Properties

Label 280.2.x.a.97.7
Level $280$
Weight $2$
Character 280.97
Analytic conductor $2.236$
Analytic rank $0$
Dimension $24$
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] = [280,2,Mod(97,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.x (of order \(4\), degree \(2\), 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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.7
Character \(\chi\) \(=\) 280.97
Dual form 280.2.x.a.153.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0703127 + 0.0703127i) q^{3} +(2.16104 + 0.574360i) q^{5} +(-0.562657 - 2.58523i) q^{7} -2.99011i q^{9} +O(q^{10})\) \(q+(0.0703127 + 0.0703127i) q^{3} +(2.16104 + 0.574360i) q^{5} +(-0.562657 - 2.58523i) q^{7} -2.99011i q^{9} +0.777018 q^{11} +(3.93876 + 3.93876i) q^{13} +(0.111564 + 0.192334i) q^{15} +(-0.982018 + 0.982018i) q^{17} +1.14872 q^{19} +(0.142213 - 0.221337i) q^{21} +(-1.46167 + 1.46167i) q^{23} +(4.34022 + 2.48243i) q^{25} +(0.421181 - 0.421181i) q^{27} -4.69033i q^{29} -6.45186i q^{31} +(0.0546342 + 0.0546342i) q^{33} +(0.268926 - 5.90996i) q^{35} +(-1.30390 - 1.30390i) q^{37} +0.553890i q^{39} +9.81800i q^{41} +(-7.13800 + 7.13800i) q^{43} +(1.71740 - 6.46176i) q^{45} +(-7.34914 + 7.34914i) q^{47} +(-6.36683 + 2.90920i) q^{49} -0.138097 q^{51} +(-2.08092 + 2.08092i) q^{53} +(1.67917 + 0.446288i) q^{55} +(0.0807696 + 0.0807696i) q^{57} -8.29508 q^{59} -5.88837i q^{61} +(-7.73013 + 1.68241i) q^{63} +(6.24956 + 10.7741i) q^{65} +(-6.30957 - 6.30957i) q^{67} -0.205548 q^{69} +12.3373 q^{71} +(-7.23861 - 7.23861i) q^{73} +(0.130626 + 0.479719i) q^{75} +(-0.437195 - 2.00877i) q^{77} -2.83831i q^{79} -8.91111 q^{81} +(10.4188 + 10.4188i) q^{83} +(-2.68621 + 1.55815i) q^{85} +(0.329790 - 0.329790i) q^{87} -3.41911 q^{89} +(7.96643 - 12.3988i) q^{91} +(0.453647 - 0.453647i) q^{93} +(2.48243 + 0.659779i) q^{95} +(-8.50258 + 8.50258i) q^{97} -2.32337i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{7} + 8 q^{11} - 8 q^{15} + 16 q^{21} - 32 q^{23} + 8 q^{25} + 12 q^{35} - 8 q^{37} + 16 q^{43} - 24 q^{51} - 16 q^{53} + 20 q^{63} - 48 q^{65} - 32 q^{67} - 32 q^{71} - 40 q^{77} - 72 q^{81} + 16 q^{85} - 64 q^{91} + 72 q^{93} - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(-1\)

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
\(3\) 0.0703127 + 0.0703127i 0.0405951 + 0.0405951i 0.727113 0.686518i \(-0.240862\pi\)
−0.686518 + 0.727113i \(0.740862\pi\)
\(4\) 0 0
\(5\) 2.16104 + 0.574360i 0.966448 + 0.256862i
\(6\) 0 0
\(7\) −0.562657 2.58523i −0.212664 0.977125i
\(8\) 0 0
\(9\) 2.99011i 0.996704i
\(10\) 0 0
\(11\) 0.777018 0.234280 0.117140 0.993115i \(-0.462627\pi\)
0.117140 + 0.993115i \(0.462627\pi\)
\(12\) 0 0
\(13\) 3.93876 + 3.93876i 1.09241 + 1.09241i 0.995270 + 0.0971446i \(0.0309709\pi\)
0.0971446 + 0.995270i \(0.469029\pi\)
\(14\) 0 0
\(15\) 0.111564 + 0.192334i 0.0288057 + 0.0496603i
\(16\) 0 0
\(17\) −0.982018 + 0.982018i −0.238174 + 0.238174i −0.816094 0.577920i \(-0.803865\pi\)
0.577920 + 0.816094i \(0.303865\pi\)
\(18\) 0 0
\(19\) 1.14872 0.263534 0.131767 0.991281i \(-0.457935\pi\)
0.131767 + 0.991281i \(0.457935\pi\)
\(20\) 0 0
\(21\) 0.142213 0.221337i 0.0310333 0.0482996i
\(22\) 0 0
\(23\) −1.46167 + 1.46167i −0.304780 + 0.304780i −0.842881 0.538101i \(-0.819142\pi\)
0.538101 + 0.842881i \(0.319142\pi\)
\(24\) 0 0
\(25\) 4.34022 + 2.48243i 0.868044 + 0.496487i
\(26\) 0 0
\(27\) 0.421181 0.421181i 0.0810563 0.0810563i
\(28\) 0 0
\(29\) 4.69033i 0.870973i −0.900195 0.435486i \(-0.856576\pi\)
0.900195 0.435486i \(-0.143424\pi\)
\(30\) 0 0
\(31\) 6.45186i 1.15879i −0.815048 0.579394i \(-0.803289\pi\)
0.815048 0.579394i \(-0.196711\pi\)
\(32\) 0 0
\(33\) 0.0546342 + 0.0546342i 0.00951060 + 0.00951060i
\(34\) 0 0
\(35\) 0.268926 5.90996i 0.0454568 0.998966i
\(36\) 0 0
\(37\) −1.30390 1.30390i −0.214359 0.214359i 0.591757 0.806116i \(-0.298435\pi\)
−0.806116 + 0.591757i \(0.798435\pi\)
\(38\) 0 0
\(39\) 0.553890i 0.0886933i
\(40\) 0 0
\(41\) 9.81800i 1.53331i 0.642057 + 0.766657i \(0.278081\pi\)
−0.642057 + 0.766657i \(0.721919\pi\)
\(42\) 0 0
\(43\) −7.13800 + 7.13800i −1.08853 + 1.08853i −0.0928552 + 0.995680i \(0.529599\pi\)
−0.995680 + 0.0928552i \(0.970401\pi\)
\(44\) 0 0
\(45\) 1.71740 6.46176i 0.256015 0.963263i
\(46\) 0 0
\(47\) −7.34914 + 7.34914i −1.07198 + 1.07198i −0.0747825 + 0.997200i \(0.523826\pi\)
−0.997200 + 0.0747825i \(0.976174\pi\)
\(48\) 0 0
\(49\) −6.36683 + 2.90920i −0.909548 + 0.415600i
\(50\) 0 0
\(51\) −0.138097 −0.0193374
\(52\) 0 0
\(53\) −2.08092 + 2.08092i −0.285836 + 0.285836i −0.835431 0.549595i \(-0.814782\pi\)
0.549595 + 0.835431i \(0.314782\pi\)
\(54\) 0 0
\(55\) 1.67917 + 0.446288i 0.226419 + 0.0601774i
\(56\) 0 0
\(57\) 0.0807696 + 0.0807696i 0.0106982 + 0.0106982i
\(58\) 0 0
\(59\) −8.29508 −1.07993 −0.539964 0.841688i \(-0.681562\pi\)
−0.539964 + 0.841688i \(0.681562\pi\)
\(60\) 0 0
\(61\) 5.88837i 0.753929i −0.926228 0.376965i \(-0.876968\pi\)
0.926228 0.376965i \(-0.123032\pi\)
\(62\) 0 0
\(63\) −7.73013 + 1.68241i −0.973905 + 0.211963i
\(64\) 0 0
\(65\) 6.24956 + 10.7741i 0.775163 + 1.33636i
\(66\) 0 0
\(67\) −6.30957 6.30957i −0.770837 0.770837i 0.207416 0.978253i \(-0.433495\pi\)
−0.978253 + 0.207416i \(0.933495\pi\)
\(68\) 0 0
