Properties

Label 867.2.e.f.829.4
Level $867$
Weight $2$
Character 867.829
Analytic conductor $6.923$
Analytic rank $0$
Dimension $8$
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] = [867,2,Mod(616,867)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(867, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("867.616");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 867 = 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 867.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.92302985525\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.5473632256.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 49x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 51)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 829.4
Root \(-1.10418 + 1.10418i\) of defining polynomial
Character \(\chi\) \(=\) 867.829
Dual form 867.2.e.f.616.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.56155i q^{2} +(0.707107 + 0.707107i) q^{3} -4.56155 q^{4} +(2.51840 + 2.51840i) q^{5} +(-1.81129 + 1.81129i) q^{6} -6.56155i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+2.56155i q^{2} +(0.707107 + 0.707107i) q^{3} -4.56155 q^{4} +(2.51840 + 2.51840i) q^{5} +(-1.81129 + 1.81129i) q^{6} -6.56155i q^{8} +1.00000i q^{9} +(-6.45101 + 6.45101i) q^{10} +(-1.10418 + 1.10418i) q^{11} +(-3.22550 - 3.22550i) q^{12} -0.438447 q^{13} +3.56155i q^{15} +7.68466 q^{16} -2.56155 q^{18} +4.68466i q^{19} +(-11.4878 - 11.4878i) q^{20} +(-2.82843 - 2.82843i) q^{22} +(1.72424 - 1.72424i) q^{23} +(4.63972 - 4.63972i) q^{24} +7.68466i q^{25} -1.12311i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-5.83095 - 5.83095i) q^{29} -9.12311 q^{30} +(-2.20837 - 2.20837i) q^{31} +6.56155i q^{32} -1.56155 q^{33} -4.56155i q^{36} +(3.62258 + 3.62258i) q^{37} -12.0000 q^{38} +(-0.310029 - 0.310029i) q^{39} +(16.5246 - 16.5246i) q^{40} +(-2.51840 + 2.51840i) q^{41} +4.68466i q^{43} +(5.03680 - 5.03680i) q^{44} +(-2.51840 + 2.51840i) q^{45} +(4.41674 + 4.41674i) q^{46} +11.1231 q^{47} +(5.43387 + 5.43387i) q^{48} +7.00000i q^{49} -19.6847 q^{50} +2.00000 q^{52} -12.2462i q^{53} +(-1.81129 - 1.81129i) q^{54} -5.56155 q^{55} +(-3.31255 + 3.31255i) q^{57} +(14.9363 - 14.9363i) q^{58} +7.12311i q^{59} -16.2462i q^{60} +(6.45101 - 6.45101i) q^{61} +(5.65685 - 5.65685i) q^{62} -1.43845 q^{64} +(-1.10418 - 1.10418i) q^{65} -4.00000i q^{66} +4.00000 q^{67} +2.43845 q^{69} +(4.41674 + 4.41674i) q^{71} +6.56155 q^{72} +(-8.65938 - 8.65938i) q^{73} +(-9.27944 + 9.27944i) q^{74} +(-5.43387 + 5.43387i) q^{75} -21.3693i q^{76} +(0.794156 - 0.794156i) q^{78} +(6.62511 - 6.62511i) q^{79} +(19.3530 + 19.3530i) q^{80} -1.00000 q^{81} +(-6.45101 - 6.45101i) q^{82} +0.876894i q^{83} -12.0000 q^{86} -8.24621i q^{87} +(7.24517 + 7.24517i) q^{88} +1.12311 q^{89} +(-6.45101 - 6.45101i) q^{90} +(-7.86522 + 7.86522i) q^{92} -3.12311i q^{93} +28.4924i q^{94} +(-11.7978 + 11.7978i) q^{95} +(-4.63972 + 4.63972i) q^{96} +(-2.03427 - 2.03427i) q^{97} -17.9309 q^{98} +(-1.10418 - 1.10418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 20 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 20 q^{4} - 20 q^{13} + 12 q^{16} - 4 q^{18} - 40 q^{30} + 4 q^{33} - 96 q^{38} + 56 q^{47} - 108 q^{50} + 16 q^{52} - 28 q^{55} - 28 q^{64} + 32 q^{67} + 36 q^{69} + 36 q^{72} - 8 q^{81} - 96 q^{86} - 24 q^{89} - 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).

\(n\) \(290\) \(292\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56155i 1.81129i 0.424035 + 0.905646i \(0.360613\pi\)
−0.424035 + 0.905646i \(0.639387\pi\)
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −4.56155 −2.28078
\(5\) 2.51840 + 2.51840i 1.12626 + 1.12626i 0.990780 + 0.135482i \(0.0432583\pi\)
0.135482 + 0.990780i \(0.456742\pi\)
\(6\) −1.81129 + 1.81129i −0.739457 + 0.739457i
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) 6.56155i 2.31986i
\(9\) 1.00000i 0.333333i
\(10\) −6.45101 + 6.45101i −2.03999 + 2.03999i
\(11\) −1.10418 + 1.10418i −0.332924 + 0.332924i −0.853696 0.520772i \(-0.825644\pi\)
0.520772 + 0.853696i \(0.325644\pi\)
\(12\) −3.22550 3.22550i −0.931123 0.931123i
\(13\) −0.438447 −0.121603 −0.0608017 0.998150i \(-0.519366\pi\)
−0.0608017 + 0.998150i \(0.519366\pi\)
\(14\) 0 0
\(15\) 3.56155i 0.919589i
\(16\) 7.68466 1.92116
\(17\) 0 0
\(18\) −2.56155 −0.603764
\(19\) 4.68466i 1.07473i 0.843348 + 0.537367i \(0.180581\pi\)
−0.843348 + 0.537367i \(0.819419\pi\)
\(20\) −11.4878 11.4878i −2.56875 2.56875i
\(21\) 0 0
\(22\) −2.82843 2.82843i −0.603023 0.603023i
\(23\) 1.72424 1.72424i 0.359529 0.359529i −0.504110 0.863639i \(-0.668179\pi\)
0.863639 + 0.504110i \(0.168179\pi\)
\(24\) 4.63972 4.63972i 0.947079 0.947079i
\(25\) 7.68466i 1.53693i
\(26\) 1.12311i 0.220259i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0 0
\(29\) −5.83095 5.83095i −1.08278 1.08278i −0.996249 0.0865315i \(-0.972422\pi\)
−0.0865315 0.996249i \(-0.527578\pi\)
\(30\) −9.12311 −1.66564
\(31\) −2.20837 2.20837i −0.396635 0.396635i 0.480409 0.877044i \(-0.340488\pi\)
−0.877044 + 0.480409i \(0.840488\pi\)
\(32\) 6.56155i 1.15993i
\(33\) −1.56155 −0.271831
\(34\) 0 0
\(35\) 0 0
\(36\) 4.56155i 0.760259i
\(37\) 3.62258 + 3.62258i 0.595549 + 0.595549i 0.939125 0.343576i \(-0.111638\pi\)
−0.343576 + 0.939125i \(0.611638\pi\)
\(38\) −12.0000 −1.94666
\(39\) −0.310029 0.310029i −0.0496444 0.0496444i
\(40\) 16.5246 16.5246i 2.61277 2.61277i
\(41\) −2.51840 + 2.51840i −0.393308 + 0.393308i −0.875865 0.482557i \(-0.839708\pi\)
0.482557 + 0.875865i \(0.339708\pi\)
\(42\) 0 0
\(43\) 4.68466i 0.714404i 0.934027 + 0.357202i \(0.116269\pi\)
−0.934027 + 0.357202i \(0.883731\pi\)
\(44\) 5.03680 5.03680i 0.759326 0.759326i
\(45\) −2.51840 + 2.51840i −0.375421 + 0.375421i
\(46\) 4.41674 + 4.41674i 0.651213 + 0.651213i
\(47\) 11.1231 1.62247 0.811236 0.584719i \(-0.198795\pi\)
0.811236 + 0.584719i \(0.198795\pi\)
\(48\) 5.43387 + 5.43387i 0.784312 + 0.784312i
\(49\) 7.00000i 1.00000i
\(50\) −19.6847 −2.78383
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 12.2462i 1.68215i −0.540921 0.841073i \(-0.681924\pi\)
0.540921 0.841073i \(-0.318076\pi\)
\(54\) −1.81129 1.81129i −0.246486 0.246486i
\(55\) −5.56155 −0.749920
\(56\) 0 0
\(57\) −3.31255 + 3.31255i −0.438758 + 0.438758i
\(58\) 14.9363 14.9363i 1.96123 1.96123i
