Properties

Label 1148.2.n.d.57.2
Level $1148$
Weight $2$
Character 1148.57
Analytic conductor $9.167$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1148,2,Mod(57,1148)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1148.57");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.n (of order \(5\), degree \(4\), 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: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 57.2
Character \(\chi\) \(=\) 1148.57
Dual form 1148.2.n.d.141.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.86083 q^{3} +(-3.47370 - 2.52379i) q^{5} +(0.309017 + 0.951057i) q^{7} +5.18432 q^{9} +O(q^{10})\) \(q-2.86083 q^{3} +(-3.47370 - 2.52379i) q^{5} +(0.309017 + 0.951057i) q^{7} +5.18432 q^{9} +(1.93088 - 1.40287i) q^{11} +(0.878790 - 2.70464i) q^{13} +(9.93765 + 7.22013i) q^{15} +(6.32741 - 4.59714i) q^{17} +(-0.619498 - 1.90662i) q^{19} +(-0.884044 - 2.72081i) q^{21} +(0.422882 - 1.30150i) q^{23} +(4.15199 + 12.7785i) q^{25} -6.24897 q^{27} +(-3.17810 - 2.30902i) q^{29} +(-2.30062 + 1.67150i) q^{31} +(-5.52393 + 4.01337i) q^{33} +(1.32684 - 4.08358i) q^{35} +(-9.27040 - 6.73534i) q^{37} +(-2.51407 + 7.73750i) q^{39} +(1.20070 - 6.28954i) q^{41} +(-0.353583 + 1.08822i) q^{43} +(-18.0088 - 13.0842i) q^{45} +(0.654034 - 2.01291i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-18.1016 + 13.1516i) q^{51} +(4.40632 + 3.20138i) q^{53} -10.2479 q^{55} +(1.77228 + 5.45451i) q^{57} +(-2.97301 + 9.14999i) q^{59} +(-1.65006 - 5.07837i) q^{61} +(1.60204 + 4.93059i) q^{63} +(-9.87860 + 7.17722i) q^{65} +(8.74042 + 6.35029i) q^{67} +(-1.20979 + 3.72336i) q^{69} +(5.04660 - 3.66657i) q^{71} -9.96989 q^{73} +(-11.8781 - 36.5571i) q^{75} +(1.93088 + 1.40287i) q^{77} +8.99970 q^{79} +2.32425 q^{81} -3.51170 q^{83} -33.5817 q^{85} +(9.09199 + 6.60571i) q^{87} +(1.60053 + 4.92592i) q^{89} +2.84383 q^{91} +(6.58168 - 4.78187i) q^{93} +(-2.65996 + 8.18651i) q^{95} +(-11.6968 - 8.49821i) q^{97} +(10.0103 - 7.27293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.86083 −1.65170 −0.825849 0.563891i \(-0.809304\pi\)
−0.825849 + 0.563891i \(0.809304\pi\)
\(4\) 0 0
\(5\) −3.47370 2.52379i −1.55349 1.12867i −0.941107 0.338109i \(-0.890213\pi\)
−0.612379 0.790564i \(-0.709787\pi\)
\(6\) 0 0
\(7\) 0.309017 + 0.951057i 0.116797 + 0.359466i
\(8\) 0 0
\(9\) 5.18432 1.72811
\(10\) 0 0
\(11\) 1.93088 1.40287i 0.582184 0.422981i −0.257327 0.966324i \(-0.582842\pi\)
0.839511 + 0.543343i \(0.182842\pi\)
\(12\) 0 0
\(13\) 0.878790 2.70464i 0.243733 0.750132i −0.752110 0.659038i \(-0.770964\pi\)
0.995842 0.0910938i \(-0.0290363\pi\)
\(14\) 0 0
\(15\) 9.93765 + 7.22013i 2.56589 + 1.86423i
\(16\) 0 0
\(17\) 6.32741 4.59714i 1.53462 1.11497i 0.581026 0.813885i \(-0.302652\pi\)
0.953598 0.301084i \(-0.0973485\pi\)
\(18\) 0 0
\(19\) −0.619498 1.90662i −0.142123 0.437409i 0.854507 0.519440i \(-0.173859\pi\)
−0.996630 + 0.0820311i \(0.973859\pi\)
\(20\) 0 0
\(21\) −0.884044 2.72081i −0.192914 0.593729i
\(22\) 0 0
\(23\) 0.422882 1.30150i 0.0881770 0.271381i −0.897239 0.441546i \(-0.854430\pi\)
0.985416 + 0.170165i \(0.0544301\pi\)
\(24\) 0 0
\(25\) 4.15199 + 12.7785i 0.830397 + 2.55570i
\(26\) 0 0
\(27\) −6.24897 −1.20262
\(28\) 0 0
\(29\) −3.17810 2.30902i −0.590158 0.428775i 0.252214 0.967672i \(-0.418841\pi\)
−0.842372 + 0.538897i \(0.818841\pi\)
\(30\) 0 0
\(31\) −2.30062 + 1.67150i −0.413204 + 0.300210i −0.774898 0.632087i \(-0.782199\pi\)
0.361694 + 0.932297i \(0.382199\pi\)
\(32\) 0 0
\(33\) −5.52393 + 4.01337i −0.961592 + 0.698637i
\(34\) 0 0
\(35\) 1.32684 4.08358i 0.224276 0.690251i
\(36\) 0 0
\(37\) −9.27040 6.73534i −1.52404 1.10728i −0.959437 0.281924i \(-0.909028\pi\)
−0.564608 0.825360i \(-0.690972\pi\)
\(38\) 0 0
\(39\) −2.51407 + 7.73750i −0.402573 + 1.23899i
\(40\) 0 0
\(41\) 1.20070 6.28954i 0.187519 0.982261i
\(42\) 0 0
\(43\) −0.353583 + 1.08822i −0.0539209 + 0.165951i −0.974390 0.224863i \(-0.927807\pi\)
0.920470 + 0.390814i \(0.127807\pi\)
\(44\) 0 0
\(45\) −18.0088 13.0842i −2.68459 1.95047i
\(46\) 0 0
\(47\) 0.654034 2.01291i 0.0954007 0.293613i −0.891957 0.452120i \(-0.850668\pi\)
0.987358 + 0.158507i \(0.0506679\pi\)
\(48\) 0 0
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 0 0
\(51\) −18.1016 + 13.1516i −2.53474 + 1.84159i
\(52\) 0 0
\(53\) 4.40632 + 3.20138i 0.605254 + 0.439743i 0.847740 0.530412i \(-0.177963\pi\)
−0.242486 + 0.970155i \(0.577963\pi\)
\(54\) 0 0
\(55\) −10.2479 −1.38182
\(56\) 0 0
\(57\) 1.77228 + 5.45451i 0.234744 + 0.722467i
\(58\) 0 0
\(59\) −2.97301 + 9.14999i −0.387053 + 1.19123i 0.547927 + 0.836526i \(0.315417\pi\)
−0.934980 + 0.354700i \(0.884583\pi\)
\(60\) 0 0
\(61\) −1.65006 5.07837i −0.211269 0.650219i −0.999397 0.0347084i \(-0.988950\pi\)
0.788128 0.615511i \(-0.211050\pi\)
\(62\) 0 0
\(63\) 1.60204 + 4.93059i 0.201839 + 0.621195i
\(64\) 0 0
\(65\) −9.87860 + 7.17722i −1.22529 + 0.890225i
\(66\) 0 0
\(67\) 8.74042 + 6.35029i 1.06781 + 0.775811i 0.975518 0.219921i \(-0.0705798\pi\)
0.0922947 + 0.995732i \(0.470580\pi\)
\(68\) 0 0
\(69\) −1.20979 + 3.72336i −0.145642 + 0.448240i
\(70\) 0 0
\(71\) 5.04660 3.66657i 0.598921 0.435141i −0.246575 0.969124i \(-0.579305\pi\)
0.845496 + 0.533982i \(0.179305\pi\)
\(72\) 0 0
\(73\) −9.96989 −1.16689 −0.583444 0.812153i \(-0.698295\pi\)