\(69\) −0.205548 −0.0247451
\(70\) 0 0
\(71\) 12.3373 1.46417 0.732084 0.681214i \(-0.238548\pi\)
0.732084 + 0.681214i \(0.238548\pi\)
\(72\) 0 0
\(73\) −7.23861 7.23861i −0.847216 0.847216i 0.142569 0.989785i \(-0.454464\pi\)
−0.989785 + 0.142569i \(0.954464\pi\)
\(74\) 0 0
\(75\) 0.130626 + 0.479719i 0.0150834 + 0.0553932i
\(76\) 0 0
\(77\) −0.437195 2.00877i −0.0498229 0.228921i
\(78\) 0 0
\(79\) 2.83831i 0.319335i −0.987171 0.159668i \(-0.948958\pi\)
0.987171 0.159668i \(-0.0510423\pi\)
\(80\) 0 0
\(81\) −8.91111 −0.990123
\(82\) 0 0
\(83\) 10.4188 + 10.4188i 1.14361 + 1.14361i 0.987785 + 0.155823i \(0.0498029\pi\)
0.155823 + 0.987785i \(0.450197\pi\)
\(84\) 0 0
\(85\) −2.68621 + 1.55815i −0.291361 + 0.169005i
\(86\) 0 0
\(87\) 0.329790 0.329790i 0.0353572 0.0353572i
\(88\) 0 0
\(89\) −3.41911 −0.362425 −0.181213 0.983444i \(-0.558002\pi\)
−0.181213 + 0.983444i \(0.558002\pi\)
\(90\) 0 0
\(91\) 7.96643 12.3988i 0.835108 1.29974i
\(92\) 0 0
\(93\) 0.453647 0.453647i 0.0470411 0.0470411i
\(94\) 0 0
\(95\) 2.48243 + 0.659779i 0.254692 + 0.0676919i
\(96\) 0 0
\(97\) −8.50258 + 8.50258i −0.863306 + 0.863306i −0.991721 0.128414i \(-0.959011\pi\)
0.128414 + 0.991721i \(0.459011\pi\)
\(98\) 0 0
\(99\) 2.32337i 0.233507i
\(100\) 0 0
\(101\) 4.88126i 0.485703i −0.970063 0.242852i \(-0.921917\pi\)
0.970063 0.242852i \(-0.0780828\pi\)
\(102\) 0 0
\(103\) 10.0443 + 10.0443i 0.989697 + 0.989697i 0.999947 0.0102503i \(-0.00326282\pi\)
−0.0102503 + 0.999947i \(0.503263\pi\)
\(104\) 0 0
\(105\) 0.434455 0.396637i 0.0423984 0.0387078i
\(106\) 0 0
\(107\) 5.67065 + 5.67065i 0.548203 + 0.548203i 0.925921 0.377718i \(-0.123291\pi\)
−0.377718 + 0.925921i \(0.623291\pi\)
\(108\) 0 0
\(109\) 11.9012i 1.13993i −0.821669 0.569965i \(-0.806957\pi\)
0.821669 0.569965i \(-0.193043\pi\)
\(110\) 0 0
\(111\) 0.183361i 0.0174039i
\(112\) 0 0
\(113\) −1.36519 + 1.36519i −0.128427 + 0.128427i −0.768398 0.639972i \(-0.778946\pi\)
0.639972 + 0.768398i \(0.278946\pi\)
\(114\) 0 0
\(115\) −3.99827 + 2.31921i −0.372840 + 0.216268i
\(116\) 0 0
\(117\) 11.7773 11.7773i 1.08881 1.08881i
\(118\) 0 0
\(119\) 3.09128 + 1.98620i 0.283377 + 0.182075i
\(120\) 0 0
\(121\) −10.3962 −0.945113
\(122\) 0 0
\(123\) −0.690330 + 0.690330i −0.0622450 + 0.0622450i
\(124\) 0 0
\(125\) 7.95360 + 7.85750i 0.711391 + 0.702796i
\(126\) 0 0
\(127\) −9.49331 9.49331i −0.842395 0.842395i 0.146775 0.989170i \(-0.453111\pi\)
−0.989170 + 0.146775i \(0.953111\pi\)
\(128\) 0 0
\(129\) −1.00378 −0.0883783
\(130\) 0 0
\(131\) 19.4938i 1.70318i 0.524206 + 0.851592i \(0.324362\pi\)
−0.524206 + 0.851592i \(0.675638\pi\)
\(132\) 0 0
\(133\) −0.646335 2.96971i −0.0560444 0.257506i
\(134\) 0 0
\(135\) 1.15210 0.668281i 0.0991570 0.0575165i
\(136\) 0 0
\(137\) 5.77702 + 5.77702i 0.493564 + 0.493564i 0.909427 0.415863i \(-0.136521\pi\)
−0.415863 + 0.909427i \(0.636521\pi\)
\(138\) 0 0
\(139\) 15.2115 1.29023 0.645113 0.764087i \(-0.276810\pi\)
0.645113 + 0.764087i \(0.276810\pi\)
\(140\) 0 0
\(141\) −1.03348 −0.0870344
\(142\) 0 0
\(143\) 3.06048 + 3.06048i 0.255931 + 0.255931i
\(144\) 0 0
\(145\) 2.69394 10.1360i 0.223719 0.841750i
\(146\) 0 0
\(147\) −0.652223 0.243116i −0.0537944 0.0200519i
\(148\) 0 0
\(149\) 16.5328i 1.35442i −0.735789 0.677211i \(-0.763188\pi\)
0.735789 0.677211i \(-0.236812\pi\)
\(150\) 0 0
\(151\) 12.4421 1.01252 0.506262 0.862380i \(-0.331027\pi\)
0.506262 + 0.862380i \(0.331027\pi\)
\(152\) 0 0
\(153\) 2.93634 + 2.93634i 0.237389 + 0.237389i
\(154\) 0 0
\(155\) 3.70569 13.9427i 0.297648 1.11991i
\(156\) 0 0
\(157\) 6.24218 6.24218i 0.498180 0.498180i −0.412691 0.910871i \(-0.635411\pi\)
0.910871 + 0.412691i \(0.135411\pi\)
\(158\) 0 0
\(159\) −0.292630 −0.0232070
\(160\) 0 0
\(161\) 4.60118 + 2.95634i 0.362624 + 0.232992i
\(162\) 0 0
\(163\) 9.47383 9.47383i 0.742048 0.742048i −0.230924 0.972972i \(-0.574175\pi\)
0.972972 + 0.230924i \(0.0741748\pi\)
\(164\) 0 0
\(165\) 0.0866873 + 0.149447i 0.00674859 + 0.0116344i
\(166\) 0 0
\(167\) 0.725303 0.725303i 0.0561257 0.0561257i −0.678487 0.734613i \(-0.737364\pi\)
0.734613 + 0.678487i \(0.237364\pi\)
\(168\) 0 0
\(169\) 18.0276i 1.38674i
\(170\) 0 0
\(171\) 3.43480i 0.262666i
\(172\) 0 0
\(173\) −3.12344 3.12344i −0.237471 0.237471i 0.578331 0.815802i \(-0.303704\pi\)
−0.815802 + 0.578331i \(0.803704\pi\)
\(174\) 0 0
\(175\) 3.97561 12.6172i 0.300528 0.953773i
\(176\) 0 0
\(177\) −0.583250 0.583250i −0.0438397 0.0438397i
\(178\) 0 0
\(179\) 9.18800i 0.686743i 0.939200 + 0.343372i \(0.111569\pi\)
−0.939200 + 0.343372i \(0.888431\pi\)
\(180\) 0 0
\(181\) 9.51164i 0.706995i 0.935435 + 0.353497i \(0.115008\pi\)
−0.935435 + 0.353497i \(0.884992\pi\)
\(182\) 0 0
\(183\) 0.414028 0.414028i 0.0306058 0.0306058i
\(184\) 0 0
\(185\) −2.06887 3.56669i −0.152107 0.262228i
\(186\) 0 0
\(187\) −0.763045 + 0.763045i −0.0557994 + 0.0557994i
\(188\) 0 0
\(189\) −1.32583 0.851870i −0.0964400 0.0619644i
\(190\) 0 0
\(191\) −21.2171 −1.53522 −0.767609 0.640918i \(-0.778554\pi\)
−0.767609 + 0.640918i \(0.778554\pi\)
\(192\) 0 0
\(193\) 5.15371 5.15371i 0.370972 0.370972i −0.496859 0.867831i \(-0.665513\pi\)
0.867831 + 0.496859i \(0.165513\pi\)
\(194\) 0 0
\(195\) −0.318132 + 1.19698i −0.0227819 + 0.0857175i
\(196\) 0 0