\(59\) 7.12311i 0.927349i 0.886006 + 0.463675i \(0.153469\pi\)
−0.886006 + 0.463675i \(0.846531\pi\)
\(60\) 16.2462i 2.09738i
\(61\) 6.45101 6.45101i 0.825967 0.825967i −0.160989 0.986956i \(-0.551468\pi\)
0.986956 + 0.160989i \(0.0514684\pi\)
\(62\) 5.65685 5.65685i 0.718421 0.718421i
\(63\) 0 0
\(64\) −1.43845 −0.179806
\(65\) −1.10418 1.10418i −0.136957 0.136957i
\(66\) 4.00000i 0.492366i
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 2.43845 0.293555
\(70\) 0 0
\(71\) 4.41674 + 4.41674i 0.524170 + 0.524170i 0.918828 0.394658i \(-0.129137\pi\)
−0.394658 + 0.918828i \(0.629137\pi\)
\(72\) 6.56155 0.773286
\(73\) −8.65938 8.65938i −1.01350 1.01350i −0.999908 0.0135961i \(-0.995672\pi\)
−0.0135961 0.999908i \(-0.504328\pi\)
\(74\) −9.27944 + 9.27944i −1.07871 + 1.07871i
\(75\) −5.43387 + 5.43387i −0.627450 + 0.627450i
\(76\) 21.3693i 2.45123i
\(77\) 0 0
\(78\) 0.794156 0.794156i 0.0899204 0.0899204i
\(79\) 6.62511 6.62511i 0.745383 0.745383i −0.228225 0.973608i \(-0.573292\pi\)
0.973608 + 0.228225i \(0.0732923\pi\)
\(80\) 19.3530 + 19.3530i 2.16373 + 2.16373i
\(81\) −1.00000 −0.111111
\(82\) −6.45101 6.45101i −0.712395 0.712395i
\(83\) 0.876894i 0.0962517i 0.998841 + 0.0481258i \(0.0153248\pi\)
−0.998841 + 0.0481258i \(0.984675\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −12.0000 −1.29399
\(87\) 8.24621i 0.884087i
\(88\) 7.24517 + 7.24517i 0.772337 + 0.772337i
\(89\) 1.12311 0.119049 0.0595245 0.998227i \(-0.481042\pi\)
0.0595245 + 0.998227i \(0.481042\pi\)
\(90\) −6.45101 6.45101i −0.679996 0.679996i
\(91\) 0 0
\(92\) −7.86522 + 7.86522i −0.820006 + 0.820006i
\(93\) 3.12311i 0.323851i
\(94\) 28.4924i 2.93877i
\(95\) −11.7978 + 11.7978i −1.21043 + 1.21043i
\(96\) −4.63972 + 4.63972i −0.473539 + 0.473539i
\(97\) −2.03427 2.03427i −0.206549 0.206549i 0.596250 0.802799i \(-0.296657\pi\)
−0.802799 + 0.596250i \(0.796657\pi\)
\(98\) −17.9309 −1.81129
\(99\) −1.10418 1.10418i −0.110975 0.110975i
\(100\) 35.0540i 3.50540i
\(101\) 10.8769 1.08229 0.541146 0.840929i \(-0.317991\pi\)
0.541146 + 0.840929i \(0.317991\pi\)
\(102\) 0 0
\(103\) 16.6847 1.64399 0.821994 0.569496i \(-0.192862\pi\)
0.821994 + 0.569496i \(0.192862\pi\)
\(104\) 2.87689i 0.282103i
\(105\) 0 0
\(106\) 31.3693 3.04686
\(107\) −3.31255 3.31255i −0.320237 0.320237i 0.528621 0.848858i \(-0.322709\pi\)
−0.848858 + 0.528621i \(0.822709\pi\)
\(108\) 3.22550 3.22550i 0.310374 0.310374i
\(109\) −4.86270 + 4.86270i −0.465762 + 0.465762i −0.900538 0.434776i \(-0.856827\pi\)
0.434776 + 0.900538i \(0.356827\pi\)
\(110\) 14.2462i 1.35832i
\(111\) 5.12311i 0.486264i
\(112\) 0 0
\(113\) 0.310029 0.310029i 0.0291651 0.0291651i −0.692374 0.721539i \(-0.743435\pi\)
0.721539 + 0.692374i \(0.243435\pi\)
\(114\) −8.48528 8.48528i −0.794719 0.794719i
\(115\) 8.68466 0.809849
\(116\) 26.5982 + 26.5982i 2.46958 + 2.46958i
\(117\) 0.438447i 0.0405345i
\(118\) −18.2462 −1.67970
\(119\) 0 0
\(120\) 23.3693 2.13332
\(121\) 8.56155i 0.778323i
\(122\) 16.5246 + 16.5246i 1.49607 + 1.49607i
\(123\) −3.56155 −0.321134
\(124\) 10.0736 + 10.0736i 0.904635 + 0.904635i
\(125\) −6.76104 + 6.76104i −0.604726 + 0.604726i
\(126\) 0 0
\(127\) 19.8078i 1.75765i 0.477140 + 0.878827i \(0.341674\pi\)
−0.477140 + 0.878827i \(0.658326\pi\)
\(128\) 9.43845i 0.834249i
\(129\) −3.31255 + 3.31255i −0.291654 + 0.291654i
\(130\) 2.82843 2.82843i 0.248069 0.248069i
\(131\) 10.2095 + 10.2095i 0.892010 + 0.892010i 0.994712 0.102702i \(-0.0327488\pi\)
−0.102702 + 0.994712i \(0.532749\pi\)
\(132\) 7.12311 0.619987
\(133\) 0 0
\(134\) 10.2462i 0.885138i
\(135\) −3.56155 −0.306530
\(136\) 0 0
\(137\) 0.246211 0.0210352 0.0105176 0.999945i \(-0.496652\pi\)
0.0105176 + 0.999945i \(0.496652\pi\)
\(138\) 6.24621i 0.531713i
\(139\) 0.620058 + 0.620058i 0.0525926 + 0.0525926i 0.732914 0.680321i \(-0.238160\pi\)
−0.680321 + 0.732914i \(0.738160\pi\)
\(140\) 0 0
\(141\) 7.86522 + 7.86522i 0.662371 + 0.662371i
\(142\) −11.3137 + 11.3137i −0.949425 + 0.949425i
\(143\) 0.484127 0.484127i 0.0404847 0.0404847i
\(144\) 7.68466i 0.640388i
\(145\) 29.3693i 2.43899i
\(146\) 22.1815 22.1815i 1.83575 1.83575i
\(147\) −4.94975 + 4.94975i −0.408248 + 0.408248i
\(148\) −16.5246 16.5246i −1.35831 1.35831i
\(149\) −12.2462 −1.00325 −0.501624 0.865086i \(-0.667264\pi\)
−0.501624 + 0.865086i \(0.667264\pi\)
\(150\) −13.9192 13.9192i −1.13649 1.13649i
\(151\) 8.00000i 0.651031i −0.945537 0.325515i \(-0.894462\pi\)
0.945537 0.325515i \(-0.105538\pi\)
\(152\) 30.7386 2.49323
\(153\) 0 0
\(154\) 0 0
\(155\) 11.1231i 0.893429i
\(156\) 1.41421 + 1.41421i 0.113228 + 0.113228i
\(157\) −6.68466 −0.533494 −0.266747 0.963767i \(-0.585949\pi\)
−0.266747 + 0.963767i \(0.585949\pi\)
\(158\) 16.9706 + 16.9706i 1.35011 + 1.35011i
\(159\) 8.65938 8.65938i 0.686733 0.686733i
\(160\) −16.5246 + 16.5246i −1.30638 + 1.30638i
\(161\) 0 0
\(162\) 2.56155i 0.201255i
\(163\) −10.6937 + 10.6937i −0.837591 + 0.837591i −0.988541 0.150950i \(-0.951767\pi\)
0.150950 + 0.988541i \(0.451767\pi\)
\(164\) 11.4878 11.4878i 0.897047 0.897047i
\(165\) −3.93261 3.93261i −0.306153 0.306153i
\(166\) −2.24621 −0.174340
\(167\) −14.0062 14.0062i −1.08383 1.08383i −0.996148 0.0876843i \(-0.972053\pi\)
−0.0876843 0.996148i \(-0.527947\pi\)
\(168\) 0 0
\(169\) −12.8078 −0.985213
\(170\) 0 0
\(171\) −4.68466 −0.358245
\(172\) 21.3693i 1.62940i
\(173\) −1.27828 1.27828i −0.0971860 0.0971860i 0.656842 0.754028i \(-0.271892\pi\)
−0.754028 + 0.656842i \(0.771892\pi\)
\(174\) 21.1231 1.60134
\(175\) 0 0
\(176\) −8.48528 + 8.48528i −0.639602 + 0.639602i
\(177\) −5.03680 + 5.03680i −0.378589 + 0.378589i
\(178\) 2.87689i 0.215632i
\(179\) 0.876894i 0.0655422i −0.999463 0.0327711i \(-0.989567\pi\)
0.999463 0.0327711i \(-0.0104332\pi\)
\(180\) 11.4878 11.4878i 0.856251 0.856251i
\(181\) −4.24264 + 4.24264i −0.315353 + 0.315353i −0.846979 0.531626i \(-0.821581\pi\)
0.531626 + 0.846979i \(0.321581\pi\)
\(182\) 0 0
\(183\) 9.12311 0.674399
\(184\) −11.3137 11.3137i −0.834058 0.834058i
\(185\) 18.2462i 1.34149i
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) −50.7386 −3.70050
\(189\) 0 0
\(190\) −30.2208 30.2208i −2.19245 2.19245i
\(191\) 4.87689 0.352880 0.176440 0.984311i \(-0.443542\pi\)
0.176440 + 0.984311i \(0.443542\pi\)