−0.583444 + 0.812153i \(0.698295\pi\)
\(74\) 0 0
\(75\) −11.8781 36.5571i −1.37157 4.22125i
\(76\) 0 0
\(77\) 1.93088 + 1.40287i 0.220045 + 0.159872i
\(78\) 0 0
\(79\) 8.99970 1.01255 0.506273 0.862373i \(-0.331023\pi\)
0.506273 + 0.862373i \(0.331023\pi\)
\(80\) 0 0
\(81\) 2.32425 0.258250
\(82\) 0 0
\(83\) −3.51170 −0.385459 −0.192730 0.981252i \(-0.561734\pi\)
−0.192730 + 0.981252i \(0.561734\pi\)
\(84\) 0 0
\(85\) −33.5817 −3.64245
\(86\) 0 0
\(87\) 9.09199 + 6.60571i 0.974763 + 0.708207i
\(88\) 0 0
\(89\) 1.60053 + 4.92592i 0.169656 + 0.522146i 0.999349 0.0360730i \(-0.0114849\pi\)
−0.829694 + 0.558219i \(0.811485\pi\)
\(90\) 0 0
\(91\) 2.84383 0.298114
\(92\) 0 0
\(93\) 6.58168 4.78187i 0.682488 0.495857i
\(94\) 0 0
\(95\) −2.65996 + 8.18651i −0.272906 + 0.839918i
\(96\) 0 0
\(97\) −11.6968 8.49821i −1.18763 0.862862i −0.194617 0.980879i \(-0.562346\pi\)
−0.993012 + 0.118017i \(0.962346\pi\)
\(98\) 0 0
\(99\) 10.0103 7.27293i 1.00608 0.730957i
\(100\) 0 0
\(101\) 1.90191 + 5.85346i 0.189247 + 0.582441i 0.999996 0.00295258i \(-0.000939838\pi\)
−0.810749 + 0.585394i \(0.800940\pi\)
\(102\) 0 0
\(103\) −3.43336 10.5668i −0.338299 1.04118i −0.965074 0.261978i \(-0.915625\pi\)
0.626775 0.779201i \(-0.284375\pi\)
\(104\) 0 0
\(105\) −3.79585 + 11.6824i −0.370437 + 1.14009i
\(106\) 0 0
\(107\) −4.05459 12.4787i −0.391972 1.20637i −0.931295 0.364266i \(-0.881320\pi\)
0.539323 0.842099i \(-0.318680\pi\)
\(108\) 0 0
\(109\) −7.78660 −0.745821 −0.372911 0.927867i \(-0.621640\pi\)
−0.372911 + 0.927867i \(0.621640\pi\)
\(110\) 0 0
\(111\) 26.5210 + 19.2686i 2.51726 + 1.82890i
\(112\) 0 0
\(113\) 5.32239 3.86694i 0.500689 0.363772i −0.308591 0.951195i \(-0.599858\pi\)
0.809280 + 0.587423i \(0.199858\pi\)
\(114\) 0 0
\(115\) −4.75367 + 3.45375i −0.443282 + 0.322063i
\(116\) 0 0
\(117\) 4.55593 14.0217i 0.421196 1.29631i
\(118\) 0 0
\(119\) 6.32741 + 4.59714i 0.580033 + 0.421419i
\(120\) 0 0
\(121\) −1.63891 + 5.04406i −0.148992 + 0.458551i
\(122\) 0 0
\(123\) −3.43501 + 17.9933i −0.309724 + 1.62240i
\(124\) 0 0
\(125\) 11.1933 34.4495i 1.00116 3.08126i
\(126\) 0 0
\(127\) −7.12801 5.17880i −0.632508 0.459544i 0.224760 0.974414i \(-0.427840\pi\)
−0.857268 + 0.514870i \(0.827840\pi\)
\(128\) 0 0
\(129\) 1.01154 3.11320i 0.0890611 0.274102i
\(130\) 0 0
\(131\) 4.77066 3.46609i 0.416815 0.302833i −0.359540 0.933130i \(-0.617066\pi\)
0.776355 + 0.630296i \(0.217066\pi\)
\(132\) 0 0
\(133\) 1.62187 1.17836i 0.140634 0.102176i
\(134\) 0 0
\(135\) 21.7071 + 15.7711i 1.86825 + 1.35736i
\(136\) 0 0
\(137\) −19.7196 −1.68476 −0.842381 0.538882i \(-0.818847\pi\)
−0.842381 + 0.538882i \(0.818847\pi\)
\(138\) 0 0
\(139\) 7.12532 + 21.9295i 0.604362 + 1.86003i 0.501120 + 0.865378i \(0.332922\pi\)
0.103242 + 0.994656i \(0.467078\pi\)
\(140\) 0 0
\(141\) −1.87108 + 5.75859i −0.157573 + 0.484960i
\(142\) 0 0
\(143\) −2.09741 6.45517i −0.175394 0.539809i
\(144\) 0 0
\(145\) 5.21227 + 16.0417i 0.432855 + 1.33219i
\(146\) 0 0
\(147\) 2.31446 1.68155i 0.190893 0.138692i
\(148\) 0 0
\(149\) 5.65346 + 4.10748i 0.463149 + 0.336498i 0.794765 0.606917i \(-0.207594\pi\)
−0.331616 + 0.943414i \(0.607594\pi\)
\(150\) 0 0
\(151\) 4.94583 15.2217i 0.402486 1.23872i −0.520490 0.853868i \(-0.674251\pi\)
0.922976 0.384857i \(-0.125749\pi\)
\(152\) 0 0
\(153\) 32.8034 23.8330i 2.65200 1.92679i
\(154\) 0 0
\(155\) 12.2102 0.980745
\(156\) 0 0
\(157\) −5.59637 17.2239i −0.446639 1.37461i −0.880676 0.473719i \(-0.842911\pi\)
0.434037 0.900895i \(-0.357089\pi\)
\(158\) 0 0
\(159\) −12.6057 9.15858i −0.999697 0.726323i
\(160\) 0 0
\(161\) 1.36848 0.107851
\(162\) 0 0
\(163\) 2.57568 0.201743 0.100871 0.994899i \(-0.467837\pi\)
0.100871 + 0.994899i \(0.467837\pi\)
\(164\) 0 0
\(165\) 29.3174 2.28235
\(166\) 0 0
\(167\) −19.0198 −1.47180 −0.735900 0.677090i \(-0.763241\pi\)
−0.735900 + 0.677090i \(0.763241\pi\)
\(168\) 0 0
\(169\) 3.97442 + 2.88759i 0.305725 + 0.222122i
\(170\) 0 0
\(171\) −3.21168 9.88454i −0.245603 0.755889i
\(172\) 0 0
\(173\) 14.1626 1.07676 0.538380 0.842702i \(-0.319036\pi\)
0.538380 + 0.842702i \(0.319036\pi\)
\(174\) 0 0
\(175\) −10.8700 + 7.89755i −0.821698 + 0.596999i
\(176\) 0 0
\(177\) 8.50527 26.1765i 0.639295 1.96755i
\(178\) 0 0
\(179\) 8.17454 + 5.93915i 0.610994 + 0.443913i 0.849764 0.527163i \(-0.176744\pi\)
−0.238770 + 0.971076i \(0.576744\pi\)
\(180\) 0 0
\(181\) −13.7295 + 9.97509i −1.02051 + 0.741443i −0.966387 0.257091i \(-0.917236\pi\)
−0.0541216 + 0.998534i \(0.517236\pi\)
\(182\) 0 0
\(183\) 4.72054 + 14.5283i 0.348953 + 1.07397i
\(184\) 0 0
\(185\) 15.2040 + 46.7931i 1.11782 + 3.44030i
\(186\) 0 0
\(187\) 5.76832 17.7531i 0.421822 1.29823i
\(188\) 0 0
\(189\) −1.93104 5.94313i −0.140462 0.432299i
\(190\) 0 0
\(191\) −8.74500 −0.632766 −0.316383 0.948632i \(-0.602468\pi\)
−0.316383 + 0.948632i \(0.602468\pi\)
\(192\) 0 0
\(193\) −7.55125 5.48630i −0.543551 0.394913i 0.281851 0.959458i \(-0.409051\pi\)
−0.825402 + 0.564545i \(0.809051\pi\)
\(194\) 0 0
\(195\) 28.2609 20.5328i 2.02381 1.47038i
\(196\) 0 0
\(197\) 9.95819 7.23505i 0.709492 0.515476i −0.173518 0.984831i \(-0.555513\pi\)
0.883010 + 0.469355i \(0.155513\pi\)
\(198\) 0 0
\(199\) −6.25698 + 19.2570i −0.443546 + 1.36509i 0.440525 + 0.897740i \(0.354792\pi\)
