Properties

Label 578.2.d.e.399.2
Level $578$
Weight $2$
Character 578.399
Analytic conductor $4.615$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [578,2,Mod(155,578)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(578, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("578.155");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 578 = 2 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 578.d (of order \(8\), degree \(4\), 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: \(4.61535323683\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\Q(\zeta_{16})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 34)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 399.2
Root \(-0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 578.399
Dual form 578.2.d.e.423.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.765367 - 1.84776i) q^{3} -1.00000i q^{4} +(0.765367 + 1.84776i) q^{6} +(3.69552 - 1.53073i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.765367 - 1.84776i) q^{3} -1.00000i q^{4} +(0.765367 + 1.84776i) q^{6} +(3.69552 - 1.53073i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(2.29610 + 5.54328i) q^{11} +(-1.84776 - 0.765367i) q^{12} +2.00000i q^{13} +(-1.53073 + 3.69552i) q^{14} -1.00000 q^{16} +1.00000 q^{18} +(2.82843 - 2.82843i) q^{19} -8.00000i q^{21} +(-5.54328 - 2.29610i) q^{22} +(1.84776 - 0.765367i) q^{24} +(-3.53553 - 3.53553i) q^{25} +(-1.41421 - 1.41421i) q^{26} +(3.69552 - 1.53073i) q^{27} +(-1.53073 - 3.69552i) q^{28} +(-1.53073 + 3.69552i) q^{31} +(0.707107 - 0.707107i) q^{32} +12.0000 q^{33} +(-0.707107 + 0.707107i) q^{36} +(1.53073 - 3.69552i) q^{37} +4.00000i q^{38} +(3.69552 + 1.53073i) q^{39} +(-5.54328 + 2.29610i) q^{41} +(5.65685 + 5.65685i) q^{42} +(-5.65685 - 5.65685i) q^{43} +(5.54328 - 2.29610i) q^{44} +(-0.765367 + 1.84776i) q^{48} +(6.36396 - 6.36396i) q^{49} +5.00000 q^{50} +2.00000 q^{52} +(4.24264 - 4.24264i) q^{53} +(-1.53073 + 3.69552i) q^{54} +(3.69552 + 1.53073i) q^{56} +(-3.06147 - 7.39104i) q^{57} +(-3.69552 + 1.53073i) q^{61} +(-1.53073 - 3.69552i) q^{62} +(-3.69552 - 1.53073i) q^{63} +1.00000i q^{64} +(-8.48528 + 8.48528i) q^{66} -8.00000 q^{67} -1.00000i q^{72} +(-1.84776 - 0.765367i) q^{73} +(1.53073 + 3.69552i) q^{74} +(-9.23880 + 3.82683i) q^{75} +(-2.82843 - 2.82843i) q^{76} +(16.9706 + 16.9706i) q^{77} +(-3.69552 + 1.53073i) q^{78} +(3.06147 + 7.39104i) q^{79} -11.0000i q^{81} +(2.29610 - 5.54328i) q^{82} -8.00000 q^{84} +8.00000 q^{86} +(-2.29610 + 5.54328i) q^{88} +6.00000i q^{89} +(3.06147 + 7.39104i) q^{91} +(5.65685 + 5.65685i) q^{93} +(-0.765367 - 1.84776i) q^{96} +(12.9343 + 5.35757i) q^{97} +9.00000i q^{98} +(2.29610 - 5.54328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{16} + 8 q^{18} + 96 q^{33} + 40 q^{50} + 16 q^{52} - 64 q^{67} - 64 q^{84} + 64 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/578\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.765367 1.84776i 0.441885 1.06680i −0.533402 0.845862i \(-0.679087\pi\)
0.975287 0.220942i \(-0.0709133\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(6\) 0.765367 + 1.84776i 0.312460 + 0.754344i
\(7\) 3.69552 1.53073i 1.39677 0.578563i 0.447862 0.894103i \(-0.352186\pi\)
0.948912 + 0.315540i \(0.102186\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) 2.29610 + 5.54328i 0.692300 + 1.67136i 0.740094 + 0.672504i \(0.234781\pi\)
−0.0477934 + 0.998857i \(0.515219\pi\)
\(12\) −1.84776 0.765367i −0.533402 0.220942i
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) −1.53073 + 3.69552i −0.409106 + 0.987669i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0 0
\(18\) 1.00000 0.235702
\(19\) 2.82843 2.82843i 0.648886 0.648886i −0.303838 0.952724i \(-0.598268\pi\)
0.952724 + 0.303838i \(0.0982682\pi\)