\(197\) 3.83269 + 3.83269i 0.273068 + 0.273068i 0.830334 0.557266i \(-0.188150\pi\)
−0.557266 + 0.830334i \(0.688150\pi\)
\(198\) 0 0
\(199\) 13.4648 0.954496 0.477248 0.878769i \(-0.341634\pi\)
0.477248 + 0.878769i \(0.341634\pi\)
\(200\) 0 0
\(201\) 0.887286i 0.0625844i
\(202\) 0 0
\(203\) −12.1256 + 2.63905i −0.851049 + 0.185225i
\(204\) 0 0
\(205\) −5.63907 + 21.2171i −0.393850 + 1.48187i
\(206\) 0 0
\(207\) 4.37057 + 4.37057i 0.303775 + 0.303775i
\(208\) 0 0
\(209\) 0.892576 0.0617408
\(210\) 0 0
\(211\) 8.11050 0.558350 0.279175 0.960240i \(-0.409939\pi\)
0.279175 + 0.960240i \(0.409939\pi\)
\(212\) 0 0
\(213\) 0.867469 + 0.867469i 0.0594380 + 0.0594380i
\(214\) 0 0
\(215\) −19.5253 + 11.3257i −1.33162 + 0.772410i
\(216\) 0 0
\(217\) −16.6795 + 3.63018i −1.13228 + 0.246433i
\(218\) 0 0
\(219\) 1.01793i 0.0687855i
\(220\) 0 0
\(221\) −7.73586 −0.520370
\(222\) 0 0
\(223\) −18.5407 18.5407i −1.24157 1.24157i −0.959348 0.282226i \(-0.908927\pi\)
−0.282226 0.959348i \(-0.591073\pi\)
\(224\) 0 0
\(225\) 7.42276 12.9777i 0.494850 0.865183i
\(226\) 0 0
\(227\) −4.84230 + 4.84230i −0.321395 + 0.321395i −0.849302 0.527907i \(-0.822977\pi\)
0.527907 + 0.849302i \(0.322977\pi\)
\(228\) 0 0
\(229\) 4.14288 0.273769 0.136884 0.990587i \(-0.456291\pi\)
0.136884 + 0.990587i \(0.456291\pi\)
\(230\) 0 0
\(231\) 0.110502 0.171982i 0.00727048 0.0113156i
\(232\) 0 0
\(233\) 17.7734 17.7734i 1.16437 1.16437i 0.180864 0.983508i \(-0.442110\pi\)
0.983508 0.180864i \(-0.0578895\pi\)
\(234\) 0 0
\(235\) −20.1029 + 11.6608i −1.31137 + 0.760664i
\(236\) 0 0
\(237\) 0.199570 0.199570i 0.0129634 0.0129634i
\(238\) 0 0
\(239\) 24.8714i 1.60880i 0.594090 + 0.804399i \(0.297512\pi\)
−0.594090 + 0.804399i \(0.702488\pi\)
\(240\) 0 0
\(241\) 5.11385i 0.329412i 0.986343 + 0.164706i \(0.0526676\pi\)
−0.986343 + 0.164706i \(0.947332\pi\)
\(242\) 0 0
\(243\) −1.89011 1.89011i −0.121250 0.121250i
\(244\) 0 0
\(245\) −15.4299 + 2.63005i −0.985782 + 0.168028i
\(246\) 0 0
\(247\) 4.52453 + 4.52453i 0.287889 + 0.287889i
\(248\) 0 0
\(249\) 1.46514i 0.0928497i
\(250\) 0 0
\(251\) 21.4745i 1.35546i −0.735311 0.677729i \(-0.762964\pi\)
0.735311 0.677729i \(-0.237036\pi\)
\(252\) 0 0
\(253\) −1.13575 + 1.13575i −0.0714037 + 0.0714037i
\(254\) 0 0
\(255\) −0.298433 0.0793172i −0.0186886 0.00496703i
\(256\) 0 0
\(257\) 2.08456 2.08456i 0.130031 0.130031i −0.639096 0.769127i \(-0.720691\pi\)
0.769127 + 0.639096i \(0.220691\pi\)
\(258\) 0 0
\(259\) −2.63723 + 4.10452i −0.163869 + 0.255043i
\(260\) 0 0
\(261\) −14.0246 −0.868102
\(262\) 0 0
\(263\) 6.37087 6.37087i 0.392845 0.392845i −0.482855 0.875700i \(-0.660400\pi\)
0.875700 + 0.482855i \(0.160400\pi\)
\(264\) 0 0
\(265\) −5.69214 + 3.30176i −0.349666 + 0.202825i
\(266\) 0 0
\(267\) −0.240407 0.240407i −0.0147127 0.0147127i
\(268\) 0 0
\(269\) −9.57242 −0.583641 −0.291820 0.956473i \(-0.594261\pi\)
−0.291820 + 0.956473i \(0.594261\pi\)
\(270\) 0 0
\(271\) 12.1076i 0.735486i −0.929927 0.367743i \(-0.880131\pi\)
0.929927 0.367743i \(-0.119869\pi\)
\(272\) 0 0
\(273\) 1.43193 0.311650i 0.0866645 0.0188619i
\(274\) 0 0
\(275\) 3.37243 + 1.92890i 0.203365 + 0.116317i
\(276\) 0 0
\(277\) 16.2663 + 16.2663i 0.977345 + 0.977345i 0.999749 0.0224036i \(-0.00713189\pi\)
−0.0224036 + 0.999749i \(0.507132\pi\)
\(278\) 0 0
\(279\) −19.2918 −1.15497
\(280\) 0 0
\(281\) −0.910882 −0.0543387 −0.0271693 0.999631i \(-0.508649\pi\)
−0.0271693 + 0.999631i \(0.508649\pi\)
\(282\) 0 0
\(283\) −12.5625 12.5625i −0.746766 0.746766i 0.227105 0.973870i \(-0.427074\pi\)
−0.973870 + 0.227105i \(0.927074\pi\)
\(284\) 0 0
\(285\) 0.128156 + 0.220938i 0.00759130 + 0.0130872i
\(286\) 0 0
\(287\) 25.3818 5.52417i 1.49824 0.326081i
\(288\) 0 0
\(289\) 15.0713i 0.886546i
\(290\) 0 0
\(291\) −1.19568 −0.0700920
\(292\) 0 0
\(293\) −6.48178 6.48178i −0.378670 0.378670i 0.491952 0.870622i \(-0.336283\pi\)
−0.870622 + 0.491952i \(0.836283\pi\)
\(294\) 0 0
\(295\) −17.9260 4.76436i −1.04369 0.277392i
\(296\) 0 0
\(297\) 0.327265 0.327265i 0.0189899 0.0189899i
\(298\) 0 0
\(299\) −11.5144 −0.665892
\(300\) 0 0
\(301\) 22.4696 + 14.4371i 1.29513 + 0.832142i
\(302\) 0 0
\(303\) 0.343215 0.343215i 0.0197172 0.0197172i
\(304\) 0 0
\(305\) 3.38205 12.7250i 0.193655 0.728633i
\(306\) 0 0
\(307\) 8.48970 8.48970i 0.484533 0.484533i −0.422043 0.906576i \(-0.638687\pi\)
0.906576 + 0.422043i \(0.138687\pi\)
\(308\) 0 0
\(309\) 1.41249i 0.0803537i
\(310\) 0 0
\(311\) 25.9749i 1.47290i 0.676490 + 0.736452i \(0.263500\pi\)
−0.676490 + 0.736452i \(0.736500\pi\)
\(312\) 0 0
\(313\) −12.3142 12.3142i −0.696037 0.696037i 0.267516 0.963553i \(-0.413797\pi\)
−0.963553 + 0.267516i \(0.913797\pi\)
\(314\) 0 0
\(315\) −17.6715 0.804119i −0.995674 0.0453070i
\(316\) 0 0
\(317\) 14.4909 + 14.4909i 0.813888 + 0.813888i 0.985214 0.171327i \(-0.0548053\pi\)
−0.171327 + 0.985214i \(0.554805\pi\)
\(318\) 0 0
\(319\) 3.64447i 0.204051i
\(320\) 0 0
\(321\) 0.797438i 0.0445086i
\(322\) 0 0
\(323\) −1.12806 + 1.12806i −0.0627671 + 0.0627671i
\(324\) 0 0
\(325\) 7.31737 + 26.8728i 0.405895 + 1.49063i
\(326\) 0 0
\(327\) 0.836807 0.836807i 0.0462755 0.0462755i
\(328\) 0 0
\(329\) 23.1343 + 14.8642i 1.27543 + 0.819489i
\(330\) 0 0
\(331\) −27.4165 −1.50695 −0.753474 0.657477i \(-0.771624\pi\)