−0.884071 + 0.467353i \(0.845208\pi\)
\(200\) 0 0
\(201\) −25.0048 18.1671i −1.76370 1.28141i
\(202\) 0 0
\(203\) 1.21393 3.73608i 0.0852009 0.262221i
\(204\) 0 0
\(205\) −20.0444 + 18.8176i −1.39996 + 1.31428i
\(206\) 0 0
\(207\) 2.19236 6.74738i 0.152379 0.468976i
\(208\) 0 0
\(209\) −3.87092 2.81239i −0.267757 0.194537i
\(210\) 0 0
\(211\) −4.73030 + 14.5584i −0.325647 + 1.00224i 0.645501 + 0.763760i \(0.276649\pi\)
−0.971148 + 0.238479i \(0.923351\pi\)
\(212\) 0 0
\(213\) −14.4374 + 10.4894i −0.989237 + 0.718723i
\(214\) 0 0
\(215\) 3.97467 2.88777i 0.271070 0.196944i
\(216\) 0 0
\(217\) −2.30062 1.67150i −0.156176 0.113469i
\(218\) 0 0
\(219\) 28.5221 1.92735
\(220\) 0 0
\(221\) −6.87312 21.1533i −0.462336 1.42292i
\(222\) 0 0
\(223\) −8.57042 + 26.3770i −0.573918 + 1.76634i 0.0659172 + 0.997825i \(0.479003\pi\)
−0.639835 + 0.768512i \(0.720997\pi\)
\(224\) 0 0
\(225\) 21.5253 + 66.2479i 1.43502 + 4.41653i
\(226\) 0 0
\(227\) 6.55351 + 20.1696i 0.434972 + 1.33871i 0.893116 + 0.449827i \(0.148514\pi\)
−0.458144 + 0.888878i \(0.651486\pi\)
\(228\) 0 0
\(229\) −20.9804 + 15.2431i −1.38642 + 1.00729i −0.390175 + 0.920741i \(0.627585\pi\)
−0.996247 + 0.0865540i \(0.972415\pi\)
\(230\) 0 0
\(231\) −5.52393 4.01337i −0.363448 0.264060i
\(232\) 0 0
\(233\) 3.35757 10.3336i 0.219962 0.676974i −0.778802 0.627270i \(-0.784172\pi\)
0.998764 0.0497036i \(-0.0158277\pi\)
\(234\) 0 0
\(235\) −7.35208 + 5.34160i −0.479597 + 0.348448i
\(236\) 0 0
\(237\) −25.7466 −1.67242
\(238\) 0 0
\(239\) 1.75412 + 5.39864i 0.113465 + 0.349209i 0.991624 0.129160i \(-0.0412282\pi\)
−0.878159 + 0.478369i \(0.841228\pi\)
\(240\) 0 0
\(241\) 19.0987 + 13.8760i 1.23025 + 0.893831i 0.996909 0.0785629i \(-0.0250332\pi\)
0.233344 + 0.972394i \(0.425033\pi\)
\(242\) 0 0
\(243\) 12.0976 0.776064
\(244\) 0 0
\(245\) 4.29373 0.274316
\(246\) 0 0
\(247\) −5.70113 −0.362754
\(248\) 0 0
\(249\) 10.0464 0.636663
\(250\) 0 0
\(251\) −14.7736 10.7337i −0.932503 0.677503i 0.0141011 0.999901i \(-0.495511\pi\)
−0.946604 + 0.322397i \(0.895511\pi\)
\(252\) 0 0
\(253\) −1.00929 3.10629i −0.0634538 0.195291i
\(254\) 0 0
\(255\) 96.0715 6.01623
\(256\) 0 0
\(257\) −10.2419 + 7.44120i −0.638875 + 0.464170i −0.859463 0.511197i \(-0.829202\pi\)
0.220589 + 0.975367i \(0.429202\pi\)
\(258\) 0 0
\(259\) 3.54098 10.8980i 0.220026 0.677169i
\(260\) 0 0
\(261\) −16.4763 11.9707i −1.01986 0.740969i
\(262\) 0 0
\(263\) 8.65956 6.29154i 0.533972 0.387953i −0.287870 0.957670i \(-0.592947\pi\)
0.821841 + 0.569717i \(0.192947\pi\)
\(264\) 0 0
\(265\) −7.22662 22.2412i −0.443928 1.36627i
\(266\) 0 0
\(267\) −4.57883 14.0922i −0.280220 0.862428i
\(268\) 0 0
\(269\) 0.440874 1.35687i 0.0268806 0.0827299i −0.936716 0.350090i \(-0.886151\pi\)
0.963597 + 0.267360i \(0.0861512\pi\)
\(270\) 0 0
\(271\) −3.64011 11.2031i −0.221121 0.680541i −0.998662 0.0517087i \(-0.983533\pi\)
0.777541 0.628832i \(-0.216467\pi\)
\(272\) 0 0
\(273\) −8.13569 −0.492394
\(274\) 0 0
\(275\) 25.9436 + 18.8491i 1.56446 + 1.13664i
\(276\) 0 0
\(277\) 17.7737 12.9133i 1.06792 0.775886i 0.0923794 0.995724i \(-0.470553\pi\)
0.975536 + 0.219838i \(0.0705528\pi\)
\(278\) 0 0
\(279\) −11.9272 + 8.66559i −0.714061 + 0.518796i
\(280\) 0 0
\(281\) 1.85782 5.71778i 0.110828 0.341094i −0.880226 0.474555i \(-0.842609\pi\)
0.991054 + 0.133461i \(0.0426090\pi\)
\(282\) 0 0
\(283\) 1.53212 + 1.11315i 0.0910751 + 0.0661699i 0.632391 0.774649i \(-0.282074\pi\)
−0.541316 + 0.840819i \(0.682074\pi\)
\(284\) 0 0
\(285\) 7.60968 23.4202i 0.450758 1.38729i
\(286\) 0 0
\(287\) 6.35275 0.801636i 0.374991 0.0473191i
\(288\) 0 0
\(289\) 13.6492 42.0080i 0.802896 2.47106i
\(290\) 0 0
\(291\) 33.4625 + 24.3119i 1.96160 + 1.42519i
\(292\) 0 0
\(293\) −1.46997 + 4.52410i −0.0858766 + 0.264301i −0.984769 0.173869i \(-0.944373\pi\)
0.898892 + 0.438170i \(0.144373\pi\)
\(294\) 0 0
\(295\) 33.4200 24.2810i 1.94579 1.41370i
\(296\) 0 0
\(297\) −12.0660 + 8.76650i −0.700143 + 0.508684i
\(298\) 0 0
\(299\) −3.14845 2.28749i −0.182080 0.132289i
\(300\) 0 0
\(301\) −1.14422 −0.0659516
\(302\) 0 0
\(303\) −5.44102 16.7457i −0.312578 0.962018i
\(304\) 0 0
\(305\) −7.08493 + 21.8052i −0.405682 + 1.24856i
\(306\) 0 0
\(307\) −4.32593 13.3138i −0.246894 0.759861i −0.995319 0.0966421i \(-0.969190\pi\)
0.748425 0.663219i \(-0.230810\pi\)
\(308\) 0 0
\(309\) 9.82226 + 30.2298i 0.558769 + 1.71971i
\(310\) 0 0
\(311\) −7.99874 + 5.81142i −0.453567 + 0.329535i −0.791002 0.611813i \(-0.790440\pi\)
0.337436 + 0.941349i \(0.390440\pi\)
\(312\) 0 0
\(313\) 6.94427 + 5.04531i 0.392513 + 0.285178i 0.766485 0.642263i \(-0.222004\pi\)
−0.373971 + 0.927440i \(0.622004\pi\)
\(314\) 0 0
\(315\) 6.87875 21.1706i 0.387573 1.19283i
\(316\) 0 0
\(317\) −4.07374 + 2.95975i −0.228804 + 0.166236i −0.696281 0.717769i \(-0.745163\pi\)
0.467477 + 0.884005i \(0.345163\pi\)
\(318\) 0 0
\(319\) −9.37580 −0.524944
\(320\) 0 0
\(321\) 11.5995 + 35.6995i 0.647419 + 1.99255i
\(322\) 0 0
\(323\) −12.6848 9.21606i −0.705802 0.512795i
\(324\) 0 0
\(325\) 38.2100 2.11951
\(326\) 0 0
\(327\) 22.2761 1.23187
\(328\) 0 0
\(329\) 2.11650 0.116686
\(330\) 0 0
\(331\) −31.4824 −1.73043 −0.865216 0.501400i \(-0.832819\pi\)
−0.865216 + 0.501400i \(0.832819\pi\)
