\(451\) −25.6495 −1.20779
\(452\) 0 0
\(453\) 35.1172i 1.64995i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 20.4235i 0.955372i 0.878531 + 0.477686i \(0.158524\pi\)
−0.878531 + 0.477686i \(0.841476\pi\)
\(458\) 0 0
\(459\) 24.8248 1.15872
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) 6.50958i 0.302526i −0.988494 0.151263i \(-0.951666\pi\)
0.988494 0.151263i \(-0.0483340\pi\)
\(464\) 0 0
\(465\) −4.86254 + 15.8265i −0.225495 + 0.733938i
\(466\) 0 0
\(467\) 19.1676i 0.886973i −0.896281 0.443486i \(-0.853741\pi\)
0.896281 0.443486i \(-0.146259\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 18.8248 0.867399
\(472\) 0 0
\(473\) 14.8087i 0.680907i
\(474\) 0 0
\(475\) 17.6873 + 12.0014i 0.811549 + 0.550660i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.8248 0.585978 0.292989 0.956116i \(-0.405350\pi\)
0.292989 + 0.956116i \(0.405350\pi\)
\(480\) 0 0
\(481\) 34.1993 1.55936
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.54983 14.8087i 0.206597 0.672431i
\(486\) 0 0
\(487\) 33.4427i 1.51543i 0.652584 + 0.757716i \(0.273685\pi\)
−0.652584 + 0.757716i \(0.726315\pi\)
\(488\) 0 0
\(489\) 12.8248 0.579955
\(490\) 0 0
\(491\) −13.4502 −0.606997 −0.303499 0.952832i \(-0.598155\pi\)
−0.303499 + 0.952832i \(0.598155\pi\)
\(492\) 0 0
\(493\) 15.6460i 0.704660i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −39.3746 −1.76265 −0.881324 0.472512i \(-0.843347\pi\)
−0.881324 + 0.472512i \(0.843347\pi\)
\(500\) 0 0
\(501\) 21.8248 0.975058
\(502\) 0 0
\(503\) 16.1797i 0.721418i 0.932678 + 0.360709i \(0.117465\pi\)
−0.932678 + 0.360709i \(0.882535\pi\)
\(504\) 0 0
\(505\) 3.31271 + 1.01779i 0.147414 + 0.0452913i
\(506\) 0 0
\(507\) 41.7419i 1.85382i
\(508\) 0 0
\(509\) 29.5498 1.30977 0.654887 0.755727i \(-0.272716\pi\)
0.654887 + 0.755727i \(0.272716\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 22.2131i 0.980733i
\(514\) 0 0
\(515\) 1.68729 5.49178i 0.0743510 0.241997i
\(516\) 0 0
\(517\) 4.89261i 0.215177i
\(518\) 0 0
\(519\) 32.4743 1.42546
\(520\) 0 0
\(521\) −12.8248 −0.561863 −0.280931 0.959728i \(-0.590643\pi\)
−0.280931 + 0.959728i \(0.590643\pi\)
\(522\) 0 0
\(523\) 11.7057i 0.511856i −0.966696 0.255928i \(-0.917619\pi\)
0.966696 0.255928i \(-0.0823810\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.4235i 0.889663i
\(528\) 0 0
\(529\) 22.1993 0.965189
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 68.6750i 2.97464i
\(534\) 0 0
\(535\) 9.13746 29.7405i 0.395047 1.28579i
\(536\) 0 0
\(537\) 0.476171i 0.0205483i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.45017 −0.105341 −0.0526704 0.998612i \(-0.516773\pi\)
−0.0526704 + 0.998612i \(0.516773\pi\)
\(542\) 0 0
\(543\) 28.9687i 1.24317i
\(544\) 0 0
\(545\) −7.58762 2.33122i −0.325018 0.0998585i
\(546\) 0 0
\(547\) 36.1271i 1.54468i 0.635208 + 0.772341i \(0.280914\pi\)
−0.635208 + 0.772341i \(0.719086\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 14.0000 0.596420
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −20.7870 6.38658i −0.882357 0.271095i
\(556\) 0 0
\(557\) 5.61478i 0.237906i 0.992900 + 0.118953i \(0.0379538\pi\)