\(192\) −1.01714 1.01714i −0.0734055 0.0734055i
\(193\) 5.48276 5.48276i 0.394657 0.394657i −0.481686 0.876344i \(-0.659976\pi\)
0.876344 + 0.481686i \(0.159976\pi\)
\(194\) 5.21089 5.21089i 0.374120 0.374120i
\(195\) 1.56155i 0.111825i
\(196\) 31.9309i 2.28078i
\(197\) −6.31508 + 6.31508i −0.449931 + 0.449931i −0.895331 0.445401i \(-0.853061\pi\)
0.445401 + 0.895331i \(0.353061\pi\)
\(198\) 2.82843 2.82843i 0.201008 0.201008i
\(199\) 11.3137 + 11.3137i 0.802008 + 0.802008i 0.983409 0.181402i \(-0.0580634\pi\)
−0.181402 + 0.983409i \(0.558063\pi\)
\(200\) 50.4233 3.56547
\(201\) 2.82843 + 2.82843i 0.199502 + 0.199502i
\(202\) 27.8617i 1.96035i
\(203\) 0 0
\(204\) 0 0
\(205\) −12.6847 −0.885935
\(206\) 42.7386i 2.97774i
\(207\) 1.72424 + 1.72424i 0.119843 + 0.119843i
\(208\) −3.36932 −0.233620
\(209\) −5.17273 5.17273i −0.357805 0.357805i
\(210\) 0 0
\(211\) 9.45353 9.45353i 0.650808 0.650808i −0.302379 0.953188i \(-0.597781\pi\)
0.953188 + 0.302379i \(0.0977810\pi\)
\(212\) 55.8617i 3.83660i
\(213\) 6.24621i 0.427983i
\(214\) 8.48528 8.48528i 0.580042 0.580042i
\(215\) −11.7978 + 11.7978i −0.804606 + 0.804606i
\(216\) 4.63972 + 4.63972i 0.315693 + 0.315693i
\(217\) 0 0
\(218\) −12.4561 12.4561i −0.843631 0.843631i
\(219\) 12.2462i 0.827522i
\(220\) 25.3693 1.71040
\(221\) 0 0
\(222\) −13.1231 −0.880765
\(223\) 14.9309i 0.999845i 0.866070 + 0.499922i \(0.166638\pi\)
−0.866070 + 0.499922i \(0.833362\pi\)
\(224\) 0 0
\(225\) −7.68466 −0.512311
\(226\) 0.794156 + 0.794156i 0.0528264 + 0.0528264i
\(227\) 9.93766 9.93766i 0.659586 0.659586i −0.295696 0.955282i \(-0.595552\pi\)
0.955282 + 0.295696i \(0.0955516\pi\)
\(228\) 15.1104 15.1104i 1.00071 1.00071i
\(229\) 6.00000i 0.396491i 0.980152 + 0.198246i \(0.0635244\pi\)
−0.980152 + 0.198246i \(0.936476\pi\)
\(230\) 22.2462i 1.46687i
\(231\) 0 0
\(232\) −38.2601 + 38.2601i −2.51190 + 2.51190i
\(233\) −2.51840 2.51840i −0.164986 0.164986i 0.619786 0.784771i \(-0.287220\pi\)
−0.784771 + 0.619786i \(0.787220\pi\)
\(234\) 1.12311 0.0734197
\(235\) 28.0124 + 28.0124i 1.82733 + 1.82733i
\(236\) 32.4924i 2.11508i
\(237\) 9.36932 0.608603
\(238\) 0 0
\(239\) −6.24621 −0.404034 −0.202017 0.979382i \(-0.564750\pi\)
−0.202017 + 0.979382i \(0.564750\pi\)
\(240\) 27.3693i 1.76668i
\(241\) −2.38247 2.38247i −0.153468 0.153468i 0.626197 0.779665i \(-0.284611\pi\)
−0.779665 + 0.626197i \(0.784611\pi\)
\(242\) −21.9309 −1.40977
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −29.4266 + 29.4266i −1.88385 + 1.88385i
\(245\) −17.6288 + 17.6288i −1.12626 + 1.12626i
\(246\) 9.12311i 0.581668i
\(247\) 2.05398i 0.130691i
\(248\) −14.4903 + 14.4903i −0.920137 + 0.920137i
\(249\) −0.620058 + 0.620058i −0.0392946 + 0.0392946i
\(250\) −17.3188 17.3188i −1.09533 1.09533i
\(251\) −8.49242 −0.536037 −0.268018 0.963414i \(-0.586369\pi\)
−0.268018 + 0.963414i \(0.586369\pi\)
\(252\) 0 0
\(253\) 3.80776i 0.239392i
\(254\) −50.7386 −3.18363
\(255\) 0 0
\(256\) −27.0540 −1.69087
\(257\) 15.3693i 0.958712i 0.877621 + 0.479356i \(0.159130\pi\)
−0.877621 + 0.479356i \(0.840870\pi\)
\(258\) −8.48528 8.48528i −0.528271 0.528271i
\(259\) 0 0
\(260\) 5.03680 + 5.03680i 0.312369 + 0.312369i
\(261\) 5.83095 5.83095i 0.360927 0.360927i
\(262\) −26.1522 + 26.1522i −1.61569 + 1.61569i
\(263\) 20.4924i 1.26362i −0.775125 0.631808i \(-0.782313\pi\)
0.775125 0.631808i \(-0.217687\pi\)
\(264\) 10.2462i 0.630611i
\(265\) 30.8408 30.8408i 1.89454 1.89454i
\(266\) 0 0
\(267\) 0.794156 + 0.794156i 0.0486015 + 0.0486015i
\(268\) −18.2462 −1.11456
\(269\) −11.6237 11.6237i −0.708712 0.708712i 0.257553 0.966264i \(-0.417084\pi\)
−0.966264 + 0.257553i \(0.917084\pi\)
\(270\) 9.12311i 0.555215i
\(271\) 19.8078 1.20324 0.601618 0.798784i \(-0.294523\pi\)
0.601618 + 0.798784i \(0.294523\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0.630683i 0.0381010i
\(275\) −8.48528 8.48528i −0.511682 0.511682i
\(276\) −11.1231 −0.669532
\(277\) 4.24264 + 4.24264i 0.254916 + 0.254916i 0.822982 0.568067i \(-0.192309\pi\)
−0.568067 + 0.822982i \(0.692309\pi\)
\(278\) −1.58831 + 1.58831i −0.0952606 + 0.0952606i
\(279\) 2.20837 2.20837i 0.132212 0.132212i
\(280\) 0 0
\(281\) 10.8769i 0.648861i −0.945910 0.324431i \(-0.894827\pi\)
0.945910 0.324431i \(-0.105173\pi\)
\(282\) −20.1472 + 20.1472i −1.19975 + 1.19975i
\(283\) −15.1104 + 15.1104i −0.898219 + 0.898219i −0.995279 0.0970592i \(-0.969056\pi\)
0.0970592 + 0.995279i \(0.469056\pi\)
\(284\) −20.1472 20.1472i −1.19552 1.19552i
\(285\) −16.6847 −0.988314
\(286\) 1.24012 + 1.24012i 0.0733296 + 0.0733296i
\(287\) 0 0
\(288\) −6.56155 −0.386643
\(289\) 0 0
\(290\) 75.2311 4.41772
\(291\) 2.87689i 0.168647i
\(292\) 39.5002 + 39.5002i 2.31158 + 2.31158i
\(293\) −1.12311 −0.0656125 −0.0328063 0.999462i \(-0.510444\pi\)
−0.0328063 + 0.999462i \(0.510444\pi\)
\(294\) −12.6790 12.6790i −0.739457 0.739457i
\(295\) −17.9388 + 17.9388i −1.04444 + 1.04444i
\(296\) 23.7698 23.7698i 1.38159 1.38159i
\(297\) 1.56155i 0.0906105i
\(298\) 31.3693i 1.81718i
\(299\) −0.755989 + 0.755989i −0.0437200 + 0.0437200i
\(300\) 24.7869 24.7869i 1.43107 1.43107i
\(301\) 0 0
\(302\) 20.4924 1.17921
\(303\) 7.69113 + 7.69113i 0.441844 + 0.441844i
\(304\) 36.0000i 2.06474i
\(305\) 32.4924 1.86051
\(306\) 0 0
\(307\) 32.4924 1.85444 0.927220 0.374516i \(-0.122191\pi\)
0.927220 + 0.374516i \(0.122191\pi\)
\(308\) 0 0
\(309\) 11.7978 + 11.7978i 0.671155 + 0.671155i
\(310\) 28.4924 1.61826
\(311\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(312\) −2.03427 + 2.03427i −0.115168 + 0.115168i
\(313\) 23.7698 23.7698i 1.34355 1.34355i 0.451046 0.892501i \(-0.351051\pi\)
0.892501 0.451046i \(-0.148949\pi\)
\(314\) 17.1231i 0.966313i
\(315\) 0 0
\(316\) −30.2208 + 30.2208i −1.70005 + 1.70005i
\(317\) 12.7279 12.7279i 0.714871 0.714871i −0.252679 0.967550i \(-0.581312\pi\)
0.967550 + 0.252679i \(0.0813116\pi\)
\(318\) 22.1815 + 22.1815i 1.24387 + 1.24387i
\(319\) 12.8769 0.720968
\(320\) −3.62258 3.62258i −0.202509 0.202509i
\(321\) 4.68466i 0.261472i
\(322\) 0 0
\(323\) 0 0
\(324\) 4.56155 0.253420
\(325\) 3.36932i 0.186896i
\(326\) −27.3924 27.3924i −1.51712 1.51712i
\(327\) −6.87689 −0.380293
\(328\) 16.5246 + 16.5246i 0.912419 + 0.912419i
\(329\) 0 0
\(330\) 10.0736 10.0736i 0.554533 0.554533i