−0.753474 + 0.657477i \(0.771624\pi\)
\(332\) 0 0
\(333\) −3.89880 + 3.89880i −0.213653 + 0.213653i
\(334\) 0 0
\(335\) −10.0113 17.2592i −0.546976 0.942972i
\(336\) 0 0
\(337\) −11.1698 11.1698i −0.608460 0.608460i 0.334084 0.942543i \(-0.391573\pi\)
−0.942543 + 0.334084i \(0.891573\pi\)
\(338\) 0 0
\(339\) −0.191981 −0.0104270
\(340\) 0 0
\(341\) 5.01321i 0.271480i
\(342\) 0 0
\(343\) 11.1033 + 14.8229i 0.599521 + 0.800359i
\(344\) 0 0
\(345\) −0.444199 0.118059i −0.0239149 0.00635607i
\(346\) 0 0
\(347\) −11.4376 11.4376i −0.614004 0.614004i 0.329983 0.943987i \(-0.392957\pi\)
−0.943987 + 0.329983i \(0.892957\pi\)
\(348\) 0 0
\(349\) −17.1401 −0.917487 −0.458744 0.888569i \(-0.651700\pi\)
−0.458744 + 0.888569i \(0.651700\pi\)
\(350\) 0 0
\(351\) 3.31786 0.177094
\(352\) 0 0
\(353\) 11.1570 + 11.1570i 0.593826 + 0.593826i 0.938663 0.344837i \(-0.112066\pi\)
−0.344837 + 0.938663i \(0.612066\pi\)
\(354\) 0 0
\(355\) 26.6614 + 7.08605i 1.41504 + 0.376088i
\(356\) 0 0
\(357\) 0.0777011 + 0.357012i 0.00411238 + 0.0188951i
\(358\) 0 0
\(359\) 20.9982i 1.10824i −0.832437 0.554120i \(-0.813055\pi\)
0.832437 0.554120i \(-0.186945\pi\)
\(360\) 0 0
\(361\) −17.6804 −0.930550
\(362\) 0 0
\(363\) −0.730988 0.730988i −0.0383669 0.0383669i
\(364\) 0 0
\(365\) −11.4854 19.8005i −0.601173 1.03641i
\(366\) 0 0
\(367\) −2.32101 + 2.32101i −0.121156 + 0.121156i −0.765085 0.643929i \(-0.777303\pi\)
0.643929 + 0.765085i \(0.277303\pi\)
\(368\) 0 0
\(369\) 29.3569 1.52826
\(370\) 0 0
\(371\) 6.55049 + 4.20880i 0.340084 + 0.218510i
\(372\) 0 0
\(373\) 25.8674 25.8674i 1.33937 1.33937i 0.442691 0.896674i \(-0.354024\pi\)
0.896674 0.442691i \(-0.145976\pi\)
\(374\) 0 0
\(375\) 0.00675707 + 1.11172i 0.000348933 + 0.0574090i
\(376\) 0 0
\(377\) 18.4741 18.4741i 0.951463 0.951463i
\(378\) 0 0
\(379\) 13.1682i 0.676406i 0.941073 + 0.338203i \(0.109819\pi\)
−0.941073 + 0.338203i \(0.890181\pi\)
\(380\) 0 0
\(381\) 1.33500i 0.0683942i
\(382\) 0 0
\(383\) −13.7289 13.7289i −0.701514 0.701514i 0.263221 0.964736i \(-0.415215\pi\)
−0.964736 + 0.263221i \(0.915215\pi\)
\(384\) 0 0
\(385\) 0.208960 4.59215i 0.0106496 0.234037i
\(386\) 0 0
\(387\) 21.3434 + 21.3434i 1.08495 + 1.08495i
\(388\) 0 0
\(389\) 13.4553i 0.682209i −0.940025 0.341104i \(-0.889199\pi\)
0.940025 0.341104i \(-0.110801\pi\)
\(390\) 0 0
\(391\) 2.87078i 0.145181i
\(392\) 0 0
\(393\) −1.37066 + 1.37066i −0.0691408 + 0.0691408i
\(394\) 0 0
\(395\) 1.63021 6.13372i 0.0820250 0.308621i
\(396\) 0 0
\(397\) −9.78221 + 9.78221i −0.490955 + 0.490955i −0.908607 0.417652i \(-0.862853\pi\)
0.417652 + 0.908607i \(0.362853\pi\)
\(398\) 0 0
\(399\) 0.163362 0.254254i 0.00817835 0.0127286i
\(400\) 0 0
\(401\) −10.6960 −0.534134 −0.267067 0.963678i \(-0.586055\pi\)
−0.267067 + 0.963678i \(0.586055\pi\)
\(402\) 0 0
\(403\) 25.4123 25.4123i 1.26588 1.26588i
\(404\) 0 0
\(405\) −19.2573 5.11818i −0.956903 0.254325i
\(406\) 0 0
\(407\) −1.01315 1.01315i −0.0502201 0.0502201i
\(408\) 0 0
\(409\) 30.2026 1.49342 0.746712 0.665148i \(-0.231631\pi\)
0.746712 + 0.665148i \(0.231631\pi\)
\(410\) 0 0
\(411\) 0.812396i 0.0400725i
\(412\) 0 0
\(413\) 4.66729 + 21.4447i 0.229662 + 1.05522i
\(414\) 0 0
\(415\) 16.5313 + 28.4995i 0.811489 + 1.39899i
\(416\) 0 0
\(417\) 1.06957 + 1.06957i 0.0523768 + 0.0523768i
\(418\) 0 0
\(419\) 29.8749 1.45948 0.729742 0.683722i \(-0.239640\pi\)
0.729742 + 0.683722i \(0.239640\pi\)
\(420\) 0 0
\(421\) 35.1836 1.71474 0.857372 0.514697i \(-0.172096\pi\)
0.857372 + 0.514697i \(0.172096\pi\)
\(422\) 0 0
\(423\) 21.9748 + 21.9748i 1.06845 + 1.06845i
\(424\) 0 0
\(425\) −6.69997 + 1.82438i −0.324996 + 0.0884954i
\(426\) 0 0
\(427\) −15.2228 + 3.31314i −0.736683 + 0.160334i
\(428\) 0 0
\(429\) 0.430382i 0.0207790i
\(430\) 0 0
\(431\) −20.9552 −1.00937 −0.504687 0.863302i \(-0.668392\pi\)
−0.504687 + 0.863302i \(0.668392\pi\)
\(432\) 0 0
\(433\) −12.5824 12.5824i −0.604670 0.604670i 0.336878 0.941548i \(-0.390629\pi\)
−0.941548 + 0.336878i \(0.890629\pi\)
\(434\) 0 0
\(435\) 0.902109 0.523272i 0.0432528 0.0250890i
\(436\) 0 0
\(437\) −1.67905 + 1.67905i −0.0803200 + 0.0803200i
\(438\) 0 0
\(439\) 7.23208 0.345168 0.172584 0.984995i \(-0.444788\pi\)
0.172584 + 0.984995i \(0.444788\pi\)
\(440\) 0 0
\(441\) 8.69882 + 19.0375i 0.414230 + 0.906550i
\(442\) 0 0
\(443\) 3.46509 3.46509i 0.164632 0.164632i −0.619983 0.784615i \(-0.712861\pi\)
0.784615 + 0.619983i \(0.212861\pi\)
\(444\) 0 0
\(445\) −7.38885 1.96380i −0.350265 0.0930931i
\(446\) 0 0
\(447\) 1.16247 1.16247i 0.0549829 0.0549829i
\(448\) 0 0
\(449\) 6.08724i 0.287274i −0.989630 0.143637i \(-0.954120\pi\)
0.989630 0.143637i \(-0.0458798\pi\)
\(450\) 0 0
\(451\) 7.62876i 0.359224i
\(452\) 0 0
\(453\) 0.874838 + 0.874838i 0.0411035 + 0.0411035i
\(454\) 0 0
\(455\) 24.3372 22.2187i 1.14094 1.04163i
\(456\) 0 0
\(457\) −19.2746 19.2746i −0.901630 0.901630i 0.0939472 0.995577i \(-0.470052\pi\)
−0.995577 + 0.0939472i \(0.970052\pi\)
\(458\) 0 0
\(459\) 0.827214i 0.0386111i
\(460\) 0 0
\(461\) 30.3964i 1.41570i −0.706363 0.707850i \(-0.749665\pi\)
0.706363 0.707850i \(-0.250335\pi\)
\(462\) 0 0
\(463\) 12.0768 12.0768i 0.561259 0.561259i −0.368406 0.929665i \(-0.620096\pi\)
0.929665 + 0.368406i \(0.120096\pi\)
\(464\) 0 0