−0.992900 + 0.118953i \(0.962046\pi\)
\(558\) 0 0
\(559\) −39.6495 −1.67700
\(560\) 0 0
\(561\) 18.8248 0.794782
\(562\) 0 0
\(563\) 12.2394i 0.515831i −0.966167 0.257916i \(-0.916964\pi\)
0.966167 0.257916i \(-0.0830356\pi\)
\(564\) 0 0
\(565\) 8.54983 27.8279i 0.359694 1.17073i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 29.3746 1.23145 0.615723 0.787962i \(-0.288864\pi\)
0.615723 + 0.787962i \(0.288864\pi\)
\(570\) 0 0
\(571\) −0.274917 −0.0115049 −0.00575246 0.999983i \(-0.501831\pi\)
−0.00575246 + 0.999983i \(0.501831\pi\)
\(572\) 0 0
\(573\) 39.5336i 1.65154i
\(574\) 0 0
\(575\) 2.51204 3.70219i 0.104760 0.154392i
\(576\) 0 0
\(577\) 8.24163i 0.343103i −0.985175 0.171552i \(-0.945122\pi\)
0.985175 0.171552i \(-0.0548781\pi\)
\(578\) 0 0
\(579\) 15.9244 0.661796
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 16.8443i 0.697621i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.9715i 0.576665i −0.957530 0.288333i \(-0.906899\pi\)
0.957530 0.288333i \(-0.0931009\pi\)
\(588\) 0 0
\(589\) −18.2749 −0.753005
\(590\) 0 0
\(591\) 45.0997 1.85515
\(592\) 0 0
\(593\) 20.3084i 0.833968i −0.908914 0.416984i \(-0.863087\pi\)
0.908914 0.416984i \(-0.136913\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 16.8443i 0.689393i
\(598\) 0 0
\(599\) 2.27492 0.0929506 0.0464753 0.998919i \(-0.485201\pi\)
0.0464753 + 0.998919i \(0.485201\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −12.4502 3.82518i −0.506171 0.155516i
\(606\) 0 0
\(607\) 32.1868i 1.30642i −0.757176 0.653211i \(-0.773421\pi\)
0.757176 0.653211i \(-0.226579\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13.0997 −0.529956
\(612\) 0 0
\(613\) 37.0219i 1.49530i −0.664093 0.747650i \(-0.731182\pi\)
0.664093 0.747650i \(-0.268818\pi\)
\(614\) 0 0
\(615\) −12.8248 + 41.7419i −0.517144 + 1.68319i
\(616\) 0 0
\(617\) 3.57919i 0.144093i 0.997401 + 0.0720464i \(0.0229530\pi\)
−0.997401 + 0.0720464i \(0.977047\pi\)
\(618\) 0 0
\(619\) −43.9244 −1.76547 −0.882736 0.469870i \(-0.844301\pi\)
−0.882736 + 0.469870i \(0.844301\pi\)
\(620\) 0 0
\(621\) −4.64950 −0.186578
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.23713 + 23.2309i 0.369485 + 0.929237i
\(626\) 0 0
\(627\) 16.8443i 0.672698i
\(628\) 0 0
\(629\) 26.8248 1.06957
\(630\) 0 0
\(631\) 2.90033 0.115460 0.0577302 0.998332i \(-0.481614\pi\)
0.0577302 + 0.998332i \(0.481614\pi\)
\(632\) 0 0
\(633\) 34.0339i 1.35273i
\(634\) 0 0
\(635\) −1.17525 + 3.82518i −0.0466383 + 0.151798i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.0997 1.10987 0.554935 0.831894i \(-0.312743\pi\)
0.554935 + 0.831894i \(0.312743\pi\)
\(642\) 0 0
\(643\) 38.3353i 1.51180i −0.654689 0.755898i \(-0.727200\pi\)
0.654689 0.755898i \(-0.272800\pi\)
\(644\) 0 0
\(645\) 24.0997 + 7.40437i 0.948924 + 0.291547i
\(646\) 0 0
\(647\) 0.779710i 0.0306535i 0.999883 + 0.0153268i \(0.00487885\pi\)
−0.999883 + 0.0153268i \(0.995121\pi\)
\(648\) 0 0
\(649\) −9.72508 −0.381743
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 37.0219i 1.44878i 0.689392 + 0.724389i \(0.257878\pi\)