\(331\) 34.9309i 1.91997i −0.280044 0.959987i \(-0.590349\pi\)
0.280044 0.959987i \(-0.409651\pi\)
\(332\) 4.00000i 0.219529i
\(333\) −3.62258 + 3.62258i −0.198516 + 0.198516i
\(334\) 35.8776 35.8776i 1.96314 1.96314i
\(335\) 10.0736 + 10.0736i 0.550379 + 0.550379i
\(336\) 0 0
\(337\) 11.8360 + 11.8360i 0.644748 + 0.644748i 0.951719 0.306971i \(-0.0993154\pi\)
−0.306971 + 0.951719i \(0.599315\pi\)
\(338\) 32.8078i 1.78451i
\(339\) 0.438447 0.0238132
\(340\) 0 0
\(341\) 4.87689 0.264099
\(342\) 12.0000i 0.648886i
\(343\) 0 0
\(344\) 30.7386 1.65732
\(345\) 6.14098 + 6.14098i 0.330619 + 0.330619i
\(346\) 3.27439 3.27439i 0.176032 0.176032i
\(347\) −6.00505 + 6.00505i −0.322368 + 0.322368i −0.849675 0.527307i \(-0.823202\pi\)
0.527307 + 0.849675i \(0.323202\pi\)
\(348\) 37.6155i 2.01640i
\(349\) 11.5616i 0.618876i 0.950920 + 0.309438i \(0.100141\pi\)
−0.950920 + 0.309438i \(0.899859\pi\)
\(350\) 0 0
\(351\) 0.310029 0.310029i 0.0165481 0.0165481i
\(352\) −7.24517 7.24517i −0.386169 0.386169i
\(353\) 10.4924 0.558455 0.279228 0.960225i \(-0.409922\pi\)
0.279228 + 0.960225i \(0.409922\pi\)
\(354\) −12.9020 12.9020i −0.685735 0.685735i
\(355\) 22.2462i 1.18071i
\(356\) −5.12311 −0.271524
\(357\) 0 0
\(358\) 2.24621 0.118716
\(359\) 14.2462i 0.751886i −0.926643 0.375943i \(-0.877319\pi\)
0.926643 0.375943i \(-0.122681\pi\)
\(360\) 16.5246 + 16.5246i 0.870923 + 0.870923i
\(361\) −2.94602 −0.155054
\(362\) −10.8677 10.8677i −0.571196 0.571196i
\(363\) −6.05393 + 6.05393i −0.317749 + 0.317749i
\(364\) 0 0
\(365\) 43.6155i 2.28294i
\(366\) 23.3693i 1.22153i
\(367\) −1.24012 + 1.24012i −0.0647335 + 0.0647335i −0.738732 0.673999i \(-0.764575\pi\)
0.673999 + 0.738732i \(0.264575\pi\)
\(368\) 13.2502 13.2502i 0.690715 0.690715i
\(369\) −2.51840 2.51840i −0.131103 0.131103i
\(370\) −46.7386 −2.42983
\(371\) 0 0
\(372\) 14.2462i 0.738632i
\(373\) −0.246211 −0.0127483 −0.00637417 0.999980i \(-0.502029\pi\)
−0.00637417 + 0.999980i \(0.502029\pi\)
\(374\) 0 0
\(375\) −9.56155 −0.493756
\(376\) 72.9848i 3.76391i
\(377\) 2.55656 + 2.55656i 0.131670 + 0.131670i
\(378\) 0 0
\(379\) −8.48528 8.48528i −0.435860 0.435860i 0.454756 0.890616i \(-0.349726\pi\)
−0.890616 + 0.454756i \(0.849726\pi\)
\(380\) 53.8164 53.8164i 2.76073 2.76073i
\(381\) −14.0062 + 14.0062i −0.717560 + 0.717560i
\(382\) 12.4924i 0.639168i
\(383\) 6.24621i 0.319166i 0.987184 + 0.159583i \(0.0510150\pi\)
−0.987184 + 0.159583i \(0.948985\pi\)
\(384\) −6.67399 + 6.67399i −0.340581 + 0.340581i
\(385\) 0 0
\(386\) 14.0444 + 14.0444i 0.714840 + 0.714840i
\(387\) −4.68466 −0.238135
\(388\) 9.27944 + 9.27944i 0.471092 + 0.471092i
\(389\) 35.8617i 1.81826i −0.416510 0.909131i \(-0.636747\pi\)
0.416510 0.909131i \(-0.363253\pi\)
\(390\) 4.00000 0.202548
\(391\) 0 0
\(392\) 45.9309 2.31986
\(393\) 14.4384i 0.728323i
\(394\) −16.1764 16.1764i −0.814956 0.814956i
\(395\) 33.3693 1.67899
\(396\) 5.03680 + 5.03680i 0.253109 + 0.253109i
\(397\) 13.6962 13.6962i 0.687391 0.687391i −0.274263 0.961655i \(-0.588434\pi\)
0.961655 + 0.274263i \(0.0884340\pi\)
\(398\) −28.9807 + 28.9807i −1.45267 + 1.45267i
\(399\) 0 0
\(400\) 59.0540i 2.95270i
\(401\) 27.7024 27.7024i 1.38339 1.38339i 0.544871 0.838520i \(-0.316579\pi\)
0.838520 0.544871i \(-0.183421\pi\)
\(402\) −7.24517 + 7.24517i −0.361356 + 0.361356i
\(403\) 0.968253 + 0.968253i 0.0482321 + 0.0482321i
\(404\) −49.6155 −2.46846
\(405\) −2.51840 2.51840i −0.125140 0.125140i
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) −14.6847 −0.726110 −0.363055 0.931768i \(-0.618266\pi\)
−0.363055 + 0.931768i \(0.618266\pi\)
\(410\) 32.4924i 1.60469i
\(411\) 0.174098 + 0.174098i 0.00858760 + 0.00858760i
\(412\) −76.1080 −3.74957
\(413\) 0 0
\(414\) −4.41674 + 4.41674i −0.217071 + 0.217071i
\(415\) −2.20837 + 2.20837i −0.108405 + 0.108405i
\(416\) 2.87689i 0.141051i
\(417\) 0.876894i 0.0429417i
\(418\) 13.2502 13.2502i 0.648089 0.648089i
\(419\) 0.348195 0.348195i 0.0170105 0.0170105i −0.698550 0.715561i \(-0.746171\pi\)
0.715561 + 0.698550i \(0.246171\pi\)
\(420\) 0 0
\(421\) −24.4384 −1.19106 −0.595529 0.803334i \(-0.703057\pi\)
−0.595529 + 0.803334i \(0.703057\pi\)
\(422\) 24.2157 + 24.2157i 1.17880 + 1.17880i
\(423\) 11.1231i 0.540824i
\(424\) −80.3542 −3.90234
\(425\) 0 0
\(426\) −16.0000 −0.775203
\(427\) 0 0
\(428\) 15.1104 + 15.1104i 0.730388 + 0.730388i
\(429\) 0.684658 0.0330556
\(430\) −30.2208 30.2208i −1.45738 1.45738i
\(431\) 16.9706 16.9706i 0.817443 0.817443i −0.168294 0.985737i \(-0.553826\pi\)
0.985737 + 0.168294i \(0.0538257\pi\)
\(432\) −5.43387 + 5.43387i −0.261437 + 0.261437i
\(433\) 26.6847i 1.28238i 0.767381 + 0.641191i \(0.221560\pi\)
−0.767381 + 0.641191i \(0.778440\pi\)
\(434\) 0 0
\(435\) 20.7672 20.7672i 0.995713 0.995713i
\(436\) 22.1815 22.1815i 1.06230 1.06230i
\(437\) 8.07749 + 8.07749i 0.386399 + 0.386399i
\(438\) 31.3693 1.49888
\(439\) 15.7304 + 15.7304i 0.750773 + 0.750773i 0.974624 0.223850i \(-0.0718627\pi\)
−0.223850 + 0.974624i \(0.571863\pi\)
\(440\) 36.4924i 1.73971i
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −31.1231 −1.47870 −0.739352 0.673319i \(-0.764868\pi\)
−0.739352 + 0.673319i \(0.764868\pi\)
\(444\) 23.3693i 1.10906i
\(445\) 2.82843 + 2.82843i 0.134080 + 0.134080i
\(446\) −38.2462 −1.81101
\(447\) −8.65938 8.65938i −0.409575 0.409575i
\(448\) 0 0
\(449\) 25.9781 25.9781i 1.22598 1.22598i 0.260514 0.965470i \(-0.416108\pi\)
0.965470 0.260514i \(-0.0838920\pi\)
\(450\) 19.6847i 0.927944i
\(451\) 5.56155i 0.261883i
\(452\) −1.41421 + 1.41421i −0.0665190 + 0.0665190i
\(453\) 5.65685 5.65685i 0.265782 0.265782i
\(454\) 25.4558 + 25.4558i 1.19470 + 1.19470i
\(455\) 0 0
\(456\) 21.7355 + 21.7355i 1.01786 + 1.01786i
\(457\) 13.8078i 0.645900i −0.946416 0.322950i \(-0.895325\pi\)
0.946416 0.322950i \(-0.104675\pi\)
\(458\) −15.3693 −0.718161
\(459\) 0 0
\(460\) −39.6155 −1.84708
\(461\) 8.24621i 0.384064i 0.981389 + 0.192032i \(0.0615078\pi\)
−0.981389 + 0.192032i \(0.938492\pi\)
\(462\) 0 0
\(463\) 40.9848 1.90473 0.952364 0.304965i \(-0.0986447\pi\)
0.952364 + 0.304965i \(0.0986447\pi\)
\(464\) −44.8089 44.8089i −2.08020 2.08020i
\(465\) 7.86522 7.86522i 0.364741 0.364741i
\(466\) 6.45101 6.45101i 0.298837 0.298837i
\(467\) 21.3693i 0.988854i 0.869219 + 0.494427i \(0.164622\pi\)