\(465\) 1.24091 0.719795i 0.0575458 0.0333797i
\(466\) 0 0
\(467\) −4.89096 + 4.89096i −0.226327 + 0.226327i −0.811156 0.584830i \(-0.801161\pi\)
0.584830 + 0.811156i \(0.301161\pi\)
\(468\) 0 0
\(469\) −12.7616 + 19.8618i −0.589275 + 0.917134i
\(470\) 0 0
\(471\) 0.877809 0.0404473
\(472\) 0 0
\(473\) −5.54635 + 5.54635i −0.255022 + 0.255022i
\(474\) 0 0
\(475\) 4.98570 + 2.85162i 0.228760 + 0.130841i
\(476\) 0 0
\(477\) 6.22217 + 6.22217i 0.284894 + 0.284894i
\(478\) 0 0
\(479\) 22.8349 1.04335 0.521676 0.853144i \(-0.325307\pi\)
0.521676 + 0.853144i \(0.325307\pi\)
\(480\) 0 0
\(481\) 10.2715i 0.468339i
\(482\) 0 0
\(483\) 0.115653 + 0.531390i 0.00526241 + 0.0241791i
\(484\) 0 0
\(485\) −23.2580 + 13.4909i −1.05609 + 0.612591i
\(486\) 0 0
\(487\) −11.1182 11.1182i −0.503812 0.503812i 0.408808 0.912620i \(-0.365944\pi\)
−0.912620 + 0.408808i \(0.865944\pi\)
\(488\) 0 0
\(489\) 1.33226 0.0602470
\(490\) 0 0
\(491\) 4.45336 0.200977 0.100489 0.994938i \(-0.467959\pi\)
0.100489 + 0.994938i \(0.467959\pi\)
\(492\) 0 0
\(493\) 4.60599 + 4.60599i 0.207443 + 0.207443i
\(494\) 0 0
\(495\) 1.33445 5.02091i 0.0599791 0.225673i
\(496\) 0 0
\(497\) −6.94167 31.8948i −0.311376 1.43068i
\(498\) 0 0
\(499\) 27.6446i 1.23754i −0.785572 0.618770i \(-0.787631\pi\)
0.785572 0.618770i \(-0.212369\pi\)
\(500\) 0 0
\(501\) 0.101996 0.00455685
\(502\) 0 0
\(503\) −16.9763 16.9763i −0.756936 0.756936i 0.218828 0.975764i \(-0.429777\pi\)
−0.975764 + 0.218828i \(0.929777\pi\)
\(504\) 0 0
\(505\) 2.80360 10.5486i 0.124759 0.469407i
\(506\) 0 0
\(507\) −1.26757 + 1.26757i −0.0562948 + 0.0562948i
\(508\) 0 0
\(509\) −32.3762 −1.43505 −0.717525 0.696533i \(-0.754725\pi\)
−0.717525 + 0.696533i \(0.754725\pi\)
\(510\) 0 0
\(511\) −14.6406 + 22.7863i −0.647663 + 1.00801i
\(512\) 0 0
\(513\) 0.483819 0.483819i 0.0213611 0.0213611i
\(514\) 0 0
\(515\) 15.9372 + 27.4753i 0.702276 + 1.21071i
\(516\) 0 0
\(517\) −5.71041 + 5.71041i −0.251144 + 0.251144i
\(518\) 0 0
\(519\) 0.439236i 0.0192803i
\(520\) 0 0
\(521\) 4.38603i 0.192156i −0.995374 0.0960778i \(-0.969370\pi\)
0.995374 0.0960778i \(-0.0306297\pi\)
\(522\) 0 0
\(523\) 4.73788 + 4.73788i 0.207173 + 0.207173i 0.803065 0.595892i \(-0.203201\pi\)
−0.595892 + 0.803065i \(0.703201\pi\)
\(524\) 0 0
\(525\) 1.16669 0.607616i 0.0509184 0.0265185i
\(526\) 0 0
\(527\) 6.33583 + 6.33583i 0.275993 + 0.275993i
\(528\) 0 0
\(529\) 18.7270i 0.814218i
\(530\) 0 0
\(531\) 24.8032i 1.07637i
\(532\) 0 0
\(533\) −38.6707 + 38.6707i −1.67502 + 1.67502i
\(534\) 0 0
\(535\) 8.99753 + 15.5115i 0.388997 + 0.670622i
\(536\) 0 0
\(537\) −0.646033 + 0.646033i −0.0278784 + 0.0278784i
\(538\) 0 0
\(539\) −4.94714 + 2.26050i −0.213089 + 0.0973665i
\(540\) 0 0
\(541\) 7.48796 0.321933 0.160966 0.986960i \(-0.448539\pi\)
0.160966 + 0.986960i \(0.448539\pi\)
\(542\) 0 0
\(543\) −0.668790 + 0.668790i −0.0287005 + 0.0287005i
\(544\) 0 0
\(545\) 6.83558 25.7191i 0.292804 1.10168i
\(546\) 0 0
\(547\) 1.12562 + 1.12562i 0.0481278 + 0.0481278i 0.730761 0.682633i \(-0.239165\pi\)
−0.682633 + 0.730761i \(0.739165\pi\)
\(548\) 0 0
\(549\) −17.6069 −0.751444
\(550\) 0 0
\(551\) 5.38788i 0.229531i
\(552\) 0 0
\(553\) −7.33770 + 1.59700i −0.312031 + 0.0679113i
\(554\) 0 0
\(555\) 0.105315 0.396252i 0.00447039 0.0168199i
\(556\) 0 0
\(557\) 20.9130 + 20.9130i 0.886113 + 0.886113i 0.994147 0.108034i \(-0.0344557\pi\)
−0.108034 + 0.994147i \(0.534456\pi\)
\(558\) 0 0
\(559\) −56.2297 −2.37826
\(560\) 0 0
\(561\) −0.107304 −0.00453036
\(562\) 0 0
\(563\) −5.94306 5.94306i −0.250470 0.250470i 0.570693 0.821163i \(-0.306675\pi\)
−0.821163 + 0.570693i \(0.806675\pi\)
\(564\) 0 0
\(565\) −3.73436 + 2.16613i −0.157106 + 0.0911299i
\(566\) 0 0
\(567\) 5.01390 + 23.0373i 0.210564 + 0.967474i
\(568\) 0 0
\(569\) 6.64150i 0.278426i −0.990262 0.139213i \(-0.955543\pi\)
0.990262 0.139213i \(-0.0444573\pi\)
\(570\) 0 0
\(571\) 33.4643 1.40044 0.700218 0.713929i \(-0.253086\pi\)
0.700218 + 0.713929i \(0.253086\pi\)
\(572\) 0 0
\(573\) −1.49183 1.49183i −0.0623223 0.0623223i
\(574\) 0 0
\(575\) −9.97249 + 2.71548i −0.415882 + 0.113243i
\(576\) 0 0
\(577\) −7.86048 + 7.86048i −0.327236 + 0.327236i −0.851535 0.524299i \(-0.824328\pi\)
0.524299 + 0.851535i \(0.324328\pi\)
\(578\) 0 0
\(579\) 0.724743 0.0301193
\(580\) 0 0
\(581\) 21.0727 32.7971i 0.874244 1.36065i
\(582\) 0 0
\(583\) −1.61691 + 1.61691i −0.0669655 + 0.0669655i
\(584\) 0 0
\(585\) 32.2157 18.6869i 1.33196 0.772608i
\(586\) 0 0
\(587\) 7.65881 7.65881i 0.316113 0.316113i −0.531159 0.847272i \(-0.678243\pi\)
0.847272 + 0.531159i \(0.178243\pi\)
\(588\) 0 0
\(589\) 7.41137i 0.305380i
\(590\) 0 0
\(591\) 0.538974i 0.0221704i
\(592\) 0 0
\(593\) 8.24682 + 8.24682i 0.338656 + 0.338656i 0.855861 0.517205i \(-0.173028\pi\)
−0.517205 + 0.855861i \(0.673028\pi\)
\(594\) 0 0
\(595\) 5.53960 + 6.06778i 0.227101 + 0.248755i
\(596\) 0 0
\(597\) 0.946748 + 0.946748i 0.0387478 + 0.0387478i
\(598\) 0 0
\(599\) 1.72554i 0.0705038i 0.999378 + 0.0352519i \(0.0112233\pi\)
−0.999378 + 0.0352519i \(0.988777\pi\)
\(600\) 0 0
\(601\) 39.3868i 1.60662i −0.595561 0.803310i \(-0.703070\pi\)
0.595561 0.803310i \(-0.296930\pi\)
\(602\) 0 0
\(603\) −18.8663 + 18.8663i −0.768296 + 0.768296i
\(604\) 0 0