\(332\) 0 0
\(333\) −48.0608 34.9182i −2.63371 1.91350i
\(334\) 0 0
\(335\) −14.3348 44.1180i −0.783194 2.41042i
\(336\) 0 0
\(337\) −9.15986 −0.498970 −0.249485 0.968379i \(-0.580261\pi\)
−0.249485 + 0.968379i \(0.580261\pi\)
\(338\) 0 0
\(339\) −15.2264 + 11.0627i −0.826987 + 0.600841i
\(340\) 0 0
\(341\) −2.09734 + 6.45494i −0.113577 + 0.349555i
\(342\) 0 0
\(343\) −0.809017 0.587785i −0.0436828 0.0317374i
\(344\) 0 0
\(345\) 13.5994 9.88056i 0.732169 0.531952i
\(346\) 0 0
\(347\) −5.34576 16.4526i −0.286976 0.883220i −0.985800 0.167926i \(-0.946293\pi\)
0.698824 0.715294i \(-0.253707\pi\)
\(348\) 0 0
\(349\) 0.160432 + 0.493758i 0.00858771 + 0.0264303i 0.955259 0.295772i \(-0.0955769\pi\)
−0.946671 + 0.322202i \(0.895577\pi\)
\(350\) 0 0
\(351\) −5.49154 + 16.9012i −0.293117 + 0.902120i
\(352\) 0 0
\(353\) 1.83645 + 5.65200i 0.0977442 + 0.300826i 0.987959 0.154715i \(-0.0494460\pi\)
−0.890215 + 0.455541i \(0.849446\pi\)
\(354\) 0 0
\(355\) −26.7840 −1.42155
\(356\) 0 0
\(357\) −18.1016 13.1516i −0.958040 0.696057i
\(358\) 0 0
\(359\) −29.4848 + 21.4220i −1.55615 + 1.13061i −0.617072 + 0.786907i \(0.711681\pi\)
−0.939079 + 0.343702i \(0.888319\pi\)
\(360\) 0 0
\(361\) 12.1199 8.80562i 0.637890 0.463454i
\(362\) 0 0
\(363\) 4.68865 14.4302i 0.246090 0.757388i
\(364\) 0 0
\(365\) 34.6324 + 25.1619i 1.81274 + 1.31704i
\(366\) 0 0
\(367\) 3.95425 12.1699i 0.206410 0.635265i −0.793242 0.608906i \(-0.791609\pi\)
0.999653 0.0263590i \(-0.00839130\pi\)
\(368\) 0 0
\(369\) 6.22484 32.6070i 0.324052 1.69745i
\(370\) 0 0
\(371\) −1.68306 + 5.17993i −0.0873803 + 0.268929i
\(372\) 0 0
\(373\) 0.556622 + 0.404409i 0.0288208 + 0.0209395i 0.602102 0.798419i \(-0.294330\pi\)
−0.573282 + 0.819358i \(0.694330\pi\)
\(374\) 0 0
\(375\) −32.0222 + 98.5541i −1.65362 + 5.08931i
\(376\) 0 0
\(377\) −9.03796 + 6.56646i −0.465478 + 0.338190i
\(378\) 0 0
\(379\) −21.9355 + 15.9371i −1.12675 + 0.818633i −0.985219 0.171301i \(-0.945203\pi\)
−0.141533 + 0.989934i \(0.545203\pi\)
\(380\) 0 0
\(381\) 20.3920 + 14.8156i 1.04471 + 0.759029i
\(382\) 0 0
\(383\) −32.1677 −1.64369 −0.821846 0.569709i \(-0.807056\pi\)
−0.821846 + 0.569709i \(0.807056\pi\)
\(384\) 0 0
\(385\) −3.16676 9.74630i −0.161393 0.496717i
\(386\) 0 0
\(387\) −1.83309 + 5.64167i −0.0931811 + 0.286782i
\(388\) 0 0
\(389\) −6.24481 19.2195i −0.316624 0.974469i −0.975081 0.221851i \(-0.928790\pi\)
0.658456 0.752619i \(-0.271210\pi\)
\(390\) 0 0
\(391\) −3.30741 10.1792i −0.167263 0.514782i
\(392\) 0 0
\(393\) −13.6480 + 9.91587i −0.688452 + 0.500190i
\(394\) 0 0
\(395\) −31.2623 22.7134i −1.57298 1.14283i
\(396\) 0 0
\(397\) 4.81492 14.8188i 0.241654 0.743734i −0.754515 0.656283i \(-0.772128\pi\)
0.996169 0.0874511i \(-0.0278722\pi\)
\(398\) 0 0
\(399\) −4.63988 + 3.37107i −0.232285 + 0.168765i
\(400\) 0 0
\(401\) −8.25948 −0.412459 −0.206229 0.978504i \(-0.566119\pi\)
−0.206229 + 0.978504i \(0.566119\pi\)
\(402\) 0 0
\(403\) 2.49904 + 7.69125i 0.124486 + 0.383128i
\(404\) 0 0
\(405\) −8.07374 5.86592i −0.401187 0.291480i
\(406\) 0 0
\(407\) −27.3489 −1.35563
\(408\) 0 0
\(409\) 24.2378 1.19848 0.599240 0.800569i \(-0.295470\pi\)
0.599240 + 0.800569i \(0.295470\pi\)
\(410\) 0 0
\(411\) 56.4144 2.78272
\(412\) 0 0
\(413\) −9.62086 −0.473412
\(414\) 0 0
\(415\) 12.1986 + 8.86280i 0.598806 + 0.435058i
\(416\) 0 0
\(417\) −20.3843 62.7364i −0.998223 3.07222i
\(418\) 0 0
\(419\) −17.2743 −0.843904 −0.421952 0.906618i \(-0.638655\pi\)
−0.421952 + 0.906618i \(0.638655\pi\)
\(420\) 0 0
\(421\) −15.9576 + 11.5939i −0.777727 + 0.565052i −0.904296 0.426906i \(-0.859603\pi\)
0.126569 + 0.991958i \(0.459603\pi\)
\(422\) 0 0
\(423\) 3.39073 10.4356i 0.164863 0.507395i
\(424\) 0 0
\(425\) 85.0159 + 61.7676i 4.12387 + 2.99617i
\(426\) 0 0
\(427\) 4.31992 3.13861i 0.209056 0.151888i
\(428\) 0 0
\(429\) 6.00033 + 18.4671i 0.289699 + 0.891601i
\(430\) 0 0
\(431\) −1.42075 4.37263i −0.0684353 0.210622i 0.910990 0.412428i \(-0.135319\pi\)
−0.979426 + 0.201806i \(0.935319\pi\)
\(432\) 0 0
\(433\) 0.792408 2.43878i 0.0380807 0.117200i −0.930209 0.367030i \(-0.880375\pi\)
0.968290 + 0.249830i \(0.0803746\pi\)
\(434\) 0 0
\(435\) −14.9114 45.8925i −0.714946 2.20038i
\(436\) 0 0
\(437\) −2.74344 −0.131236
\(438\) 0 0
\(439\) 13.0515 + 9.48244i 0.622912 + 0.452572i 0.853937 0.520376i \(-0.174208\pi\)
−0.231025 + 0.972948i \(0.574208\pi\)
\(440\) 0 0
\(441\) −4.19421 + 3.04727i −0.199724 + 0.145108i
\(442\) 0 0
\(443\) 26.8166 19.4834i 1.27410 0.925684i 0.274737 0.961519i \(-0.411409\pi\)
0.999358 + 0.0358351i \(0.0114091\pi\)
\(444\) 0 0
\(445\) 6.87223 21.1505i 0.325775 1.00263i
\(446\) 0 0
\(447\) −16.1736 11.7508i −0.764983 0.555792i
\(448\) 0 0
\(449\) 4.65246 14.3188i 0.219563 0.675746i −0.779235 0.626732i \(-0.784392\pi\)
0.998798 0.0490138i \(-0.0156078\pi\)
\(450\) 0 0
\(451\) −6.50498 13.8288i −0.306308 0.651173i
\(452\) 0 0
\(453\) −14.1492 + 43.5467i −0.664786 + 2.04600i
\(454\) 0 0
\(455\) −9.87860 7.17722i −0.463116 0.336473i
\(456\) 0 0
\(457\) 7.99588 24.6088i 0.374032 1.15115i −0.570098 0.821577i \(-0.693095\pi\)
0.944130 0.329574i \(-0.106905\pi\)
\(458\) 0 0
\(459\) −39.5398 + 28.7274i −1.84556 + 1.34088i
\(460\) 0 0
\(461\) 19.6842 14.3014i 0.916783 0.666082i −0.0259378 0.999664i \(-0.508257\pi\)