\(20\) 0 0
\(21\) 8.00000i 1.74574i
\(22\) −5.54328 2.29610i −1.18183 0.489530i
\(23\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(24\) 1.84776 0.765367i 0.377172 0.156230i
\(25\) −3.53553 3.53553i −0.707107 0.707107i
\(26\) −1.41421 1.41421i −0.277350 0.277350i
\(27\) 3.69552 1.53073i 0.711203 0.294590i
\(28\) −1.53073 3.69552i −0.289281 0.698387i
\(29\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(30\) 0 0
\(31\) −1.53073 + 3.69552i −0.274928 + 0.663735i −0.999681 0.0252745i \(-0.991954\pi\)
0.724753 + 0.689009i \(0.241954\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 12.0000 2.08893
\(34\) 0 0
\(35\) 0 0
\(36\) −0.707107 + 0.707107i −0.117851 + 0.117851i
\(37\) 1.53073 3.69552i 0.251651 0.607539i −0.746687 0.665176i \(-0.768356\pi\)
0.998338 + 0.0576366i \(0.0183565\pi\)
\(38\) 4.00000i 0.648886i
\(39\) 3.69552 + 1.53073i 0.591756 + 0.245114i
\(40\) 0 0
\(41\) −5.54328 + 2.29610i −0.865714 + 0.358591i −0.770940 0.636908i \(-0.780213\pi\)
−0.0947747 + 0.995499i \(0.530213\pi\)
\(42\) 5.65685 + 5.65685i 0.872872 + 0.872872i
\(43\) −5.65685 5.65685i −0.862662 0.862662i 0.128984 0.991647i \(-0.458828\pi\)
−0.991647 + 0.128984i \(0.958828\pi\)
\(44\) 5.54328 2.29610i 0.835680 0.346150i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −0.765367 + 1.84776i −0.110471 + 0.266701i
\(49\) 6.36396 6.36396i 0.909137 0.909137i
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 4.24264 4.24264i 0.582772 0.582772i −0.352892 0.935664i \(-0.614802\pi\)
0.935664 + 0.352892i \(0.114802\pi\)
\(54\) −1.53073 + 3.69552i −0.208306 + 0.502896i
\(55\) 0 0
\(56\) 3.69552 + 1.53073i 0.493834 + 0.204553i
\(57\) −3.06147 7.39104i −0.405501 0.978967i
\(58\) 0 0
\(59\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(60\) 0 0
\(61\) −3.69552 + 1.53073i −0.473163 + 0.195990i −0.606505 0.795080i \(-0.707429\pi\)
0.133342 + 0.991070i \(0.457429\pi\)
\(62\) −1.53073 3.69552i −0.194403 0.469331i
\(63\) −3.69552 1.53073i −0.465592 0.192854i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −8.48528 + 8.48528i −1.04447 + 1.04447i
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −1.84776 0.765367i −0.216264 0.0895794i 0.271921 0.962319i \(-0.412341\pi\)
−0.488185 + 0.872740i \(0.662341\pi\)
\(74\) 1.53073 + 3.69552i 0.177944 + 0.429595i
\(75\) −9.23880 + 3.82683i −1.06680 + 0.441885i
\(76\) −2.82843 2.82843i −0.324443 0.324443i
\(77\) 16.9706 + 16.9706i 1.93398 + 1.93398i
\(78\) −3.69552 + 1.53073i −0.418435 + 0.173321i
\(79\) 3.06147 + 7.39104i 0.344442 + 0.831557i 0.997255 + 0.0740378i \(0.0235886\pi\)
−0.652813 + 0.757519i \(0.726411\pi\)
\(80\) 0 0
\(81\) 11.0000i 1.22222i
\(82\) 2.29610 5.54328i 0.253562 0.612153i
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) −8.00000 −0.872872
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) −2.29610 + 5.54328i −0.244765 + 0.590915i
\(89\) 6.00000i 0.635999i 0.948091 + 0.317999i \(0.103011\pi\)
−0.948091 + 0.317999i \(0.896989\pi\)
\(90\) 0 0
\(91\) 3.06147 + 7.39104i 0.320929 + 0.774791i
\(92\) 0 0
\(93\) 5.65685 + 5.65685i 0.586588 + 0.586588i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.765367 1.84776i −0.0781149 0.188586i
\(97\) 12.9343 + 5.35757i 1.31328 + 0.543979i 0.925840 0.377916i \(-0.123359\pi\)
0.387441 + 0.921895i \(0.373359\pi\)
\(98\) 9.00000i 0.909137i
\(99\) 2.29610 5.54328i 0.230767 0.557120i
\(100\) −3.53553 + 3.53553i −0.353553 + 0.353553i
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) −1.41421 + 1.41421i −0.138675 + 0.138675i
\(105\) 0 0
\(106\) 6.00000i 0.582772i
\(107\) 5.54328 + 2.29610i 0.535889 + 0.221972i 0.634180 0.773185i \(-0.281338\pi\)
−0.0982914 + 0.995158i \(0.531338\pi\)
\(108\) −1.53073 3.69552i −0.147295 0.355601i
\(109\) 14.7821 6.12293i 1.41587 0.586471i 0.462048 0.886855i \(-0.347115\pi\)