−0.869219 + 0.494427i \(0.835378\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 0 0
\(470\) −71.7553 + 71.7553i −3.30982 + 3.30982i
\(471\) −4.72677 4.72677i −0.217798 0.217798i
\(472\) 46.7386 2.15132
\(473\) −5.17273 5.17273i −0.237842 0.237842i
\(474\) 24.0000i 1.10236i
\(475\) −36.0000 −1.65179
\(476\) 0 0
\(477\) 12.2462 0.560715
\(478\) 16.0000i 0.731823i
\(479\) −17.1828 17.1828i −0.785103 0.785103i 0.195584 0.980687i \(-0.437340\pi\)
−0.980687 + 0.195584i \(0.937340\pi\)
\(480\) −23.3693 −1.06666
\(481\) −1.58831 1.58831i −0.0724208 0.0724208i
\(482\) 6.10281 6.10281i 0.277976 0.277976i
\(483\) 0 0
\(484\) 39.0540i 1.77518i
\(485\) 10.2462i 0.465256i
\(486\) 1.81129 1.81129i 0.0821618 0.0821618i
\(487\) −12.2820 + 12.2820i −0.556549 + 0.556549i −0.928323 0.371774i \(-0.878750\pi\)
0.371774 + 0.928323i \(0.378750\pi\)
\(488\) −42.3286 42.3286i −1.91613 1.91613i
\(489\) −15.1231 −0.683890
\(490\) −45.1571 45.1571i −2.03999 2.03999i
\(491\) 21.3693i 0.964384i 0.876066 + 0.482192i \(0.160159\pi\)
−0.876066 + 0.482192i \(0.839841\pi\)
\(492\) 16.2462 0.732436
\(493\) 0 0
\(494\) 5.26137 0.236720
\(495\) 5.56155i 0.249973i
\(496\) −16.9706 16.9706i −0.762001 0.762001i
\(497\) 0 0
\(498\) −1.58831 1.58831i −0.0711739 0.0711739i
\(499\) −9.45353 + 9.45353i −0.423198 + 0.423198i −0.886303 0.463105i \(-0.846735\pi\)
0.463105 + 0.886303i \(0.346735\pi\)
\(500\) 30.8408 30.8408i 1.37924 1.37924i
\(501\) 19.8078i 0.884946i
\(502\) 21.7538i 0.970919i
\(503\) −20.9032 + 20.9032i −0.932026 + 0.932026i −0.997832 0.0658060i \(-0.979038\pi\)
0.0658060 + 0.997832i \(0.479038\pi\)
\(504\) 0 0
\(505\) 27.3924 + 27.3924i 1.21894 + 1.21894i
\(506\) −9.75379 −0.433609
\(507\) −9.05646 9.05646i −0.402211 0.402211i
\(508\) 90.3542i 4.00882i
\(509\) 25.1231 1.11356 0.556781 0.830659i \(-0.312036\pi\)
0.556781 + 0.830659i \(0.312036\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 50.4233i 2.22842i
\(513\) −3.31255 3.31255i −0.146253 0.146253i
\(514\) −39.3693 −1.73651
\(515\) 42.0186 + 42.0186i 1.85156 + 1.85156i
\(516\) 15.1104 15.1104i 0.665198 0.665198i
\(517\) −12.2820 + 12.2820i −0.540160 + 0.540160i
\(518\) 0 0
\(519\) 1.80776i 0.0793520i
\(520\) −7.24517 + 7.24517i −0.317722 + 0.317722i
\(521\) 25.1458 25.1458i 1.10166 1.10166i 0.107447 0.994211i \(-0.465732\pi\)
0.994211 0.107447i \(-0.0342677\pi\)
\(522\) 14.9363 + 14.9363i 0.653744 + 0.653744i
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −46.5713 46.5713i −2.03448 2.03448i
\(525\) 0 0
\(526\) 52.4924 2.28878
\(527\) 0 0
\(528\) −12.0000 −0.522233
\(529\) 17.0540i 0.741477i
\(530\) 79.0004 + 79.0004i 3.43156 + 3.43156i
\(531\) −7.12311 −0.309116
\(532\) 0 0
\(533\) 1.10418 1.10418i 0.0478275 0.0478275i
\(534\) −2.03427 + 2.03427i −0.0880315 + 0.0880315i
\(535\) 16.6847i 0.721341i
\(536\) 26.2462i 1.13366i
\(537\) 0.620058 0.620058i 0.0267575 0.0267575i
\(538\) 29.7748 29.7748i 1.28368 1.28368i
\(539\) −7.72929 7.72929i −0.332924 0.332924i
\(540\) 16.2462 0.699126
\(541\) −24.1180 24.1180i −1.03691 1.03691i −0.999292 0.0376201i \(-0.988022\pi\)
−0.0376201 0.999292i \(-0.511978\pi\)
\(542\) 50.7386i 2.17941i
\(543\) −6.00000 −0.257485
\(544\) 0 0
\(545\) −24.4924 −1.04914
\(546\) 0 0
\(547\) −19.7990 19.7990i −0.846544 0.846544i 0.143156 0.989700i \(-0.454275\pi\)
−0.989700 + 0.143156i \(0.954275\pi\)
\(548\) −1.12311 −0.0479767
\(549\) 6.45101 + 6.45101i 0.275322 + 0.275322i
\(550\) 21.7355 21.7355i 0.926805 0.926805i
\(551\) 27.3160 27.3160i 1.16370 1.16370i
\(552\) 16.0000i 0.681005i
\(553\) 0 0
\(554\) −10.8677 + 10.8677i −0.461726 + 0.461726i
\(555\) −12.9020 + 12.9020i −0.547660 + 0.547660i
\(556\) −2.82843 2.82843i −0.119952 0.119952i
\(557\) −26.4924 −1.12252 −0.561260 0.827640i \(-0.689683\pi\)
−0.561260 + 0.827640i \(0.689683\pi\)
\(558\) 5.65685 + 5.65685i 0.239474 + 0.239474i
\(559\) 2.05398i 0.0868739i
\(560\) 0 0
\(561\) 0 0
\(562\) 27.8617 1.17528
\(563\) 31.1231i 1.31168i −0.754899 0.655841i \(-0.772314\pi\)
0.754899 0.655841i \(-0.227686\pi\)
\(564\) −35.8776 35.8776i −1.51072 1.51072i
\(565\) 1.56155 0.0656950
\(566\) −38.7061 38.7061i −1.62694 1.62694i
\(567\) 0 0
\(568\) 28.9807 28.9807i 1.21600 1.21600i
\(569\) 21.1231i 0.885527i 0.896639 + 0.442763i \(0.146002\pi\)
−0.896639 + 0.442763i \(0.853998\pi\)
\(570\) 42.7386i 1.79012i
\(571\) −21.7355 + 21.7355i −0.909602 + 0.909602i −0.996240 0.0866377i \(-0.972388\pi\)
0.0866377 + 0.996240i \(0.472388\pi\)
\(572\) −2.20837 + 2.20837i −0.0923366 + 0.0923366i
\(573\) 3.44849 + 3.44849i 0.144063 + 0.144063i
\(574\) 0 0
\(575\) 13.2502 + 13.2502i 0.552572 + 0.552572i
\(576\) 1.43845i 0.0599353i
\(577\) −3.94602 −0.164275 −0.0821376 0.996621i \(-0.526175\pi\)
−0.0821376 + 0.996621i \(0.526175\pi\)
\(578\) 0 0
\(579\) 7.75379 0.322236
\(580\) 133.970i 5.56279i
\(581\) 0 0
\(582\) 7.36932 0.305468
\(583\) 13.5221 + 13.5221i 0.560027 + 0.560027i
\(584\) −56.8190 + 56.8190i −2.35119 + 2.35119i
\(585\) 1.10418 1.10418i 0.0456524 0.0456524i
\(586\) 2.87689i 0.118843i
\(587\) 28.9848i 1.19633i −0.801372 0.598166i \(-0.795896\pi\)
0.801372 0.598166i \(-0.204104\pi\)
\(588\) 22.5785 22.5785i 0.931123 0.931123i
\(589\) 10.3455 10.3455i 0.426277 0.426277i
\(590\) −45.9512 45.9512i −1.89178 1.89178i
\(591\) −8.93087 −0.367367
\(592\) 27.8383 + 27.8383i 1.14415 + 1.14415i
\(593\) 27.7538i 1.13971i −0.821745 0.569856i \(-0.806999\pi\)
0.821745 0.569856i \(-0.193001\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) 55.8617 2.28819
\(597\) 16.0000i 0.654836i
\(598\) −1.93651 1.93651i −0.0791896 0.0791896i
\(599\) 0.384472 0.0157091 0.00785455 0.999969i \(-0.497500\pi\)
0.00785455 + 0.999969i \(0.497500\pi\)
\(600\) 35.6547 + 35.6547i 1.45560 + 1.45560i
\(601\) 21.9096 21.9096i 0.893711 0.893711i −0.101159 0.994870i \(-0.532255\pi\)
0.994870 + 0.101159i \(0.0322552\pi\)
\(602\) 0 0
\(603\) 4.00000i 0.162893i
\(604\) 36.4924i 1.48486i
\(605\) −21.5614 + 21.5614i −0.876596 + 0.876596i
\(606\) −19.7012 + 19.7012i −0.800308 + 0.800308i
\(607\) −6.62511 6.62511i −0.268905 0.268905i 0.559754 0.828659i \(-0.310896\pi\)
−0.828659 + 0.559754i \(0.810896\pi\)
\(608\) −30.7386 −1.24662
\(609\) 0 0
\(610\) 83.2311i 3.36993i
\(611\) −4.87689 −0.197298
\(612\) 0 0
\(613\) 14.6847 0.593108 0.296554 0.955016i \(-0.404163\pi\)