0.942721 + 0.333581i \(0.108257\pi\)
\(462\) 0 0
\(463\) −4.51693 3.28175i −0.209920 0.152516i 0.477858 0.878437i \(-0.341413\pi\)
−0.687777 + 0.725922i \(0.741413\pi\)
\(464\) 0 0
\(465\) −34.9312 −1.61990
\(466\) 0 0
\(467\) 0.645695 + 1.98725i 0.0298792 + 0.0919588i 0.964884 0.262676i \(-0.0846051\pi\)
−0.935005 + 0.354635i \(0.884605\pi\)
\(468\) 0 0
\(469\) −3.33854 + 10.2750i −0.154160 + 0.474455i
\(470\) 0 0
\(471\) 16.0103 + 49.2745i 0.737713 + 2.27045i
\(472\) 0 0
\(473\) 0.843898 + 2.59725i 0.0388025 + 0.119422i
\(474\) 0 0
\(475\) 21.7916 15.8325i 0.999867 0.726446i
\(476\) 0 0
\(477\) 22.8438 + 16.5970i 1.04594 + 0.759923i
\(478\) 0 0
\(479\) 2.79687 8.60787i 0.127792 0.393304i −0.866607 0.498991i \(-0.833704\pi\)
0.994399 + 0.105687i \(0.0337042\pi\)
\(480\) 0 0
\(481\) −26.3634 + 19.1541i −1.20207 + 0.873353i
\(482\) 0 0
\(483\) −3.91497 −0.178137
\(484\) 0 0
\(485\) 19.1834 + 59.0405i 0.871074 + 2.68089i
\(486\) 0 0
\(487\) −6.76593 4.91574i −0.306594 0.222753i 0.423840 0.905737i \(-0.360682\pi\)
−0.730433 + 0.682984i \(0.760682\pi\)
\(488\) 0 0
\(489\) −7.36857 −0.333218
\(490\) 0 0
\(491\) −27.5935 −1.24528 −0.622638 0.782510i \(-0.713939\pi\)
−0.622638 + 0.782510i \(0.713939\pi\)
\(492\) 0 0
\(493\) −30.7240 −1.38374
\(494\) 0 0
\(495\) −53.1283 −2.38794
\(496\) 0 0
\(497\) 5.04660 + 3.66657i 0.226371 + 0.164468i
\(498\) 0 0
\(499\) −5.61824 17.2912i −0.251507 0.774059i −0.994498 0.104757i \(-0.966593\pi\)
0.742991 0.669302i \(-0.233407\pi\)
\(500\) 0 0
\(501\) 54.4125 2.43097
\(502\) 0 0
\(503\) 8.91619 6.47799i 0.397553 0.288839i −0.370990 0.928637i \(-0.620982\pi\)
0.768544 + 0.639797i \(0.220982\pi\)
\(504\) 0 0
\(505\) 8.16627 25.1332i 0.363394 1.11841i
\(506\) 0 0
\(507\) −11.3701 8.26089i −0.504966 0.366879i
\(508\) 0 0
\(509\) 20.2038 14.6789i 0.895519 0.650633i −0.0417920 0.999126i \(-0.513307\pi\)
0.937311 + 0.348494i \(0.113307\pi\)
\(510\) 0 0
\(511\) −3.08087 9.48193i −0.136290 0.419456i
\(512\) 0 0
\(513\) 3.87123 + 11.9144i 0.170919 + 0.526034i
\(514\) 0 0
\(515\) −14.7419 + 45.3710i −0.649607 + 1.99929i
\(516\) 0 0
\(517\) −1.56099 4.80422i −0.0686521 0.211290i
\(518\) 0 0
\(519\) −40.5167 −1.77848
\(520\) 0 0
\(521\) −5.14579 3.73863i −0.225441 0.163792i 0.469332 0.883022i \(-0.344495\pi\)
−0.694772 + 0.719230i \(0.744495\pi\)
\(522\) 0 0
\(523\) 1.11940 0.813292i 0.0489480 0.0355628i −0.563042 0.826428i \(-0.690369\pi\)
0.611990 + 0.790865i \(0.290369\pi\)
\(524\) 0 0
\(525\) 31.0973 22.5935i 1.35720 0.986062i
\(526\) 0 0
\(527\) −6.87288 + 21.1525i −0.299387 + 0.921419i
\(528\) 0 0
\(529\) 17.0923 + 12.4183i 0.743145 + 0.539926i
\(530\) 0 0
\(531\) −15.4131 + 47.4365i −0.668869 + 2.05857i
\(532\) 0 0
\(533\) −15.9558 8.77466i −0.691121 0.380073i
\(534\) 0 0
\(535\) −17.4093 + 53.5803i −0.752670 + 2.31648i
\(536\) 0 0
\(537\) −23.3859 16.9909i −1.00918 0.733210i
\(538\) 0 0
\(539\) −0.737532 + 2.26989i −0.0317678 + 0.0977711i
\(540\) 0 0
\(541\) −10.6277 + 7.72150i −0.456922 + 0.331973i −0.792323 0.610102i \(-0.791128\pi\)
0.335401 + 0.942076i \(0.391128\pi\)
\(542\) 0 0
\(543\) 39.2778 28.5370i 1.68557 1.22464i
\(544\) 0 0
\(545\) 27.0483 + 19.6518i 1.15862 + 0.841789i
\(546\) 0 0
\(547\) 10.3714 0.443448 0.221724 0.975109i \(-0.428832\pi\)
0.221724 + 0.975109i \(0.428832\pi\)
\(548\) 0 0
\(549\) −8.55447 26.3279i −0.365096 1.12365i
\(550\) 0 0
\(551\) −2.43360 + 7.48986i −0.103675 + 0.319079i
\(552\) 0 0
\(553\) 2.78106 + 8.55922i 0.118263 + 0.363975i
\(554\) 0 0
\(555\) −43.4960 133.867i −1.84630 5.68233i
\(556\) 0 0
\(557\) 15.3510 11.1531i 0.650442 0.472574i −0.212980 0.977057i \(-0.568317\pi\)
0.863422 + 0.504483i \(0.168317\pi\)
\(558\) 0 0
\(559\) 2.63251 + 1.91263i 0.111343 + 0.0808955i
\(560\) 0 0
\(561\) −16.5022 + 50.7885i −0.696722 + 2.14429i
\(562\) 0 0
\(563\) 0.262642 0.190821i 0.0110690 0.00804213i −0.582237 0.813019i \(-0.697822\pi\)
0.593306 + 0.804977i \(0.297822\pi\)
\(564\) 0 0
\(565\) −28.2478 −1.18839
\(566\) 0 0
\(567\) 0.718232 + 2.21049i 0.0301629 + 0.0928319i
\(568\) 0 0
\(569\) 14.1732 + 10.2974i 0.594172 + 0.431691i 0.843805 0.536649i \(-0.180310\pi\)
−0.249634 + 0.968340i \(0.580310\pi\)
\(570\) 0 0
\(571\) −13.9911 −0.585507 −0.292754 0.956188i \(-0.594572\pi\)
−0.292754 + 0.956188i \(0.594572\pi\)
\(572\) 0 0
\(573\) 25.0179 1.04514
\(574\) 0 0
\(575\) 18.3870 0.766790
\(576\) 0 0
\(577\) −3.08012 −0.128227 −0.0641135 0.997943i \(-0.520422\pi\)
−0.0641135 + 0.997943i \(0.520422\pi\)
\(578\) 0 0
\(579\) 21.6028 + 15.6954i 0.897782 + 0.652277i
\(580\) 0 0
\(581\) −1.08518 3.33983i −0.0450207 0.138559i
\(582\) 0 0
\(583\) 12.9992 0.538372
\(584\) 0 0
\(585\) −51.2138 + 37.2090i −2.11743 + 1.53840i
\(586\) 0 0
\(587\) 6.06783 18.6748i 0.250446 0.770793i −0.744247 0.667905i \(-0.767191\pi\)
0.994693 0.102889i \(-0.0328086\pi\)
\(588\) 0 0
\(589\) 4.61214 + 3.35092i 0.190040 + 0.138072i
\(590\) 0 0
\(591\) −28.4887 + 20.6982i −1.17187 + 0.851411i
\(592\) 0 0
\(593\) 5.53839 + 17.0454i 0.227434 + 0.699971i 0.998035 + 0.0626532i \(0.0199562\pi\)
−0.770601 + 0.637318i \(0.780044\pi\)
\(594\) 0 0
\(595\) −10.3773 31.9381i −0.425429 1.30934i
\(596\) 0 0
\(597\) 17.9001 55.0910i 0.732604 2.25472i
\(598\) 0 0