−0.689392 + 0.724389i \(0.742122\pi\)
\(654\) 0 0
\(655\) −39.0619 12.0014i −1.52627 0.468932i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 25.4502 0.991398 0.495699 0.868494i \(-0.334912\pi\)
0.495699 + 0.868494i \(0.334912\pi\)
\(660\) 0 0
\(661\) −15.5498 −0.604818 −0.302409 0.953178i \(-0.597791\pi\)
−0.302409 + 0.953178i \(0.597791\pi\)
\(662\) 0 0
\(663\) 50.4021i 1.95746i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2.93039i 0.113465i
\(668\) 0 0
\(669\) −15.0997 −0.583787
\(670\) 0 0
\(671\) 3.52575 0.136110
\(672\) 0 0
\(673\) 3.57919i 0.137968i −0.997618 0.0689838i \(-0.978024\pi\)
0.997618 0.0689838i \(-0.0219757\pi\)
\(674\) 0 0
\(675\) 14.5876 21.4989i 0.561478 0.827492i
\(676\) 0 0
\(677\) 24.6098i 0.945831i 0.881108 + 0.472916i \(0.156798\pi\)
−0.881108 + 0.472916i \(0.843202\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −11.1752 −0.428236
\(682\) 0 0
\(683\) 15.7035i 0.600879i 0.953801 + 0.300440i \(0.0971334\pi\)
−0.953801 + 0.300440i \(0.902867\pi\)
\(684\) 0 0
\(685\) −6.03779 + 19.6517i −0.230692 + 0.750854i
\(686\) 0 0
\(687\) 7.40437i 0.282494i
\(688\) 0 0
\(689\) 45.0997 1.71816
\(690\) 0 0
\(691\) −7.37459 −0.280542 −0.140271 0.990113i \(-0.544797\pi\)
−0.140271 + 0.990113i \(0.544797\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 36.5498 + 11.2296i 1.38641 + 0.425961i
\(696\) 0 0
\(697\) 53.8662i 2.04033i
\(698\) 0 0
\(699\) −32.2749 −1.22075
\(700\) 0 0
\(701\) −13.8248 −0.522154 −0.261077 0.965318i \(-0.584078\pi\)
−0.261077 + 0.965318i \(0.584078\pi\)
\(702\) 0 0
\(703\) 24.0027i 0.905280i
\(704\) 0 0
\(705\) 7.96221 + 2.44631i 0.299874 + 0.0921332i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 25.5498 0.959544 0.479772 0.877393i \(-0.340719\pi\)
0.479772 + 0.877393i \(0.340719\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.82518i 0.143254i
\(714\) 0 0
\(715\) −9.09967 + 29.6175i −0.340308 + 1.10763i
\(716\) 0 0
\(717\) 25.2011i 0.941151i
\(718\) 0 0
\(719\) −7.37459 −0.275026 −0.137513 0.990500i \(-0.543911\pi\)
−0.137513 + 0.990500i \(0.543911\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 22.2131i 0.826115i
\(724\) 0 0
\(725\) 13.5498 + 9.19397i 0.503228 + 0.341455i
\(726\) 0 0
\(727\) 18.6915i 0.693228i −0.938008 0.346614i \(-0.887331\pi\)
0.938008 0.346614i \(-0.112669\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −31.0997 −1.15026
\(732\) 0 0
\(733\) 33.3276i 1.23098i −0.788144 0.615491i \(-0.788958\pi\)
0.788144 0.615491i \(-0.211042\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.6531i 1.16596i
\(738\) 0 0
\(739\) −31.9244 −1.17436 −0.587179 0.809457i \(-0.699762\pi\)
−0.587179 + 0.809457i \(0.699762\pi\)
\(740\) 0 0
\(741\) 45.0997 1.65678
\(742\) 0 0
\(743\) 19.5287i 0.716440i 0.933637 + 0.358220i \(0.116616\pi\)
−0.933637 + 0.358220i \(0.883384\pi\)
\(744\) 0 0
\(745\) −16.1375 4.95807i −0.591231 0.181650i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −22.2749 −0.812823 −0.406412 0.913690i \(-0.633220\pi\)
−0.406412 + 0.913690i \(0.633220\pi\)
\(752\) 0 0
\(753\) 9.43996i 0.344011i
\(754\) 0 0
\(755\) −43.3368 13.3148i −1.57719 0.484575i