\(605\) −22.4667 5.97119i −0.913403 0.242763i
\(606\) 0 0
\(607\) 13.0555 13.0555i 0.529905 0.529905i −0.390639 0.920544i \(-0.627746\pi\)
0.920544 + 0.390639i \(0.127746\pi\)
\(608\) 0 0
\(609\) −1.03814 0.667024i −0.0420676 0.0270292i
\(610\) 0 0
\(611\) −57.8930 −2.34210
\(612\) 0 0
\(613\) −19.5565 + 19.5565i −0.789878 + 0.789878i −0.981474 0.191596i \(-0.938634\pi\)
0.191596 + 0.981474i \(0.438634\pi\)
\(614\) 0 0
\(615\) −1.88833 + 1.09534i −0.0761449 + 0.0441682i
\(616\) 0 0
\(617\) −4.82431 4.82431i −0.194219 0.194219i 0.603297 0.797517i \(-0.293853\pi\)
−0.797517 + 0.603297i \(0.793853\pi\)
\(618\) 0 0
\(619\) −35.5806 −1.43011 −0.715053 0.699070i \(-0.753598\pi\)
−0.715053 + 0.699070i \(0.753598\pi\)
\(620\) 0 0
\(621\) 1.23126i 0.0494087i
\(622\) 0 0
\(623\) 1.92379 + 8.83919i 0.0770749 + 0.354135i
\(624\) 0 0
\(625\) 12.6750 + 21.5486i 0.507002 + 0.861945i
\(626\) 0 0
\(627\) 0.0627594 + 0.0627594i 0.00250637 + 0.00250637i
\(628\) 0 0
\(629\) 2.56090 0.102110
\(630\) 0 0
\(631\) 28.6285 1.13968 0.569841 0.821755i \(-0.307005\pi\)
0.569841 + 0.821755i \(0.307005\pi\)
\(632\) 0 0
\(633\) 0.570271 + 0.570271i 0.0226663 + 0.0226663i
\(634\) 0 0
\(635\) −15.0629 25.9680i −0.597752 1.03051i
\(636\) 0 0
\(637\) −36.5360 13.6188i −1.44761 0.539596i
\(638\) 0 0
\(639\) 36.8899i 1.45934i
\(640\) 0 0
\(641\) −20.9369 −0.826956 −0.413478 0.910514i \(-0.635686\pi\)
−0.413478 + 0.910514i \(0.635686\pi\)
\(642\) 0 0
\(643\) 13.5706 + 13.5706i 0.535174 + 0.535174i 0.922108 0.386934i \(-0.126466\pi\)
−0.386934 + 0.922108i \(0.626466\pi\)
\(644\) 0 0
\(645\) −2.16922 0.576534i −0.0854130 0.0227010i
\(646\) 0 0
\(647\) 12.1526 12.1526i 0.477768 0.477768i −0.426649 0.904417i \(-0.640306\pi\)
0.904417 + 0.426649i \(0.140306\pi\)
\(648\) 0 0
\(649\) −6.44543 −0.253005
\(650\) 0 0
\(651\) −1.42803 0.917535i −0.0559690 0.0359610i
\(652\) 0 0
\(653\) −16.3014 + 16.3014i −0.637921 + 0.637921i −0.950042 0.312121i \(-0.898961\pi\)
0.312121 + 0.950042i \(0.398961\pi\)
\(654\) 0 0
\(655\) −11.1965 + 42.1270i −0.437482 + 1.64604i
\(656\) 0 0
\(657\) −21.6443 + 21.6443i −0.844423 + 0.844423i
\(658\) 0 0
\(659\) 24.5415i 0.956001i −0.878360 0.478000i \(-0.841362\pi\)
0.878360 0.478000i \(-0.158638\pi\)
\(660\) 0 0
\(661\) 22.1516i 0.861596i 0.902448 + 0.430798i \(0.141768\pi\)
−0.902448 + 0.430798i \(0.858232\pi\)
\(662\) 0 0
\(663\) −0.543929 0.543929i −0.0211245 0.0211245i
\(664\) 0 0
\(665\) 0.308921 6.78889i 0.0119794 0.263262i
\(666\) 0 0
\(667\) 6.85573 + 6.85573i 0.265455 + 0.265455i
\(668\) 0 0
\(669\) 2.60729i 0.100804i
\(670\) 0 0
\(671\) 4.57537i 0.176630i
\(672\) 0 0
\(673\) −9.43387 + 9.43387i −0.363649 + 0.363649i −0.865154 0.501505i \(-0.832780\pi\)
0.501505 + 0.865154i \(0.332780\pi\)
\(674\) 0 0
\(675\) 2.87357 0.782465i 0.110604 0.0301171i
\(676\) 0 0
\(677\) −10.4956 + 10.4956i −0.403378 + 0.403378i −0.879422 0.476044i \(-0.842070\pi\)
0.476044 + 0.879422i \(0.342070\pi\)
\(678\) 0 0
\(679\) 26.7652 + 17.1971i 1.02715 + 0.659964i
\(680\) 0 0
\(681\) −0.680951 −0.0260941
\(682\) 0 0
\(683\) 7.11456 7.11456i 0.272231 0.272231i −0.557767 0.829998i \(-0.688342\pi\)
0.829998 + 0.557767i \(0.188342\pi\)
\(684\) 0 0
\(685\) 9.16630 + 15.8025i 0.350226 + 0.603782i
\(686\) 0 0
\(687\) 0.291297 + 0.291297i 0.0111137 + 0.0111137i
\(688\) 0 0
\(689\) −16.3924 −0.624502
\(690\) 0 0
\(691\) 6.29829i 0.239598i −0.992798 0.119799i \(-0.961775\pi\)
0.992798 0.119799i \(-0.0382251\pi\)
\(692\) 0 0
\(693\) −6.00645 + 1.30726i −0.228166 + 0.0496587i
\(694\) 0 0
\(695\) 32.8728 + 8.73690i 1.24694 + 0.331410i
\(696\) 0 0
\(697\) −9.64145 9.64145i −0.365196 0.365196i
\(698\) 0 0
\(699\) 2.49939 0.0945356
\(700\) 0 0
\(701\) 30.1579 1.13905 0.569523 0.821975i \(-0.307128\pi\)
0.569523 + 0.821975i \(0.307128\pi\)
\(702\) 0 0
\(703\) −1.49781 1.49781i −0.0564911 0.0564911i
\(704\) 0 0
\(705\) −2.23339 0.593587i −0.0841142 0.0223558i
\(706\) 0 0
\(707\) −12.6192 + 2.74648i −0.474593 + 0.103292i
\(708\) 0 0
\(709\) 1.75232i 0.0658099i −0.999458 0.0329049i \(-0.989524\pi\)
0.999458 0.0329049i \(-0.0104759\pi\)
\(710\) 0 0
\(711\) −8.48688 −0.318283
\(712\) 0 0
\(713\) 9.43050 + 9.43050i 0.353175 + 0.353175i
\(714\) 0 0
\(715\) 4.85602 + 8.37166i 0.181605 + 0.313082i
\(716\) 0 0
\(717\) −1.74878 + 1.74878i −0.0653093 + 0.0653093i
\(718\) 0 0
\(719\) −22.1398 −0.825675 −0.412837 0.910805i \(-0.635462\pi\)
−0.412837 + 0.910805i \(0.635462\pi\)
\(720\) 0 0
\(721\) 20.3154 31.6184i 0.756585 1.17753i
\(722\) 0 0
\(723\) −0.359569 + 0.359569i −0.0133725 + 0.0133725i
\(724\) 0 0
\(725\) 11.6434 20.3571i 0.432426 0.756043i
\(726\) 0 0
\(727\) −36.3804 + 36.3804i −1.34927 + 1.34927i −0.462825 + 0.886450i \(0.653164\pi\)
−0.886450 + 0.462825i \(0.846836\pi\)
\(728\) 0 0
\(729\) 26.4675i 0.980279i
\(730\) 0 0
\(731\) 14.0193i 0.518522i
\(732\) 0 0
\(733\) 26.3741 + 26.3741i 0.974149 + 0.974149i 0.999674 0.0255249i \(-0.00812572\pi\)
−0.0255249 + 0.999674i \(0.508126\pi\)
\(734\) 0 0
\(735\) −1.26985 0.899995i −0.0468390 0.0331968i
\(736\) 0 0
\(737\) −4.90265 4.90265i −0.180591 0.180591i
\(738\) 0 0
\(739\) 6.48932i 0.238714i −0.992851 0.119357i \(-0.961917\pi\)
0.992851 0.119357i \(-0.0380832\pi\)
\(740\) 0 0
\(741\) 0.636264i 0.0233737i
\(742\) 0 0