\(599\) −7.96065 24.5004i −0.325263 1.00106i −0.971322 0.237769i \(-0.923584\pi\)
0.646058 0.763288i \(-0.276416\pi\)
\(600\) 0 0
\(601\) 33.0305 1.34734 0.673671 0.739031i \(-0.264717\pi\)
0.673671 + 0.739031i \(0.264717\pi\)
\(602\) 0 0
\(603\) 45.3132 + 32.9220i 1.84530 + 1.34069i
\(604\) 0 0
\(605\) 18.4233 13.3853i 0.749012 0.544189i
\(606\) 0 0
\(607\) −12.6954 + 9.22372i −0.515289 + 0.374379i −0.814826 0.579705i \(-0.803168\pi\)
0.299537 + 0.954085i \(0.403168\pi\)
\(608\) 0 0
\(609\) −3.47283 + 10.6883i −0.140726 + 0.433111i
\(610\) 0 0
\(611\) −4.86944 3.53785i −0.196996 0.143126i
\(612\) 0 0
\(613\) −4.74475 + 14.6029i −0.191639 + 0.589804i 0.808361 + 0.588688i \(0.200355\pi\)
−0.999999 + 0.00111595i \(0.999645\pi\)
\(614\) 0 0
\(615\) 57.3435 53.8340i 2.31231 2.17080i
\(616\) 0 0
\(617\) −2.52826 + 7.78120i −0.101784 + 0.313259i −0.988962 0.148168i \(-0.952662\pi\)
0.887178 + 0.461427i \(0.152662\pi\)
\(618\) 0 0
\(619\) 36.4340 + 26.4708i 1.46441 + 1.06395i 0.982188 + 0.187901i \(0.0601685\pi\)
0.482217 + 0.876052i \(0.339832\pi\)
\(620\) 0 0
\(621\) −2.64258 + 8.13302i −0.106043 + 0.326367i
\(622\) 0 0
\(623\) −4.19023 + 3.04438i −0.167878 + 0.121971i
\(624\) 0 0
\(625\) −71.4755 + 51.9300i −2.85902 + 2.07720i
\(626\) 0 0
\(627\) 11.0740 + 8.04575i 0.442254 + 0.321316i
\(628\) 0 0
\(629\) −89.6209 −3.57342
\(630\) 0 0
\(631\) 4.73932 + 14.5861i 0.188669 + 0.580664i 0.999992 0.00393404i \(-0.00125225\pi\)
−0.811323 + 0.584598i \(0.801252\pi\)
\(632\) 0 0
\(633\) 13.5326 41.6489i 0.537871 1.65540i
\(634\) 0 0
\(635\) 11.6904 + 35.9792i 0.463917 + 1.42779i
\(636\) 0 0
\(637\) 0.878790 + 2.70464i 0.0348189 + 0.107162i
\(638\) 0 0
\(639\) 26.1632 19.0087i 1.03500 0.751972i
\(640\) 0 0
\(641\) −11.9045 8.64910i −0.470198 0.341619i 0.327320 0.944913i \(-0.393854\pi\)
−0.797518 + 0.603295i \(0.793854\pi\)
\(642\) 0 0
\(643\) −4.62551 + 14.2359i −0.182412 + 0.561408i −0.999894 0.0145468i \(-0.995369\pi\)
0.817482 + 0.575954i \(0.195369\pi\)
\(644\) 0 0
\(645\) −11.3708 + 8.26140i −0.447726 + 0.325292i
\(646\) 0 0
\(647\) 22.0097 0.865291 0.432646 0.901564i \(-0.357580\pi\)
0.432646 + 0.901564i \(0.357580\pi\)
\(648\) 0 0
\(649\) 7.09570 + 21.8383i 0.278531 + 0.857229i
\(650\) 0 0
\(651\) 6.58168 + 4.78187i 0.257956 + 0.187416i
\(652\) 0 0
\(653\) −5.64792 −0.221020 −0.110510 0.993875i \(-0.535248\pi\)
−0.110510 + 0.993875i \(0.535248\pi\)
\(654\) 0 0
\(655\) −25.3195 −0.989316
\(656\) 0 0
\(657\) −51.6872 −2.01651
\(658\) 0 0
\(659\) 20.5700 0.801295 0.400647 0.916232i \(-0.368785\pi\)
0.400647 + 0.916232i \(0.368785\pi\)
\(660\) 0 0
\(661\) −12.5451 9.11458i −0.487950 0.354516i 0.316446 0.948611i \(-0.397511\pi\)
−0.804395 + 0.594094i \(0.797511\pi\)
\(662\) 0 0
\(663\) 19.6628 + 60.5159i 0.763640 + 2.35024i
\(664\) 0 0
\(665\) −8.60781 −0.333796
\(666\) 0 0
\(667\) −4.34915 + 3.15984i −0.168400 + 0.122350i
\(668\) 0 0
\(669\) 24.5185 75.4601i 0.947939 2.91746i
\(670\) 0 0
\(671\) −10.3104 7.49093i −0.398028 0.289184i
\(672\) 0 0
\(673\) −24.1078 + 17.5154i −0.929288 + 0.675167i −0.945818 0.324696i \(-0.894738\pi\)
0.0165303 + 0.999863i \(0.494738\pi\)
\(674\) 0 0
\(675\) −25.9457 79.8525i −0.998649 3.07352i
\(676\) 0 0
\(677\) −7.05408 21.7102i −0.271110 0.834392i −0.990222 0.139498i \(-0.955451\pi\)
0.719112 0.694894i \(-0.244549\pi\)
\(678\) 0 0
\(679\) 4.46777 13.7504i 0.171457 0.527692i
\(680\) 0 0
\(681\) −18.7485 57.7018i −0.718442 2.21114i
\(682\) 0 0
\(683\) −7.00946 −0.268210 −0.134105 0.990967i \(-0.542816\pi\)
−0.134105 + 0.990967i \(0.542816\pi\)
\(684\) 0 0
\(685\) 68.5001 + 49.7682i 2.61725 + 1.90155i
\(686\) 0 0
\(687\) 60.0212 43.6080i 2.28995 1.66375i
\(688\) 0 0
\(689\) 12.5308 9.10415i 0.477385 0.346841i
\(690\) 0 0
\(691\) 12.9075 39.7251i 0.491023 1.51121i −0.332041 0.943265i \(-0.607737\pi\)
0.823064 0.567949i \(-0.192263\pi\)
\(692\) 0 0
\(693\) 10.0103 + 7.27293i 0.380261 + 0.276276i
\(694\) 0 0
\(695\) 30.5942 94.1593i 1.16050 3.57166i
\(696\) 0 0
\(697\) −21.3165 45.3163i −0.807420 1.71648i
\(698\) 0 0
\(699\) −9.60544 + 29.5625i −0.363311 + 1.11816i
\(700\) 0 0
\(701\) 41.6561 + 30.2649i 1.57333 + 1.14309i 0.923878 + 0.382686i \(0.125001\pi\)
0.649450 + 0.760404i \(0.274999\pi\)
\(702\) 0 0
\(703\) −7.09874 + 21.8477i −0.267734 + 0.824000i
\(704\) 0 0
\(705\) 21.0330 15.2814i 0.792150 0.575531i
\(706\) 0 0
\(707\) −4.97925 + 3.61764i −0.187264 + 0.136055i
\(708\) 0 0
\(709\) −5.92265 4.30306i −0.222430 0.161605i 0.470990 0.882139i \(-0.343897\pi\)
−0.693420 + 0.720534i \(0.743897\pi\)
\(710\) 0 0
\(711\) 46.6574 1.74979
\(712\) 0 0
\(713\) 1.20256 + 3.70110i 0.0450362 + 0.138607i
\(714\) 0 0
\(715\) −9.00572 + 27.7168i −0.336795 + 1.03655i
\(716\) 0 0
\(717\) −5.01824 15.4446i −0.187410 0.576788i
\(718\) 0 0
\(719\) 4.99380 + 15.3693i 0.186237 + 0.573179i 0.999967 0.00806352i \(-0.00256672\pi\)
−0.813730 + 0.581243i \(0.802567\pi\)
\(720\) 0 0
\(721\) 8.98866 6.53065i 0.334755 0.243214i
\(722\) 0 0
\(723\) −54.6380 39.6968i −2.03201 1.47634i
\(724\) 0 0
\(725\) 16.3104 50.1984i 0.605755 1.86432i
\(726\) 0 0
\(727\) −5.25915 + 3.82099i −0.195051 + 0.141713i −0.681024 0.732261i \(-0.738465\pi\)
0.485973 + 0.873974i \(0.338465\pi\)
\(728\) 0 0
\(729\) −41.5820 −1.54007
\(730\) 0 0
\(731\) 2.76541 + 8.51106i 0.102282 + 0.314793i