0.296554 + 0.955016i \(0.404163\pi\)
\(614\) 83.2311i 3.35893i
\(615\) −8.96941 8.96941i −0.361681 0.361681i
\(616\) 0 0
\(617\) −31.2868 31.2868i −1.25956 1.25956i −0.951304 0.308255i \(-0.900255\pi\)
−0.308255 0.951304i \(-0.599745\pi\)
\(618\) −30.2208 + 30.2208i −1.21566 + 1.21566i
\(619\) 3.79668 3.79668i 0.152601 0.152601i −0.626677 0.779279i \(-0.715586\pi\)
0.779279 + 0.626677i \(0.215586\pi\)
\(620\) 50.7386i 2.03771i
\(621\) 2.43845i 0.0978515i
\(622\) 0 0
\(623\) 0 0
\(624\) −2.38247 2.38247i −0.0953750 0.0953750i
\(625\) 4.36932 0.174773
\(626\) 60.8875 + 60.8875i 2.43355 + 2.43355i
\(627\) 7.31534i 0.292147i
\(628\) 30.4924 1.21678
\(629\) 0 0
\(630\) 0 0
\(631\) 0.684658i 0.0272558i 0.999907 + 0.0136279i \(0.00433803\pi\)
−0.999907 + 0.0136279i \(0.995662\pi\)
\(632\) −43.4710 43.4710i −1.72918 1.72918i
\(633\) 13.3693 0.531383
\(634\) 32.6032 + 32.6032i 1.29484 + 1.29484i
\(635\) −49.8838 + 49.8838i −1.97958 + 1.97958i
\(636\) −39.5002 + 39.5002i −1.56629 + 1.56629i
\(637\) 3.06913i 0.121603i
\(638\) 32.9848i 1.30588i
\(639\) −4.41674 + 4.41674i −0.174723 + 0.174723i
\(640\) −23.7698 + 23.7698i −0.939583 + 0.939583i
\(641\) −20.4572 20.4572i −0.808011 0.808011i 0.176321 0.984333i \(-0.443580\pi\)
−0.984333 + 0.176321i \(0.943580\pi\)
\(642\) 12.0000 0.473602
\(643\) 9.72540 + 9.72540i 0.383532 + 0.383532i 0.872373 0.488841i \(-0.162580\pi\)
−0.488841 + 0.872373i \(0.662580\pi\)
\(644\) 0 0
\(645\) −16.6847 −0.656958
\(646\) 0 0
\(647\) −9.36932 −0.368346 −0.184173 0.982894i \(-0.558961\pi\)
−0.184173 + 0.982894i \(0.558961\pi\)
\(648\) 6.56155i 0.257762i
\(649\) −7.86522 7.86522i −0.308737 0.308737i
\(650\) 8.63068 0.338523
\(651\) 0 0
\(652\) 48.7797 48.7797i 1.91036 1.91036i
\(653\) −23.2856 + 23.2856i −0.911238 + 0.911238i −0.996370 0.0851321i \(-0.972869\pi\)
0.0851321 + 0.996370i \(0.472869\pi\)
\(654\) 17.6155i 0.688822i
\(655\) 51.4233i 2.00927i
\(656\) −19.3530 + 19.3530i −0.755609 + 0.755609i
\(657\) 8.65938 8.65938i 0.337835 0.337835i
\(658\) 0 0
\(659\) 9.86174 0.384159 0.192079 0.981379i \(-0.438477\pi\)
0.192079 + 0.981379i \(0.438477\pi\)
\(660\) 17.9388 + 17.9388i 0.698267 + 0.698267i
\(661\) 13.3153i 0.517907i −0.965890 0.258953i \(-0.916622\pi\)
0.965890 0.258953i \(-0.0833776\pi\)
\(662\) 89.4773 3.47763
\(663\) 0 0
\(664\) 5.75379 0.223290
\(665\) 0 0
\(666\) −9.27944 9.27944i −0.359571 0.359571i
\(667\) −20.1080 −0.778583
\(668\) 63.8900 + 63.8900i 2.47198 + 2.47198i
\(669\) −10.5577 + 10.5577i −0.408185 + 0.408185i
\(670\) −25.8040 + 25.8040i −0.996897 + 0.996897i
\(671\) 14.2462i 0.549969i
\(672\) 0 0
\(673\) −0.522293 + 0.522293i −0.0201329 + 0.0201329i −0.717102 0.696969i \(-0.754532\pi\)
0.696969 + 0.717102i \(0.254532\pi\)
\(674\) −30.3185 + 30.3185i −1.16783 + 1.16783i
\(675\) −5.43387 5.43387i −0.209150 0.209150i
\(676\) 58.4233 2.24705
\(677\) 0.930087 + 0.930087i 0.0357461 + 0.0357461i 0.724754 0.689008i \(-0.241953\pi\)
−0.689008 + 0.724754i \(0.741953\pi\)
\(678\) 1.12311i 0.0431326i
\(679\) 0 0
\(680\) 0 0
\(681\) 14.0540 0.538550
\(682\) 12.4924i 0.478360i
\(683\) 6.76104 + 6.76104i 0.258704 + 0.258704i 0.824527 0.565823i \(-0.191441\pi\)
−0.565823 + 0.824527i \(0.691441\pi\)
\(684\) 21.3693 0.817076
\(685\) 0.620058 + 0.620058i 0.0236912 + 0.0236912i
\(686\) 0 0
\(687\) −4.24264 + 4.24264i −0.161867 + 0.161867i
\(688\) 36.0000i 1.37249i
\(689\) 5.36932i 0.204555i
\(690\) −15.7304 + 15.7304i −0.598848 + 0.598848i
\(691\) 20.4954 20.4954i 0.779681 0.779681i −0.200095 0.979776i \(-0.564125\pi\)
0.979776 + 0.200095i \(0.0641252\pi\)
\(692\) 5.83095 + 5.83095i 0.221660 + 0.221660i
\(693\) 0 0
\(694\) −15.3823 15.3823i −0.583902 0.583902i
\(695\) 3.12311i 0.118466i
\(696\) −54.1080 −2.05096
\(697\) 0 0
\(698\) −29.6155 −1.12096
\(699\) 3.56155i 0.134710i
\(700\) 0 0
\(701\) −15.3693 −0.580491 −0.290246 0.956952i \(-0.593737\pi\)
−0.290246 + 0.956952i \(0.593737\pi\)
\(702\) 0.794156 + 0.794156i 0.0299735 + 0.0299735i
\(703\) −16.9706 + 16.9706i −0.640057 + 0.640057i
\(704\) 1.58831 1.58831i 0.0598617 0.0598617i
\(705\) 39.6155i 1.49201i
\(706\) 26.8769i 1.01153i
\(707\) 0 0
\(708\) 22.9756 22.9756i 0.863476 0.863476i
\(709\) −31.6350 31.6350i −1.18808 1.18808i −0.977598 0.210479i \(-0.932498\pi\)
−0.210479 0.977598i \(-0.567502\pi\)
\(710\) −56.9848 −2.13860
\(711\) 6.62511 + 6.62511i 0.248461 + 0.248461i
\(712\) 7.36932i 0.276177i
\(713\) −7.61553 −0.285204
\(714\) 0 0
\(715\) 2.43845 0.0911928
\(716\) 4.00000i 0.149487i
\(717\) −4.41674 4.41674i −0.164946 0.164946i
\(718\) 36.4924 1.36189
\(719\) −8.34935 8.34935i −0.311378 0.311378i 0.534065 0.845443i \(-0.320664\pi\)
−0.845443 + 0.534065i \(0.820664\pi\)
\(720\) −19.3530 + 19.3530i −0.721245 + 0.721245i
\(721\) 0 0
\(722\) 7.54640i 0.280848i
\(723\) 3.36932i 0.125306i
\(724\) 19.3530 19.3530i 0.719250 0.719250i
\(725\) 44.8089 44.8089i 1.66416 1.66416i
\(726\) −15.5075 15.5075i −0.575536 0.575536i
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 111.723 4.13507
\(731\) 0 0
\(732\) −41.6155 −1.53815
\(733\) 11.7538i 0.434136i 0.976156 + 0.217068i \(0.0696494\pi\)
−0.976156 + 0.217068i \(0.930351\pi\)
\(734\) −3.17662 3.17662i −0.117251 0.117251i
\(735\) −24.9309 −0.919589
\(736\) 11.3137 + 11.3137i 0.417029 + 0.417029i
\(737\) −4.41674 + 4.41674i −0.162693 + 0.162693i
\(738\) 6.45101 6.45101i 0.237465 0.237465i
\(739\) 20.6847i 0.760897i −0.924802 0.380449i \(-0.875770\pi\)
0.924802 0.380449i \(-0.124230\pi\)
\(740\) 83.2311i 3.05963i
\(741\) 1.45238 1.45238i 0.0533545 0.0533545i
\(742\) 0 0
\(743\) 20.1472 + 20.1472i 0.739129 + 0.739129i 0.972409 0.233281i \(-0.0749462\pi\)
−0.233281 + 0.972409i \(0.574946\pi\)
\(744\) −20.4924 −0.751289
\(745\) −30.8408 30.8408i −1.12992 1.12992i
\(746\) 0.630683i 0.0230909i
\(747\) −0.876894 −0.0320839
\(748\) 0 0
\(749\) 0 0
\(750\) 24.4924i 0.894337i
\(751\) 17.9388 + 17.9388i 0.654597 + 0.654597i 0.954096 0.299500i \(-0.0968198\pi\)
−0.299500 + 0.954096i \(0.596820\pi\)
\(752\) 85.4773 3.11704
\(753\) −6.00505 6.00505i −0.218836 0.218836i
\(754\) −6.54877 + 6.54877i −0.238492 + 0.238492i
\(755\) 20.1472 20.1472i 0.733231 0.733231i
\(756\) 0 0
\(757\) 16.0540i 0.583492i 0.956496 + 0.291746i \(0.0942361\pi\)
−0.956496 + 0.291746i \(0.905764\pi\)