\(756\) 0 0
\(757\) 9.43996i 0.343101i 0.985175 + 0.171551i \(0.0548777\pi\)
−0.985175 + 0.171551i \(0.945122\pi\)
\(758\) 0 0
\(759\) −3.52575 −0.127976
\(760\) 0 0
\(761\) −29.9244 −1.08476 −0.542380 0.840133i \(-0.682477\pi\)
−0.542380 + 0.840133i \(0.682477\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.0383i 0.940189i
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −42.8248 −1.54230
\(772\) 0 0
\(773\) 27.2366i 0.979634i 0.871825 + 0.489817i \(0.162936\pi\)
−0.871825 + 0.489817i \(0.837064\pi\)
\(774\) 0 0
\(775\) −17.6873 12.0014i −0.635346 0.431102i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −48.1993 −1.72692
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) 0 0
\(783\) 17.0170i 0.608137i
\(784\) 0 0
\(785\) −7.13746 + 23.2309i −0.254747 + 0.829147i
\(786\) 0 0
\(787\) 1.73205i 0.0617409i −0.999523 0.0308705i \(-0.990172\pi\)
0.999523 0.0308705i \(-0.00982794\pi\)
\(788\) 0 0
\(789\) −46.6495 −1.66077
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 9.43996i 0.335223i
\(794\) 0 0
\(795\) −27.4124 8.42217i −0.972217 0.298704i
\(796\) 0 0
\(797\) 29.3873i 1.04095i −0.853876 0.520476i \(-0.825754\pi\)
0.853876 0.520476i \(-0.174246\pi\)
\(798\) 0 0
\(799\) −10.2749 −0.363500
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.89261i 0.172657i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 51.1818i 1.80169i
\(808\) 0 0
\(809\) −43.1993 −1.51881 −0.759404 0.650619i \(-0.774509\pi\)
−0.759404 + 0.650619i \(0.774509\pi\)
\(810\) 0 0
\(811\) 22.5498 0.791832 0.395916 0.918287i \(-0.370427\pi\)
0.395916 + 0.918287i \(0.370427\pi\)
\(812\) 0 0
\(813\) 22.2131i 0.779048i
\(814\) 0 0
\(815\) −4.86254 + 15.8265i −0.170327 + 0.554380i
\(816\) 0 0
\(817\) 27.8279i 0.973575i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 17.3746 0.606377 0.303189 0.952931i \(-0.401949\pi\)
0.303189 + 0.952931i \(0.401949\pi\)
\(822\) 0 0
\(823\) 32.3019i 1.12597i 0.826466 + 0.562987i \(0.190348\pi\)
−0.826466 + 0.562987i \(0.809652\pi\)
\(824\) 0 0
\(825\) 11.0619 16.3027i 0.385125 0.567588i
\(826\) 0 0
\(827\) 45.5670i 1.58452i −0.610183 0.792261i \(-0.708904\pi\)
0.610183 0.792261i \(-0.291096\pi\)
\(828\) 0 0
\(829\) −1.92442 −0.0668379 −0.0334189 0.999441i \(-0.510640\pi\)
−0.0334189 + 0.999441i \(0.510640\pi\)
\(830\) 0 0
\(831\) 32.2749 1.11960
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −8.27492 + 26.9331i −0.286365 + 0.932058i
\(836\) 0 0
\(837\) 22.2131i 0.767798i
\(838\) 0 0
\(839\) −10.9003 −0.376321 −0.188161 0.982138i \(-0.560253\pi\)
−0.188161 + 0.982138i \(0.560253\pi\)
\(840\) 0 0
\(841\) −18.2749 −0.630170
\(842\) 0 0
\(843\) 10.3923i 0.357930i
\(844\) 0 0
\(845\) −51.5120 15.8265i −1.77207 0.544450i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 33.9244 1.16428
\(850\) 0 0
\(851\) −5.02409 −0.172224
\(852\) 0 0
\(853\) 30.4547i 1.04275i 0.853327 + 0.521375i \(0.174581\pi\)
−0.853327 + 0.521375i \(0.825419\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 33.3276i 1.13845i 0.822182 + 0.569224i \(0.192756\pi\)
−0.822182 + 0.569224i \(0.807244\pi\)