\(732\) 0 0
\(733\) −2.34452 1.70339i −0.0865967 0.0629162i 0.543644 0.839316i \(-0.317044\pi\)
−0.630241 + 0.776399i \(0.717044\pi\)
\(734\) 0 0
\(735\) −12.2836 −0.453088
\(736\) 0 0
\(737\) 25.7854 0.949817
\(738\) 0 0
\(739\) −52.9575 −1.94807 −0.974036 0.226393i \(-0.927307\pi\)
−0.974036 + 0.226393i \(0.927307\pi\)
\(740\) 0 0
\(741\) 16.3099 0.599160
\(742\) 0 0
\(743\) 38.8527 + 28.2282i 1.42537 + 1.03559i 0.990856 + 0.134924i \(0.0430792\pi\)
0.434512 + 0.900666i \(0.356921\pi\)
\(744\) 0 0
\(745\) −9.27200 28.5363i −0.339700 1.04549i
\(746\) 0 0
\(747\) −18.2058 −0.666116
\(748\) 0 0
\(749\) 10.6151 7.71229i 0.387865 0.281801i
\(750\) 0 0
\(751\) −9.51458 + 29.2829i −0.347192 + 1.06855i 0.613208 + 0.789922i \(0.289879\pi\)
−0.960400 + 0.278626i \(0.910121\pi\)
\(752\) 0 0
\(753\) 42.2648 + 30.7072i 1.54021 + 1.11903i
\(754\) 0 0
\(755\) −55.5967 + 40.3934i −2.02337 + 1.47007i
\(756\) 0 0
\(757\) 11.5636 + 35.5892i 0.420288 + 1.29351i 0.907435 + 0.420193i \(0.138037\pi\)
−0.487147 + 0.873320i \(0.661963\pi\)
\(758\) 0 0
\(759\) 2.88742 + 8.88655i 0.104807 + 0.322562i
\(760\) 0 0
\(761\) 6.37875 19.6318i 0.231229 0.711651i −0.766370 0.642400i \(-0.777939\pi\)
0.997599 0.0692513i \(-0.0220610\pi\)
\(762\) 0 0
\(763\) −2.40619 7.40550i −0.0871100 0.268097i
\(764\) 0 0
\(765\) −174.099 −6.29455
\(766\) 0 0
\(767\) 22.1347 + 16.0818i 0.799239 + 0.580681i
\(768\) 0 0
\(769\) 12.3984 9.00796i 0.447097 0.324835i −0.341351 0.939936i \(-0.610885\pi\)
0.788449 + 0.615101i \(0.210885\pi\)
\(770\) 0 0
\(771\) 29.3004 21.2880i 1.05523 0.766668i
\(772\) 0 0
\(773\) −11.2584 + 34.6497i −0.404935 + 1.24626i 0.516014 + 0.856580i \(0.327415\pi\)
−0.920949 + 0.389682i \(0.872585\pi\)
\(774\) 0 0
\(775\) −30.9114 22.4585i −1.11037 0.806731i
\(776\) 0 0
\(777\) −10.1301 + 31.1773i −0.363416 + 1.11848i
\(778\) 0 0
\(779\) −12.7356 + 1.60707i −0.456300 + 0.0575793i
\(780\) 0 0
\(781\) 4.60068 14.1594i 0.164625 0.506665i
\(782\) 0 0
\(783\) 19.8598 + 14.4290i 0.709733 + 0.515651i
\(784\) 0 0
\(785\) −24.0293 + 73.9546i −0.857643 + 2.63955i
\(786\) 0 0
\(787\) −8.25578 + 5.99818i −0.294287 + 0.213812i −0.725125 0.688617i \(-0.758218\pi\)
0.430838 + 0.902429i \(0.358218\pi\)
\(788\) 0 0
\(789\) −24.7735 + 17.9990i −0.881960 + 0.640782i
\(790\) 0 0
\(791\) 5.32239 + 3.86694i 0.189243 + 0.137493i
\(792\) 0 0
\(793\) −15.1852 −0.539243
\(794\) 0 0
\(795\) 20.6741 + 63.6283i 0.733234 + 2.25666i
\(796\) 0 0
\(797\) 12.0070 36.9536i 0.425308 1.30896i −0.477390 0.878691i \(-0.658417\pi\)
0.902699 0.430273i \(-0.141583\pi\)
\(798\) 0 0
\(799\) −5.11528 15.7432i −0.180965 0.556955i
\(800\) 0 0
\(801\) 8.29765 + 25.5375i 0.293183 + 0.902325i
\(802\) 0 0
\(803\) −19.2507 + 13.9865i −0.679343 + 0.493572i
\(804\) 0 0
\(805\) −4.75367 3.45375i −0.167545 0.121729i
\(806\) 0 0
\(807\) −1.26126 + 3.88177i −0.0443986 + 0.136645i
\(808\) 0 0
\(809\) 21.0169 15.2696i 0.738914 0.536852i −0.153457 0.988155i \(-0.549041\pi\)
0.892371 + 0.451303i \(0.149041\pi\)
\(810\) 0 0
\(811\) 48.0855 1.68851 0.844255 0.535941i \(-0.180043\pi\)
0.844255 + 0.535941i \(0.180043\pi\)
\(812\) 0 0
\(813\) 10.4137 + 32.0502i 0.365225 + 1.12405i
\(814\) 0 0
\(815\) −8.94714 6.50048i −0.313405 0.227702i
\(816\) 0 0
\(817\) 2.29386 0.0802520
\(818\) 0 0
\(819\) 14.7433 0.515173
\(820\) 0 0
\(821\) 34.9151 1.21854 0.609272 0.792961i \(-0.291462\pi\)
0.609272 + 0.792961i \(0.291462\pi\)
\(822\) 0 0
\(823\) 37.8381 1.31895 0.659477 0.751725i \(-0.270778\pi\)
0.659477 + 0.751725i \(0.270778\pi\)
\(824\) 0 0
\(825\) −74.2201 53.9240i −2.58401 1.87739i
\(826\) 0 0
\(827\) 12.7109 + 39.1200i 0.442000 + 1.36033i 0.885741 + 0.464180i \(0.153651\pi\)
−0.443741 + 0.896155i \(0.646349\pi\)
\(828\) 0 0
\(829\) −23.5797 −0.818958 −0.409479 0.912319i \(-0.634290\pi\)
−0.409479 + 0.912319i \(0.634290\pi\)
\(830\) 0 0
\(831\) −50.8474 + 36.9428i −1.76388 + 1.28153i
\(832\) 0 0
\(833\) −2.41686 + 7.43832i −0.0837391 + 0.257723i
\(834\) 0 0
\(835\) 66.0692 + 48.0021i 2.28642 + 1.66118i
\(836\) 0 0
\(837\) 14.3765 10.4452i 0.496925 0.361037i
\(838\) 0 0
\(839\) −10.1004 31.0858i −0.348704 1.07320i −0.959571 0.281468i \(-0.909179\pi\)
0.610866 0.791734i \(-0.290821\pi\)
\(840\) 0 0
\(841\) −4.19277 12.9040i −0.144578 0.444967i
\(842\) 0 0
\(843\) −5.31490 + 16.3576i −0.183055 + 0.563385i
\(844\) 0 0
\(845\) −6.51829 20.0612i −0.224236 0.690127i
\(846\) 0 0
\(847\) −5.30364 −0.182235
\(848\) 0 0
\(849\) −4.38313 3.18453i −0.150429 0.109293i
\(850\) 0 0
\(851\) −12.6863 + 9.21715i −0.434881 + 0.315960i
\(852\) 0 0
\(853\) −22.2640 + 16.1757i −0.762304 + 0.553847i −0.899616 0.436681i \(-0.856154\pi\)
0.137312 + 0.990528i \(0.456154\pi\)
\(854\) 0 0
\(855\) −13.7901 + 42.4415i −0.471611 + 1.45147i
\(856\) 0 0
\(857\) −40.5448 29.4575i −1.38498 1.00625i −0.996395 0.0848382i \(-0.972963\pi\)
−0.388589 0.921411i \(-0.627037\pi\)
\(858\) 0 0
\(859\) 13.7081 42.1892i 0.467715 1.43948i −0.387821 0.921735i \(-0.626772\pi\)
0.855536 0.517743i \(-0.173228\pi\)
\(860\) 0 0
\(861\) −18.1741 + 2.29334i −0.619372 + 0.0781569i
\(862\) 0 0
\(863\) 11.1973 34.4617i 0.381161 1.17309i −0.558067 0.829796i \(-0.688457\pi\)
0.939227 0.343296i \(-0.111543\pi\)
\(864\) 0 0