\(743\) 7.68617 7.68617i 0.281978 0.281978i −0.551919 0.833897i \(-0.686104\pi\)
0.833897 + 0.551919i \(0.186104\pi\)
\(744\) 0 0
\(745\) 9.49580 35.7282i 0.347899 1.30898i
\(746\) 0 0
\(747\) 31.1533 31.1533i 1.13984 1.13984i
\(748\) 0 0
\(749\) 11.4693 17.8506i 0.419079 0.652246i
\(750\) 0 0
\(751\) −2.05149 −0.0748599 −0.0374300 0.999299i \(-0.511917\pi\)
−0.0374300 + 0.999299i \(0.511917\pi\)
\(752\) 0 0
\(753\) 1.50993 1.50993i 0.0550249 0.0550249i
\(754\) 0 0
\(755\) 26.8879 + 7.14625i 0.978552 + 0.260079i
\(756\) 0 0
\(757\) −4.22246 4.22246i −0.153468 0.153468i 0.626197 0.779665i \(-0.284611\pi\)
−0.779665 + 0.626197i \(0.784611\pi\)
\(758\) 0 0
\(759\) −0.159715 −0.00579728
\(760\) 0 0
\(761\) 46.0616i 1.66973i 0.550453 + 0.834866i \(0.314455\pi\)
−0.550453 + 0.834866i \(0.685545\pi\)
\(762\) 0 0
\(763\) −30.7674 + 6.69631i −1.11385 + 0.242423i
\(764\) 0 0
\(765\) 4.65905 + 8.03208i 0.168448 + 0.290401i
\(766\) 0 0
\(767\) −32.6723 32.6723i −1.17973 1.17973i
\(768\) 0 0
\(769\) 44.8809 1.61845 0.809223 0.587501i \(-0.199888\pi\)
0.809223 + 0.587501i \(0.199888\pi\)
\(770\) 0 0
\(771\) 0.293143 0.0105573
\(772\) 0 0
\(773\) 4.22724 + 4.22724i 0.152043 + 0.152043i 0.779030 0.626987i \(-0.215712\pi\)
−0.626987 + 0.779030i \(0.715712\pi\)
\(774\) 0 0
\(775\) 16.0163 28.0025i 0.575323 1.00588i
\(776\) 0 0
\(777\) −0.474031 + 0.103169i −0.0170058 + 0.00370118i
\(778\) 0 0
\(779\) 11.2781i 0.404081i
\(780\) 0 0
\(781\) 9.58630 0.343025
\(782\) 0 0
\(783\) −1.97548 1.97548i −0.0705978 0.0705978i
\(784\) 0 0
\(785\) 17.0749 9.90436i 0.609428 0.353502i
\(786\) 0 0
\(787\) −2.71942 + 2.71942i −0.0969367 + 0.0969367i −0.753912 0.656975i \(-0.771836\pi\)
0.656975 + 0.753912i \(0.271836\pi\)
\(788\) 0 0
\(789\) 0.895906 0.0318951
\(790\) 0 0
\(791\) 4.29748 + 2.76121i 0.152801 + 0.0981772i
\(792\) 0 0
\(793\) 23.1929 23.1929i 0.823603 0.823603i
\(794\) 0 0
\(795\) −0.632386 0.168075i −0.0224284 0.00596100i
\(796\) 0 0
\(797\) 28.8991 28.8991i 1.02366 1.02366i 0.0239445 0.999713i \(-0.492377\pi\)
0.999713 0.0239445i \(-0.00762250\pi\)
\(798\) 0 0
\(799\) 14.4340i 0.510637i
\(800\) 0 0
\(801\) 10.2235i 0.361231i
\(802\) 0 0
\(803\) −5.62453 5.62453i −0.198485 0.198485i
\(804\) 0 0
\(805\) 8.24535 + 9.03152i 0.290611 + 0.318319i
\(806\) 0 0
\(807\) −0.673063 0.673063i −0.0236929 0.0236929i
\(808\) 0 0
\(809\) 32.7627i 1.15187i −0.817494 0.575937i \(-0.804637\pi\)
0.817494 0.575937i \(-0.195363\pi\)
\(810\) 0 0
\(811\) 24.6348i 0.865045i 0.901623 + 0.432523i \(0.142376\pi\)
−0.901623 + 0.432523i \(0.857624\pi\)
\(812\) 0 0
\(813\) 0.851321 0.851321i 0.0298571 0.0298571i
\(814\) 0 0
\(815\) 25.9148 15.0320i 0.907755 0.526547i
\(816\) 0 0
\(817\) −8.19956 + 8.19956i −0.286866 + 0.286866i
\(818\) 0 0
\(819\) −37.0737 23.8205i −1.29546 0.832356i
\(820\) 0 0
\(821\) 36.5320 1.27498 0.637488 0.770460i \(-0.279974\pi\)
0.637488 + 0.770460i \(0.279974\pi\)
\(822\) 0 0
\(823\) −14.6526 + 14.6526i −0.510758 + 0.510758i −0.914759 0.404001i \(-0.867619\pi\)
0.404001 + 0.914759i \(0.367619\pi\)
\(824\) 0 0
\(825\) 0.101499 + 0.372751i 0.00353373 + 0.0129775i
\(826\) 0 0
\(827\) −22.1880 22.1880i −0.771552 0.771552i 0.206826 0.978378i \(-0.433687\pi\)
−0.978378 + 0.206826i \(0.933687\pi\)
\(828\) 0 0
\(829\) 46.4490 1.61324 0.806620 0.591070i \(-0.201294\pi\)
0.806620 + 0.591070i \(0.201294\pi\)
\(830\) 0 0
\(831\) 2.28745i 0.0793508i
\(832\) 0 0
\(833\) 3.39546 9.10922i 0.117646 0.315616i
\(834\) 0 0
\(835\) 1.98400 1.15083i 0.0686591 0.0398260i
\(836\) 0 0
\(837\) −2.71740 2.71740i −0.0939271 0.0939271i
\(838\) 0 0
\(839\) 20.5166 0.708312 0.354156 0.935186i \(-0.384768\pi\)
0.354156 + 0.935186i \(0.384768\pi\)
\(840\) 0 0
\(841\) 7.00080 0.241407
\(842\) 0 0
\(843\) −0.0640466 0.0640466i −0.00220588 0.00220588i
\(844\) 0 0
\(845\) −10.3543 + 38.9585i −0.356200 + 1.34021i
\(846\) 0 0
\(847\) 5.84952 + 26.8767i 0.200992 + 0.923494i
\(848\) 0 0
\(849\) 1.76661i 0.0606300i
\(850\) 0 0
\(851\) 3.81174 0.130665
\(852\) 0 0
\(853\) 17.5496 + 17.5496i 0.600887 + 0.600887i 0.940548 0.339661i \(-0.110312\pi\)
−0.339661 + 0.940548i \(0.610312\pi\)
\(854\) 0 0
\(855\) 1.97281 7.42276i 0.0674688 0.253853i
\(856\) 0 0
\(857\) −11.1708 + 11.1708i −0.381588 + 0.381588i −0.871674 0.490086i \(-0.836965\pi\)
0.490086 + 0.871674i \(0.336965\pi\)
\(858\) 0 0
\(859\) 42.5442 1.45159 0.725795 0.687911i \(-0.241472\pi\)
0.725795 + 0.687911i \(0.241472\pi\)
\(860\) 0 0
\(861\) 2.17308 + 1.39624i 0.0740585 + 0.0475839i
\(862\) 0 0
\(863\) −6.66647 + 6.66647i −0.226929 + 0.226929i −0.811409 0.584479i \(-0.801299\pi\)
0.584479 + 0.811409i \(0.301299\pi\)
\(864\) 0 0
\(865\) −4.95592 8.54388i −0.168506 0.290501i
\(866\) 0 0
\(867\) −1.05970 + 1.05970i −0.0359894 + 0.0359894i
\(868\) 0 0
\(869\) 2.20542i 0.0748138i
\(870\) 0 0
\(871\) 49.7038i 1.68415i
\(872\) 0 0
\(873\) 25.4237 + 25.4237i 0.860461 + 0.860461i
\(874\) 0 0
\(875\) 15.8383 24.9830i 0.535432 0.844578i
\(876\) 0 0
\(877\) −24.1080 24.1080i −0.814069 0.814069i 0.171172 0.985241i \(-0.445245\pi\)
−0.985241 + 0.171172i \(0.945245\pi\)
\(878\) 0 0
\(879\) 0.911503i 0.0307442i
\(880\) 0 0
\(881\) 41.2812i 1.39080i 0.718623 + 0.695399i \(0.244773\pi\)
−0.718623 + 0.695399i \(0.755227\pi\)
\(882\) 0 0