\(758\) 21.7355 21.7355i 0.789469 0.789469i
\(759\) −2.69250 + 2.69250i −0.0977314 + 0.0977314i
\(760\) 77.4121 + 77.4121i 2.80803 + 2.80803i
\(761\) 15.7538 0.571074 0.285537 0.958368i \(-0.407828\pi\)
0.285537 + 0.958368i \(0.407828\pi\)
\(762\) −35.8776 35.8776i −1.29971 1.29971i
\(763\) 0 0
\(764\) −22.2462 −0.804840
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) 3.12311i 0.112769i
\(768\) −19.1300 19.1300i −0.690296 0.690296i
\(769\) −40.5464 −1.46214 −0.731070 0.682302i \(-0.760979\pi\)
−0.731070 + 0.682302i \(0.760979\pi\)
\(770\) 0 0
\(771\) −10.8677 + 10.8677i −0.391392 + 0.391392i
\(772\) −25.0099 + 25.0099i −0.900125 + 0.900125i
\(773\) 8.63068i 0.310424i −0.987881 0.155212i \(-0.950394\pi\)
0.987881 0.155212i \(-0.0496061\pi\)
\(774\) 12.0000i 0.431331i
\(775\) 16.9706 16.9706i 0.609601 0.609601i
\(776\) −13.3480 + 13.3480i −0.479165 + 0.479165i
\(777\) 0 0
\(778\) 91.8617 3.29340
\(779\) −11.7978 11.7978i −0.422701 0.422701i
\(780\) 7.12311i 0.255048i
\(781\) −9.75379 −0.349018
\(782\) 0 0
\(783\) 8.24621 0.294696
\(784\) 53.7926i 1.92116i
\(785\) −16.8346 16.8346i −0.600854 0.600854i
\(786\) −36.9848 −1.31921
\(787\) −7.24517 7.24517i −0.258262 0.258262i 0.566085 0.824347i \(-0.308457\pi\)
−0.824347 + 0.566085i \(0.808457\pi\)
\(788\) 28.8066 28.8066i 1.02619 1.02619i
\(789\) 14.4903 14.4903i 0.515869 0.515869i
\(790\) 85.4773i 3.04114i
\(791\) 0 0
\(792\) −7.24517 + 7.24517i −0.257446 + 0.257446i
\(793\) −2.82843 + 2.82843i −0.100440 + 0.100440i
\(794\) 35.0835 + 35.0835i 1.24507 + 1.24507i
\(795\) 43.6155 1.54688
\(796\) −51.6081 51.6081i −1.82920 1.82920i
\(797\) 9.61553i 0.340599i 0.985392 + 0.170300i \(0.0544736\pi\)
−0.985392 + 0.170300i \(0.945526\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −50.4233 −1.78273
\(801\) 1.12311i 0.0396830i
\(802\) 70.9611 + 70.9611i 2.50572 + 2.50572i
\(803\) 19.1231 0.674840
\(804\) −12.9020 12.9020i −0.455019 0.455019i
\(805\) 0 0
\(806\) −2.48023 + 2.48023i −0.0873624 + 0.0873624i
\(807\) 16.4384i 0.578661i
\(808\) 71.3693i 2.51076i
\(809\) 11.2755 11.2755i 0.396427 0.396427i −0.480544 0.876971i \(-0.659561\pi\)
0.876971 + 0.480544i \(0.159561\pi\)
\(810\) 6.45101 6.45101i 0.226665 0.226665i
\(811\) −32.0810 32.0810i −1.12651 1.12651i −0.990740 0.135775i \(-0.956648\pi\)
−0.135775 0.990740i \(-0.543352\pi\)
\(812\) 0 0
\(813\) 14.0062 + 14.0062i 0.491219 + 0.491219i
\(814\) 20.4924i 0.718259i
\(815\) −53.8617 −1.88669
\(816\) 0 0
\(817\) −21.9460 −0.767794
\(818\) 37.6155i 1.31520i
\(819\) 0 0
\(820\) 57.8617 2.02062
\(821\) −8.79531 8.79531i −0.306958 0.306958i 0.536770 0.843729i \(-0.319644\pi\)
−0.843729 + 0.536770i \(0.819644\pi\)
\(822\) −0.445960 + 0.445960i −0.0155547 + 0.0155547i
\(823\) 2.48023 2.48023i 0.0864554 0.0864554i −0.662556 0.749012i \(-0.730529\pi\)
0.749012 + 0.662556i \(0.230529\pi\)
\(824\) 109.477i 3.81382i
\(825\) 12.0000i 0.417786i
\(826\) 0 0
\(827\) −33.5333 + 33.5333i −1.16607 + 1.16607i −0.182945 + 0.983123i \(0.558563\pi\)
−0.983123 + 0.182945i \(0.941437\pi\)
\(828\) −7.86522 7.86522i −0.273335 0.273335i
\(829\) −17.5076 −0.608063 −0.304032 0.952662i \(-0.598333\pi\)
−0.304032 + 0.952662i \(0.598333\pi\)
\(830\) −5.65685 5.65685i −0.196352 0.196352i
\(831\) 6.00000i 0.208138i
\(832\) 0.630683 0.0218650
\(833\) 0 0
\(834\) −2.24621 −0.0777799
\(835\) 70.5464i 2.44136i
\(836\) 23.5957 + 23.5957i 0.816073 + 0.816073i
\(837\) 3.12311 0.107950
\(838\) 0.891921 + 0.891921i 0.0308109 + 0.0308109i
\(839\) 18.4229 18.4229i 0.636031 0.636031i −0.313543 0.949574i \(-0.601516\pi\)
0.949574 + 0.313543i \(0.101516\pi\)
\(840\) 0 0
\(841\) 39.0000i 1.34483i
\(842\) 62.6004i 2.15735i
\(843\) 7.69113 7.69113i 0.264896 0.264896i
\(844\) −43.1228 + 43.1228i −1.48435 + 1.48435i
\(845\) −32.2550 32.2550i −1.10961 1.10961i
\(846\) −28.4924 −0.979590
\(847\) 0 0
\(848\) 94.1080i 3.23168i
\(849\) −21.3693 −0.733393
\(850\) 0 0
\(851\) 12.4924 0.428235
\(852\) 28.4924i 0.976134i
\(853\) 20.3213 + 20.3213i 0.695787 + 0.695787i 0.963499 0.267712i \(-0.0862674\pi\)
−0.267712 + 0.963499i \(0.586267\pi\)
\(854\) 0 0
\(855\) −11.7978 11.7978i −0.403477 0.403477i
\(856\) −21.7355 + 21.7355i −0.742904 + 0.742904i
\(857\) −4.24264 + 4.24264i −0.144926 + 0.144926i −0.775847 0.630921i \(-0.782677\pi\)
0.630921 + 0.775847i \(0.282677\pi\)
\(858\) 1.75379i 0.0598734i
\(859\) 12.0000i 0.409435i 0.978821 + 0.204717i \(0.0656275\pi\)
−0.978821 + 0.204717i \(0.934372\pi\)
\(860\) 53.8164 53.8164i 1.83513 1.83513i
\(861\) 0 0
\(862\) 43.4710 + 43.4710i 1.48063 + 1.48063i
\(863\) 9.75379 0.332023 0.166011 0.986124i \(-0.446911\pi\)
0.166011 + 0.986124i \(0.446911\pi\)
\(864\) −4.63972 4.63972i −0.157846 0.157846i
\(865\) 6.43845i 0.218914i
\(866\) −68.3542 −2.32277
\(867\) 0 0
\(868\) 0 0
\(869\) 14.6307i 0.496312i
\(870\) 53.1964 + 53.1964i 1.80353 + 1.80353i
\(871\) −1.75379 −0.0594249
\(872\) 31.9069 + 31.9069i 1.08050 + 1.08050i
\(873\) 2.03427 2.03427i 0.0688497 0.0688497i
\(874\) −20.6909 + 20.6909i −0.699880 + 0.699880i
\(875\) 0 0
\(876\) 55.8617i 1.88739i
\(877\) −24.0416 + 24.0416i −0.811828 + 0.811828i −0.984908 0.173080i \(-0.944628\pi\)
0.173080 + 0.984908i \(0.444628\pi\)
\(878\) −40.2944 + 40.2944i −1.35987 + 1.35987i
\(879\) −0.794156 0.794156i −0.0267862 0.0267862i
\(880\) −42.7386 −1.44072
\(881\) −28.4584 28.4584i −0.958787 0.958787i 0.0403969 0.999184i \(-0.487138\pi\)
−0.999184 + 0.0403969i \(0.987138\pi\)
\(882\) 17.9309i 0.603764i
\(883\) −23.4233 −0.788257 −0.394128 0.919055i \(-0.628953\pi\)
−0.394128 + 0.919055i \(0.628953\pi\)
\(884\) 0 0
\(885\) −25.3693 −0.852780
\(886\) 79.7235i 2.67836i
\(887\) −13.0380 13.0380i −0.437772 0.437772i 0.453490 0.891261i \(-0.350179\pi\)
−0.891261 + 0.453490i \(0.850179\pi\)
\(888\) 33.6155 1.12806
\(889\) 0 0
\(890\) −7.24517 + 7.24517i −0.242858 + 0.242858i
\(891\) 1.10418 1.10418i 0.0369916 0.0369916i
\(892\) 68.1080i 2.28042i
\(893\) 52.1080i 1.74373i
\(894\) 22.1815 22.1815i 0.741859 0.741859i
\(895\) 2.20837 2.20837i 0.0738176 0.0738176i
\(896\) 0 0
\(897\) −1.06913 −0.0356972
\(898\) 66.5444 + 66.5444i 2.22061 + 2.22061i
\(899\) 25.7538i 0.858937i
\(900\) 35.0540 1.16847
\(901\) 0 0
\(902\) 14.2462 0.474347
\(903\) 0 0
\(904\) −2.03427 2.03427i −0.0676589 0.0676589i
\(905\) −21.3693 −0.710340