\(858\) 0 0
\(859\) −35.3746 −1.20697 −0.603483 0.797376i \(-0.706221\pi\)
−0.603483 + 0.797376i \(0.706221\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 25.1435i 0.855895i 0.903804 + 0.427947i \(0.140763\pi\)
−0.903804 + 0.427947i \(0.859237\pi\)
\(864\) 0 0
\(865\) −12.3127 + 40.0753i −0.418645 + 1.36260i
\(866\) 0 0
\(867\) 10.0888i 0.342632i
\(868\) 0 0
\(869\) 0.625414 0.0212157
\(870\) 0 0
\(871\) 84.7492 2.87162
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 44.6722i 1.50847i −0.656602 0.754237i \(-0.728007\pi\)
0.656602 0.754237i \(-0.271993\pi\)
\(878\) 0 0
\(879\) −12.0000 −0.404750
\(880\) 0 0
\(881\) 40.0241 1.34845 0.674223 0.738528i \(-0.264479\pi\)
0.674223 + 0.738528i \(0.264479\pi\)
\(882\) 0 0
\(883\) 20.6695i 0.695585i −0.937572 0.347792i \(-0.886931\pi\)
0.937572 0.347792i \(-0.113069\pi\)
\(884\) 0 0
\(885\) −4.86254 + 15.8265i −0.163453 + 0.532003i
\(886\) 0 0
\(887\) 39.2301i 1.31722i 0.752486 + 0.658609i \(0.228855\pi\)
−0.752486 + 0.658609i \(0.771145\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −20.4743 −0.685913
\(892\) 0 0
\(893\) 9.19397i 0.307664i
\(894\) 0 0
\(895\) −0.587624 0.180541i −0.0196421 0.00603483i
\(896\) 0 0
\(897\) 9.43996i 0.315191i
\(898\) 0 0
\(899\) −14.0000 −0.466926
\(900\) 0 0
\(901\) 35.3746 1.17850
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −35.7492 10.9836i −1.18834 0.365106i
\(906\) 0 0
\(907\) 45.3210i 1.50486i 0.658672 + 0.752430i \(0.271119\pi\)
−0.658672 + 0.752430i \(0.728881\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 5.09967 0.168960 0.0844798 0.996425i \(-0.473077\pi\)
0.0844798 + 0.996425i \(0.473077\pi\)
\(912\) 0 0
\(913\) 12.9041i 0.427062i
\(914\) 0 0
\(915\) 1.76287 5.73778i 0.0582788 0.189685i
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −5.92442 −0.195429 −0.0977143 0.995215i \(-0.531153\pi\)
−0.0977143 + 0.995215i \(0.531153\pi\)
\(920\) 0 0
\(921\) −6.92442 −0.228167
\(922\) 0 0
\(923\) 64.2585i 2.11509i
\(924\) 0 0
\(925\) 15.7629 23.2309i 0.518280 0.763828i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 17.9003 0.587291 0.293645 0.955914i \(-0.405132\pi\)
0.293645 + 0.955914i \(0.405132\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 22.2131i 0.727225i
\(934\) 0 0
\(935\) −7.13746 + 23.2309i −0.233420 + 0.759732i
\(936\) 0 0
\(937\) 10.5074i 0.343262i −0.985161 0.171631i \(-0.945096\pi\)
0.985161 0.171631i \(-0.0549036\pi\)
\(938\) 0 0
\(939\) −25.0241 −0.816630
\(940\) 0 0
\(941\) 4.27492 0.139358 0.0696792 0.997569i \(-0.477802\pi\)
0.0696792 + 0.997569i \(0.477802\pi\)
\(942\) 0 0
\(943\) 10.0888i 0.328535i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 41.7419i 1.35643i 0.734865 + 0.678214i \(0.237246\pi\)
−0.734865 + 0.678214i \(0.762754\pi\)
\(948\) 0 0
\(949\) 13.0997 0.425233
\(950\) 0 0
\(951\) 6.62541 0.214844
\(952\) 0 0
\(953\) 29.6175i 0.959405i 0.877431 + 0.479702i \(0.159255\pi\)
−0.877431 + 0.479702i \(0.840745\pi\)
\(954\) 0 0
\(955\) 48.7870 + 14.9893i 1.57871 + 0.485042i
\(956\) 0 0
\(957\) 12.9041i 0.417129i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −12.7251 −0.410487