\(865\) −49.1965 35.7434i −1.67273 1.21531i
\(866\) 0 0
\(867\) −39.0481 + 120.178i −1.32614 + 4.08144i
\(868\) 0 0
\(869\) 17.3774 12.6254i 0.589487 0.428288i
\(870\) 0 0
\(871\) 24.8562 18.0591i 0.842221 0.611910i
\(872\) 0 0
\(873\) −60.6399 44.0575i −2.05235 1.49112i
\(874\) 0 0
\(875\) 36.2224 1.22454
\(876\) 0 0
\(877\) 9.02942 + 27.7897i 0.304902 + 0.938391i 0.979714 + 0.200402i \(0.0642247\pi\)
−0.674812 + 0.737990i \(0.735775\pi\)
\(878\) 0 0
\(879\) 4.20533 12.9427i 0.141842 0.436546i
\(880\) 0 0
\(881\) −7.02940 21.6343i −0.236826 0.728877i −0.996874 0.0790092i \(-0.974824\pi\)
0.760047 0.649868i \(-0.225176\pi\)
\(882\) 0 0
\(883\) 12.3418 + 37.9840i 0.415333 + 1.27826i 0.911953 + 0.410295i \(0.134574\pi\)
−0.496620 + 0.867968i \(0.665426\pi\)
\(884\) 0 0
\(885\) −95.6088 + 69.4639i −3.21385 + 2.33500i
\(886\) 0 0
\(887\) −37.4032 27.1750i −1.25588 0.912447i −0.257328 0.966324i \(-0.582842\pi\)
−0.998548 + 0.0538768i \(0.982842\pi\)
\(888\) 0 0
\(889\) 2.72266 8.37948i 0.0913150 0.281039i
\(890\) 0 0
\(891\) 4.48786 3.26062i 0.150349 0.109235i
\(892\) 0 0
\(893\) −4.24303 −0.141988
\(894\) 0 0
\(895\) −13.4067 41.2616i −0.448137 1.37922i
\(896\) 0 0
\(897\) 9.00718 + 6.54410i 0.300741 + 0.218501i
\(898\) 0 0
\(899\) 11.1711 0.372578
\(900\) 0 0
\(901\) 42.5977 1.41914
\(902\) 0 0
\(903\) 3.27341 0.108932
\(904\) 0 0
\(905\) 72.8674 2.42219
\(906\) 0 0
\(907\) −10.3969 7.55378i −0.345223 0.250819i 0.401639 0.915798i \(-0.368441\pi\)
−0.746862 + 0.664979i \(0.768441\pi\)
\(908\) 0 0
\(909\) 9.86010 + 30.3463i 0.327039 + 1.00652i
\(910\) 0 0
\(911\) −28.5040 −0.944379 −0.472189 0.881497i \(-0.656536\pi\)
−0.472189 + 0.881497i \(0.656536\pi\)
\(912\) 0 0
\(913\) −6.78069 + 4.92646i −0.224408 + 0.163042i
\(914\) 0 0
\(915\) 20.2687 62.3808i 0.670064 2.06224i
\(916\) 0 0
\(917\) 4.77066 + 3.46609i 0.157541 + 0.114460i
\(918\) 0 0
\(919\) 33.2573 24.1629i 1.09706 0.797060i 0.116481 0.993193i \(-0.462838\pi\)
0.980577 + 0.196133i \(0.0628385\pi\)
\(920\) 0 0
\(921\) 12.3757 + 38.0886i 0.407794 + 1.25506i
\(922\) 0 0
\(923\) −5.48184 16.8714i −0.180437 0.555328i
\(924\) 0 0
\(925\) 47.5770 146.427i 1.56432 4.81449i
\(926\) 0 0
\(927\) −17.7997 54.7818i −0.584618 1.79927i
\(928\) 0 0
\(929\) 6.28138 0.206085 0.103043 0.994677i \(-0.467142\pi\)
0.103043 + 0.994677i \(0.467142\pi\)
\(930\) 0 0
\(931\) 1.62187 + 1.17836i 0.0531546 + 0.0386191i
\(932\) 0 0
\(933\) 22.8830 16.6255i 0.749155 0.544293i
\(934\) 0 0
\(935\) −64.8425 + 47.1108i −2.12058 + 1.54069i
\(936\) 0 0
\(937\) −7.27331 + 22.3849i −0.237609 + 0.731284i 0.759156 + 0.650909i \(0.225612\pi\)
−0.996765 + 0.0803754i \(0.974388\pi\)
\(938\) 0 0
\(939\) −19.8663 14.4337i −0.648314 0.471027i
\(940\) 0 0
\(941\) 8.06914 24.8342i 0.263046 0.809573i −0.729091 0.684417i \(-0.760057\pi\)
0.992137 0.125156i \(-0.0399432\pi\)
\(942\) 0 0
\(943\) −7.67806 4.22245i −0.250032 0.137502i
\(944\) 0 0
\(945\) −8.29136 + 25.5182i −0.269718 + 0.830106i
\(946\) 0 0
\(947\) 10.7226 + 7.79046i 0.348439 + 0.253156i 0.748214 0.663458i \(-0.230912\pi\)
−0.399775 + 0.916613i \(0.630912\pi\)
\(948\) 0 0
\(949\) −8.76145 + 26.9650i −0.284409 + 0.875320i
\(950\) 0 0
\(951\) 11.6543 8.46733i 0.377916 0.274572i
\(952\) 0 0
\(953\) 7.21435 5.24153i 0.233696 0.169790i −0.464774 0.885429i \(-0.653865\pi\)
0.698470 + 0.715639i \(0.253865\pi\)
\(954\) 0 0
\(955\) 30.3775 + 22.0705i 0.982993 + 0.714186i
\(956\) 0 0
\(957\) 26.8225 0.867049
\(958\) 0 0
\(959\) −6.09370 18.7545i −0.196776 0.605614i
\(960\) 0 0
\(961\) −7.08058 + 21.7918i −0.228406 + 0.702961i
\(962\) 0 0
\(963\) −21.0203 64.6938i −0.677370 2.08473i
\(964\) 0 0
\(965\) 12.3845 + 38.1155i 0.398671 + 1.22698i
\(966\) 0 0
\(967\) 9.91111 7.20084i 0.318720 0.231563i −0.416909 0.908948i \(-0.636887\pi\)
0.735629 + 0.677385i \(0.236887\pi\)
\(968\) 0 0
\(969\) 36.2890 + 26.3655i 1.16577 + 0.846983i
\(970\) 0 0
\(971\) −15.1604 + 46.6590i −0.486521 + 1.49736i 0.343244 + 0.939246i \(0.388474\pi\)
−0.829765 + 0.558113i \(0.811526\pi\)
\(972\) 0 0
\(973\) −18.6543 + 13.5532i −0.598030 + 0.434494i
\(974\) 0 0
\(975\) −109.312 −3.50079
\(976\) 0 0
\(977\) −4.59866 14.1532i −0.147124 0.452802i 0.850154 0.526534i \(-0.176509\pi\)
−0.997278 + 0.0737325i \(0.976509\pi\)
\(978\) 0 0
\(979\) 10.0009 + 7.26604i 0.319629 + 0.232224i
\(980\) 0 0
\(981\) −40.3683 −1.28886
\(982\) 0 0
\(983\) −20.5699 −0.656077 −0.328038 0.944664i \(-0.606388\pi\)
−0.328038 + 0.944664i \(0.606388\pi\)
\(984\) 0 0
\(985\) −52.8515 −1.68399
\(986\) 0 0
\(987\) −6.05494 −0.192731
\(988\) 0 0
\(989\) 1.26679 + 0.920374i 0.0402815 + 0.0292662i
\(990\) 0 0
\(991\) −7.89316 24.2927i −0.250735 0.771682i −0.994640 0.103397i \(-0.967029\pi\)
0.743906 0.668285i \(-0.232971\pi\)
\(992\) 0 0
\(993\) 90.0658 2.85815
\(994\) 0 0
\(995\) 70.3355 51.1018i 2.22979 1.62003i
\(996\) 0 0
\(997\) 5.92214 18.2265i 0.187556 0.577238i −0.812427 0.583063i \(-0.801854\pi\)
0.999983 + 0.00582463i \(0.00185405\pi\)
\(998\) 0 0
\(999\) 57.9305 + 42.0890i 1.83284 + 1.33164i
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 1148.2.n.d.57.2 24
41.18 even 5 inner 1148.2.n.d.141.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1148.2.n.d.57.2 24 1.1 even 1 trivial
1148.2.n.d.141.2 yes 24 41.18 even 5 inner