\(906\) 14.4903 + 14.4903i 0.481409 + 0.481409i
\(907\) 6.97330 6.97330i 0.231545 0.231545i −0.581793 0.813337i \(-0.697648\pi\)
0.813337 + 0.581793i \(0.197648\pi\)
\(908\) −45.3312 + 45.3312i −1.50437 + 1.50437i
\(909\) 10.8769i 0.360764i
\(910\) 0 0
\(911\) 17.1828 17.1828i 0.569292 0.569292i −0.362638 0.931930i \(-0.618124\pi\)
0.931930 + 0.362638i \(0.118124\pi\)
\(912\) −25.4558 + 25.4558i −0.842927 + 0.842927i
\(913\) −0.968253 0.968253i −0.0320445 0.0320445i
\(914\) 35.3693 1.16991
\(915\) 22.9756 + 22.9756i 0.759550 + 0.759550i
\(916\) 27.3693i 0.904308i
\(917\) 0 0
\(918\) 0 0
\(919\) −16.6847 −0.550376 −0.275188 0.961390i \(-0.588740\pi\)
−0.275188 + 0.961390i \(0.588740\pi\)
\(920\) 56.9848i 1.87873i
\(921\) 22.9756 + 22.9756i 0.757072 + 0.757072i
\(922\) −21.1231 −0.695652
\(923\) −1.93651 1.93651i −0.0637409 0.0637409i
\(924\) 0 0
\(925\) −27.8383 + 27.8383i −0.915318 + 0.915318i
\(926\) 104.985i 3.45002i
\(927\) 16.6847i 0.547996i
\(928\) 38.2601 38.2601i 1.25595 1.25595i
\(929\) −2.17020 + 2.17020i −0.0712020 + 0.0712020i −0.741811 0.670609i \(-0.766033\pi\)
0.670609 + 0.741811i \(0.266033\pi\)
\(930\) 20.1472 + 20.1472i 0.660652 + 0.660652i
\(931\) −32.7926 −1.07473
\(932\) 11.4878 + 11.4878i 0.376296 + 0.376296i
\(933\) 0 0
\(934\) −54.7386 −1.79110
\(935\) 0 0
\(936\) −2.87689 −0.0940342
\(937\) 22.0000i 0.718709i 0.933201 + 0.359354i \(0.117003\pi\)
−0.933201 + 0.359354i \(0.882997\pi\)
\(938\) 0 0
\(939\) 33.6155 1.09700
\(940\) −127.780 127.780i −4.16773 4.16773i
\(941\) −21.2132 + 21.2132i −0.691531 + 0.691531i −0.962569 0.271038i \(-0.912633\pi\)
0.271038 + 0.962569i \(0.412633\pi\)
\(942\) 12.1079 12.1079i 0.394496 0.394496i
\(943\) 8.68466i 0.282811i
\(944\) 54.7386i 1.78159i
\(945\) 0 0
\(946\) 13.2502 13.2502i 0.430802 0.430802i
\(947\) 8.48528 + 8.48528i 0.275735 + 0.275735i 0.831404 0.555669i \(-0.187538\pi\)
−0.555669 + 0.831404i \(0.687538\pi\)
\(948\) −42.7386 −1.38809
\(949\) 3.79668 + 3.79668i 0.123245 + 0.123245i
\(950\) 92.2159i 2.99188i
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 36.3542 1.17763 0.588813 0.808269i \(-0.299595\pi\)
0.588813 + 0.808269i \(0.299595\pi\)
\(954\) 31.3693i 1.01562i
\(955\) 12.2820 + 12.2820i 0.397435 + 0.397435i
\(956\) 28.4924 0.921511
\(957\) 9.10534 + 9.10534i 0.294334 + 0.294334i
\(958\) 44.0147 44.0147i 1.42205 1.42205i
\(959\) 0 0
\(960\) 5.12311i 0.165348i
\(961\) 21.2462i 0.685362i
\(962\) 4.06854 4.06854i 0.131175 0.131175i
\(963\) 3.31255 3.31255i 0.106746 0.106746i
\(964\) 10.8677 + 10.8677i 0.350027 + 0.350027i
\(965\) 27.6155 0.888975
\(966\) 0 0
\(967\) 42.4384i 1.36473i −0.731012 0.682364i \(-0.760952\pi\)
0.731012 0.682364i \(-0.239048\pi\)
\(968\) 56.1771 1.80560
\(969\) 0 0
\(970\) 26.2462 0.842715
\(971\) 43.6155i 1.39969i 0.714295 + 0.699844i \(0.246747\pi\)
−0.714295 + 0.699844i \(0.753253\pi\)
\(972\) 3.22550 + 3.22550i 0.103458 + 0.103458i
\(973\) 0 0
\(974\) −31.4609 31.4609i −1.00807 1.00807i
\(975\) 2.38247 2.38247i 0.0763000 0.0763000i
\(976\) 49.5738 49.5738i 1.58682 1.58682i
\(977\) 8.24621i 0.263820i 0.991262 + 0.131910i \(0.0421109\pi\)
−0.991262 + 0.131910i \(0.957889\pi\)
\(978\) 38.7386i 1.23872i
\(979\) −1.24012 + 1.24012i −0.0396343 + 0.0396343i
\(980\) 80.4146 80.4146i 2.56875 2.56875i
\(981\) −4.86270 4.86270i −0.155254 0.155254i
\(982\) −54.7386 −1.74678
\(983\) −21.8714 21.8714i −0.697590 0.697590i 0.266300 0.963890i \(-0.414199\pi\)
−0.963890 + 0.266300i \(0.914199\pi\)
\(984\) 23.3693i 0.744987i
\(985\) −31.8078 −1.01348
\(986\) 0 0
\(987\) 0 0
\(988\) 9.36932i 0.298078i
\(989\) 8.07749 + 8.07749i 0.256849 + 0.256849i
\(990\) 14.2462 0.452774
\(991\) 30.2208 + 30.2208i 0.959995 + 0.959995i 0.999230 0.0392354i \(-0.0124922\pi\)
−0.0392354 + 0.999230i \(0.512492\pi\)
\(992\) 14.4903 14.4903i 0.460068 0.460068i
\(993\) 24.6999 24.6999i 0.783826 0.783826i
\(994\) 0 0
\(995\) 56.9848i 1.80654i
\(996\) 2.82843 2.82843i 0.0896221 0.0896221i
\(997\) 7.07107 7.07107i 0.223943 0.223943i −0.586214 0.810157i \(-0.699382\pi\)
0.810157 + 0.586214i \(0.199382\pi\)
\(998\) −24.2157 24.2157i −0.766535 0.766535i
\(999\) −5.12311 −0.162088
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 867.2.e.f.829.4 8
17.2 even 8 867.2.a.f.1.1 2
17.3 odd 16 867.2.h.j.712.4 16
17.4 even 4 inner 867.2.e.f.616.2 8
17.5 odd 16 867.2.h.j.733.1 16
17.6 odd 16 867.2.h.j.757.2 16
17.7 odd 16 867.2.h.j.688.4 16
17.8 even 8 867.2.d.c.577.3 4
17.9 even 8 867.2.d.c.577.4 4
17.10 odd 16 867.2.h.j.688.3 16
17.11 odd 16 867.2.h.j.757.1 16
17.12 odd 16 867.2.h.j.733.2 16
17.13 even 4 inner 867.2.e.f.616.1 8
17.14 odd 16 867.2.h.j.712.3 16
17.15 even 8 51.2.a.b.1.1 2
17.16 even 2 inner 867.2.e.f.829.3 8
51.2 odd 8 2601.2.a.t.1.2 2
51.32 odd 8 153.2.a.e.1.2 2
68.15 odd 8 816.2.a.m.1.2 2
85.32 odd 8 1275.2.b.d.1174.1 4
85.49 even 8 1275.2.a.n.1.2 2
85.83 odd 8 1275.2.b.d.1174.4 4
119.83 odd 8 2499.2.a.o.1.1 2
136.83 odd 8 3264.2.a.bg.1.1 2
136.117 even 8 3264.2.a.bl.1.1 2
187.32 odd 8 6171.2.a.p.1.2 2
204.83 even 8 2448.2.a.v.1.1 2
221.168 even 8 8619.2.a.q.1.2 2
255.134 odd 8 3825.2.a.s.1.1 2
357.83 even 8 7497.2.a.v.1.2 2
408.83 even 8 9792.2.a.cz.1.2 2
408.389 odd 8 9792.2.a.cy.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
51.2.a.b.1.1 2 17.15 even 8
153.2.a.e.1.2 2 51.32 odd 8
816.2.a.m.1.2 2 68.15 odd 8
867.2.a.f.1.1 2 17.2 even 8
867.2.d.c.577.3 4 17.8 even 8
867.2.d.c.577.4 4 17.9 even 8
867.2.e.f.616.1 8 17.13 even 4 inner
867.2.e.f.616.2 8 17.4 even 4 inner
867.2.e.f.829.3 8 17.16 even 2 inner
867.2.e.f.829.4 8 1.1 even 1 trivial
867.2.h.j.688.3 16 17.10 odd 16
867.2.h.j.688.4 16 17.7 odd 16
867.2.h.j.712.3 16 17.14 odd 16
867.2.h.j.712.4 16 17.3 odd 16
867.2.h.j.733.1 16 17.5 odd 16
867.2.h.j.733.2 16 17.12 odd 16
867.2.h.j.757.1 16 17.11 odd 16
867.2.h.j.757.2 16 17.6 odd 16
1275.2.a.n.1.2 2 85.49 even 8
1275.2.b.d.1174.1 4 85.32 odd 8
1275.2.b.d.1174.4 4 85.83 odd 8
2448.2.a.v.1.1 2 204.83 even 8
2499.2.a.o.1.1 2 119.83 odd 8
2601.2.a.t.1.2 2 51.2 odd 8
3264.2.a.bg.1.1 2 136.83 odd 8
3264.2.a.bl.1.1 2 136.117 even 8
3825.2.a.s.1.1 2 255.134 odd 8
6171.2.a.p.1.2 2 187.32 odd 8
7497.2.a.v.1.2 2 357.83 even 8
8619.2.a.q.1.2 2 221.168 even 8
9792.2.a.cy.1.2 2 408.389 odd 8
9792.2.a.cz.1.2 2 408.83 even 8