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −6.03779 + 19.6517i −0.194363 + 0.632611i
\(966\) 0 0
\(967\) 6.50958i 0.209334i −0.994507 0.104667i \(-0.966622\pi\)
0.994507 0.104667i \(-0.0333777\pi\)
\(968\) 0 0
\(969\) 35.3746 1.13640
\(970\) 0 0
\(971\) 15.9244 0.511039 0.255519 0.966804i \(-0.417754\pi\)
0.255519 + 0.966804i \(0.417754\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 43.6495 + 29.6175i 1.39790 + 0.948519i
\(976\) 0 0
\(977\) 16.8443i 0.538898i −0.963015 0.269449i \(-0.913158\pi\)
0.963015 0.269449i \(-0.0868416\pi\)
\(978\) 0 0
\(979\) 15.9244 0.508947
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 37.2103i 1.18682i −0.804899 0.593412i \(-0.797780\pi\)
0.804899 0.593412i \(-0.202220\pi\)
\(984\) 0 0
\(985\) −17.0997 + 55.6558i −0.544841 + 1.77334i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 5.82475 0.185216
\(990\) 0 0
\(991\) −34.4743 −1.09511 −0.547555 0.836769i \(-0.684441\pi\)
−0.547555 + 0.836769i \(0.684441\pi\)
\(992\) 0 0
\(993\) 8.35671i 0.265192i
\(994\) 0 0
\(995\) −20.7870 6.38658i −0.658991 0.202468i
\(996\) 0 0
\(997\) 4.77753i 0.151306i 0.997134 + 0.0756529i \(0.0241041\pi\)
−0.997134 + 0.0756529i \(0.975896\pi\)
\(998\) 0 0
\(999\) −29.1752 −0.923064
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 980.2.e.f.589.2 4
5.2 odd 4 4900.2.a.be.1.2 4
5.3 odd 4 4900.2.a.be.1.4 4
5.4 even 2 inner 980.2.e.f.589.4 4
7.2 even 3 140.2.q.b.109.1 yes 4
7.3 odd 6 980.2.q.g.569.2 4
7.4 even 3 140.2.q.a.9.1 4
7.5 odd 6 980.2.q.b.949.2 4
7.6 odd 2 980.2.e.c.589.3 4
21.2 odd 6 1260.2.bm.b.109.2 4
21.11 odd 6 1260.2.bm.a.289.2 4
28.11 odd 6 560.2.bw.e.289.1 4
28.23 odd 6 560.2.bw.a.529.1 4
35.2 odd 12 700.2.i.f.501.4 8
35.4 even 6 140.2.q.b.9.2 yes 4
35.9 even 6 140.2.q.a.109.1 yes 4
35.13 even 4 4900.2.a.bf.1.2 4
35.18 odd 12 700.2.i.f.401.1 8
35.19 odd 6 980.2.q.g.949.2 4
35.23 odd 12 700.2.i.f.501.1 8
35.24 odd 6 980.2.q.b.569.1 4
35.27 even 4 4900.2.a.bf.1.4 4
35.32 odd 12 700.2.i.f.401.4 8
35.34 odd 2 980.2.e.c.589.1 4
105.44 odd 6 1260.2.bm.a.109.2 4
105.74 odd 6 1260.2.bm.b.289.1 4
140.39 odd 6 560.2.bw.a.289.2 4
140.79 odd 6 560.2.bw.e.529.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.q.a.9.1 4 7.4 even 3
140.2.q.a.109.1 yes 4 35.9 even 6
140.2.q.b.9.2 yes 4 35.4 even 6
140.2.q.b.109.1 yes 4 7.2 even 3
560.2.bw.a.289.2 4 140.39 odd 6
560.2.bw.a.529.1 4 28.23 odd 6
560.2.bw.e.289.1 4 28.11 odd 6
560.2.bw.e.529.1 4 140.79 odd 6
700.2.i.f.401.1 8 35.18 odd 12
700.2.i.f.401.4 8 35.32 odd 12
700.2.i.f.501.1 8 35.23 odd 12
700.2.i.f.501.4 8 35.2 odd 12
980.2.e.c.589.1 4 35.34 odd 2
980.2.e.c.589.3 4 7.6 odd 2
980.2.e.f.589.2 4 1.1 even 1 trivial
980.2.e.f.589.4 4 5.4 even 2 inner
980.2.q.b.569.1 4 35.24 odd 6
980.2.q.b.949.2 4 7.5 odd 6
980.2.q.g.569.2 4 7.3 odd 6
980.2.q.g.949.2 4 35.19 odd 6
1260.2.bm.a.109.2 4 105.44 odd 6
1260.2.bm.a.289.2 4 21.11 odd 6
1260.2.bm.b.109.2 4 21.2 odd 6
1260.2.bm.b.289.1 4 105.74 odd 6
4900.2.a.be.1.2 4 5.2 odd 4
4900.2.a.be.1.4 4 5.3 odd 4
4900.2.a.bf.1.2 4 35.13 even 4
4900.2.a.bf.1.4 4 35.27 even 4