\(883\) −7.58783 + 7.58783i −0.255351 + 0.255351i −0.823160 0.567809i \(-0.807791\pi\)
0.567809 + 0.823160i \(0.307791\pi\)
\(884\) 0 0
\(885\) −0.925433 1.59542i −0.0311081 0.0536296i
\(886\) 0 0
\(887\) −21.2247 + 21.2247i −0.712657 + 0.712657i −0.967090 0.254433i \(-0.918111\pi\)
0.254433 + 0.967090i \(0.418111\pi\)
\(888\) 0 0
\(889\) −19.2009 + 29.8839i −0.643978 + 1.00227i
\(890\) 0 0
\(891\) −6.92409 −0.231966
\(892\) 0 0
\(893\) −8.44210 + 8.44210i −0.282504 + 0.282504i
\(894\) 0 0
\(895\) −5.27722 + 19.8557i −0.176398 + 0.663702i
\(896\) 0 0
\(897\) −0.809606 0.809606i −0.0270319 0.0270319i
\(898\) 0 0
\(899\) −30.2613 −1.00927
\(900\) 0 0
\(901\) 4.08699i 0.136157i
\(902\) 0 0
\(903\) 0.564786 + 2.59501i 0.0187949 + 0.0863567i
\(904\) 0 0
\(905\) −5.46311 + 20.5551i −0.181600 + 0.683274i
\(906\) 0 0
\(907\) −2.69307 2.69307i −0.0894219 0.0894219i 0.660981 0.750403i \(-0.270140\pi\)
−0.750403 + 0.660981i \(0.770140\pi\)
\(908\) 0 0
\(909\) −14.5955 −0.484103
\(910\) 0 0
\(911\) −41.2220 −1.36575 −0.682874 0.730536i \(-0.739270\pi\)
−0.682874 + 0.730536i \(0.739270\pi\)
\(912\) 0 0
\(913\) 8.09556 + 8.09556i 0.267924 + 0.267924i
\(914\) 0 0
\(915\) 1.13253 0.656931i 0.0374404 0.0217175i
\(916\) 0 0
\(917\) 50.3960 10.9683i 1.66422 0.362206i
\(918\) 0 0
\(919\) 4.87087i 0.160675i 0.996768 + 0.0803376i \(0.0255998\pi\)
−0.996768 + 0.0803376i \(0.974400\pi\)
\(920\) 0 0
\(921\) 1.19387 0.0393393
\(922\) 0 0
\(923\) 48.5936 + 48.5936i 1.59948 + 1.59948i
\(924\) 0 0
\(925\) −2.42236 8.89605i −0.0796469 0.292500i
\(926\) 0 0
\(927\) 30.0337 30.0337i 0.986435 0.986435i
\(928\) 0 0
\(929\) −21.6087 −0.708957 −0.354479 0.935064i \(-0.615342\pi\)
−0.354479 + 0.935064i \(0.615342\pi\)
\(930\) 0 0
\(931\) −7.31371 + 3.34185i −0.239697 + 0.109525i
\(932\) 0 0
\(933\) −1.82637 + 1.82637i −0.0597926 + 0.0597926i
\(934\) 0 0
\(935\) −2.08724 + 1.21071i −0.0682599 + 0.0395945i
\(936\) 0 0
\(937\) −5.78051 + 5.78051i −0.188841 + 0.188841i −0.795195 0.606354i \(-0.792631\pi\)
0.606354 + 0.795195i \(0.292631\pi\)
\(938\) 0 0
\(939\) 1.73168i 0.0565113i
\(940\) 0 0
\(941\) 35.5016i 1.15732i −0.815569 0.578660i \(-0.803576\pi\)
0.815569 0.578660i \(-0.196424\pi\)
\(942\) 0 0
\(943\) −14.3507 14.3507i −0.467323 0.467323i
\(944\) 0 0
\(945\) −2.37590 2.60243i −0.0772880 0.0846571i
\(946\) 0 0
\(947\) 29.6185 + 29.6185i 0.962472 + 0.962472i 0.999321 0.0368489i \(-0.0117320\pi\)
−0.0368489 + 0.999321i \(0.511732\pi\)
\(948\) 0 0
\(949\) 57.0223i 1.85102i
\(950\) 0 0
\(951\) 2.03778i 0.0660797i
\(952\) 0 0
\(953\) −2.58171 + 2.58171i −0.0836298 + 0.0836298i −0.747684 0.664054i \(-0.768834\pi\)
0.664054 + 0.747684i \(0.268834\pi\)
\(954\) 0 0
\(955\) −45.8512 12.1863i −1.48371 0.394338i
\(956\) 0 0
\(957\) 0.256253 0.256253i 0.00828347 0.00828347i
\(958\) 0 0
\(959\) 11.6844 18.1854i 0.377310 0.587237i
\(960\) 0 0
\(961\) −10.6264 −0.342788
\(962\) 0 0
\(963\) 16.9559 16.9559i 0.546396 0.546396i
\(964\) 0 0
\(965\) 14.0975 8.17731i 0.453814 0.263237i
\(966\) 0 0
\(967\) −15.8202 15.8202i −0.508744 0.508744i 0.405397 0.914141i \(-0.367133\pi\)
−0.914141 + 0.405397i \(0.867133\pi\)
\(968\) 0 0
\(969\) −0.158634 −0.00509607
\(970\) 0 0
\(971\) 26.5709i 0.852701i −0.904558 0.426351i \(-0.859799\pi\)
0.904558 0.426351i \(-0.140201\pi\)
\(972\) 0 0
\(973\) −8.55889 39.3254i −0.274385 1.26071i
\(974\) 0 0
\(975\) −1.37499 + 2.40400i −0.0440351 + 0.0769897i
\(976\) 0 0
\(977\) 40.8575 + 40.8575i 1.30715 + 1.30715i 0.923465 + 0.383683i \(0.125344\pi\)
0.383683 + 0.923465i \(0.374656\pi\)
\(978\) 0 0
\(979\) −2.65671 −0.0849089
\(980\) 0 0
\(981\) −35.5860 −1.13617
\(982\) 0 0
\(983\) −4.75434 4.75434i −0.151640 0.151640i 0.627210 0.778850i \(-0.284197\pi\)
−0.778850 + 0.627210i \(0.784197\pi\)
\(984\) 0 0
\(985\) 6.08127 + 10.4840i 0.193765 + 0.334046i
\(986\) 0 0
\(987\) 0.581493 + 2.67177i 0.0185091 + 0.0850435i
\(988\) 0 0
\(989\) 20.8668i 0.663527i
\(990\) 0 0
\(991\) 27.2402 0.865312 0.432656 0.901559i \(-0.357576\pi\)
0.432656 + 0.901559i \(0.357576\pi\)
\(992\) 0 0
\(993\) −1.92773 1.92773i −0.0611747 0.0611747i
\(994\) 0 0
\(995\) 29.0981 + 7.73365i 0.922471 + 0.245173i
\(996\) 0 0
\(997\) −6.58513 + 6.58513i −0.208553 + 0.208553i −0.803652 0.595099i \(-0.797113\pi\)
0.595099 + 0.803652i \(0.297113\pi\)
\(998\) 0 0
\(999\) −1.09835 −0.0347504
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 280.2.x.a.97.7 yes 24
4.3 odd 2 560.2.bj.d.97.6 24
5.2 odd 4 1400.2.x.b.993.7 24
5.3 odd 4 inner 280.2.x.a.153.6 yes 24
5.4 even 2 1400.2.x.b.657.6 24
7.6 odd 2 inner 280.2.x.a.97.6 24
20.3 even 4 560.2.bj.d.433.7 24
28.27 even 2 560.2.bj.d.97.7 24
35.13 even 4 inner 280.2.x.a.153.7 yes 24
35.27 even 4 1400.2.x.b.993.6 24
35.34 odd 2 1400.2.x.b.657.7 24
140.83 odd 4 560.2.bj.d.433.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.x.a.97.6 24 7.6 odd 2 inner
280.2.x.a.97.7 yes 24 1.1 even 1 trivial
280.2.x.a.153.6 yes 24 5.3 odd 4 inner
280.2.x.a.153.7 yes 24 35.13 even 4 inner
560.2.bj.d.97.6 24 4.3 odd 2
560.2.bj.d.97.7 24 28.27 even 2
560.2.bj.d.433.6 24 140.83 odd 4
560.2.bj.d.433.7 24 20.3 even 4
1400.2.x.b.657.6 24 5.4 even 2
1400.2.x.b.657.7 24 35.34 odd 2
1400.2.x.b.993.6 24 35.27 even 4
1400.2.x.b.993.7 24 5.2 odd 4