0.953818 + 0.300384i \(0.0971149\pi\)
\(110\) 0 0
\(111\) −5.65685 5.65685i −0.536925 0.536925i
\(112\) −3.69552 + 1.53073i −0.349194 + 0.144641i
\(113\) −2.29610 5.54328i −0.215999 0.521468i 0.778325 0.627861i \(-0.216070\pi\)
−0.994324 + 0.106394i \(0.966070\pi\)
\(114\) 7.39104 + 3.06147i 0.692234 + 0.286733i
\(115\) 0 0
\(116\) 0 0
\(117\) 1.41421 1.41421i 0.130744 0.130744i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −17.6777 + 17.6777i −1.60706 + 1.60706i
\(122\) 1.53073 3.69552i 0.138586 0.334576i
\(123\) 12.0000i 1.08200i
\(124\) 3.69552 + 1.53073i 0.331867 + 0.137464i
\(125\) 0 0
\(126\) 3.69552 1.53073i 0.329223 0.136369i
\(127\) −11.3137 11.3137i −1.00393 1.00393i −0.999992 0.00393704i \(-0.998747\pi\)
−0.00393704 0.999992i \(-0.501253\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −14.7821 + 6.12293i −1.30149 + 0.539094i
\(130\) 0 0
\(131\) −5.54328 2.29610i −0.484318 0.200611i 0.127145 0.991884i \(-0.459419\pi\)
−0.611463 + 0.791273i \(0.709419\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 6.12293 14.7821i 0.530926 1.28177i
\(134\) 5.65685 5.65685i 0.488678 0.488678i
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) −0.765367 + 1.84776i −0.0649176 + 0.156725i −0.953009 0.302942i \(-0.902031\pi\)
0.888091 + 0.459667i \(0.152031\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −11.0866 + 4.59220i −0.927104 + 0.384019i
\(144\) 0.707107 + 0.707107i 0.0589256 + 0.0589256i
\(145\) 0 0
\(146\) 1.84776 0.765367i 0.152922 0.0633422i
\(147\) −6.88830 16.6298i −0.568138 1.37161i
\(148\) −3.69552 1.53073i −0.303770 0.125826i
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) 3.82683 9.23880i 0.312460 0.754344i
\(151\) −11.3137 + 11.3137i −0.920697 + 0.920697i −0.997079 0.0763821i \(-0.975663\pi\)
0.0763821 + 0.997079i \(0.475663\pi\)
\(152\) 4.00000 0.324443
\(153\) 0 0
\(154\) −24.0000 −1.93398
\(155\) 0 0
\(156\) 1.53073 3.69552i 0.122557 0.295878i
\(157\) 14.0000i 1.11732i −0.829396 0.558661i \(-0.811315\pi\)
0.829396 0.558661i \(-0.188685\pi\)
\(158\) −7.39104 3.06147i −0.587999 0.243557i
\(159\) −4.59220 11.0866i −0.364185 0.879221i
\(160\) 0 0
\(161\) 0 0
\(162\) 7.77817 + 7.77817i 0.611111 + 0.611111i
\(163\) 1.84776 0.765367i 0.144728 0.0599482i −0.309144 0.951015i \(-0.600042\pi\)
0.453872 + 0.891067i \(0.350042\pi\)
\(164\) 2.29610 + 5.54328i 0.179295 + 0.432857i
\(165\) 0 0
\(166\) 0 0
\(167\) 4.59220 11.0866i 0.355355 0.857903i −0.640585 0.767887i \(-0.721308\pi\)
0.995940 0.0900162i \(-0.0286919\pi\)
\(168\) 5.65685 5.65685i 0.436436 0.436436i
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) −5.65685 + 5.65685i −0.431331 + 0.431331i
\(173\) −9.18440 + 22.1731i −0.698277 + 1.68579i 0.0291222 + 0.999576i \(0.490729\pi\)
−0.727399 + 0.686214i \(0.759271\pi\)
\(174\) 0 0
\(175\) −18.4776 7.65367i −1.39677 0.578563i
\(176\) −2.29610 5.54328i −0.173075 0.417840i
\(177\) 0 0
\(178\) −4.24264 4.24264i −0.317999 0.317999i
\(179\) −8.48528 8.48528i −0.634220 0.634220i 0.314904 0.949124i \(-0.398028\pi\)
−0.949124 + 0.314904i \(0.898028\pi\)
\(180\) 0 0
\(181\) −1.53073 3.69552i −0.113779 0.274686i 0.856725 0.515774i \(-0.172496\pi\)
−0.970503 + 0.241088i \(0.922496\pi\)
\(182\) −7.39104 3.06147i −0.547860 0.226931i
\(183\) 8.00000i 0.591377i
\(184\) 0 0
\(185\) 0 0
\(186\) −8.00000 −0.586588
\(187\) 0 0
\(188\) 0 0
\(189\) 11.3137 11.3137i 0.822951 0.822951i
\(190\) 0 0
\(191\) 24.0000i 1.73658i 0.496058 + 0.868290i \(0.334780\pi\)
−0.496058 + 0.868290i \(0.665220\pi\)
\(192\) 1.84776 + 0.765367i 0.133351 + 0.0552356i
\(193\) 3.82683 + 9.23880i 0.275462 + 0.665023i 0.999699 0.0245275i \(-0.00780812\pi\)
−0.724238 + 0.689551i \(0.757808\pi\)
\(194\) −12.9343 + 5.35757i −0.928630 + 0.384651i
\(195\) 0 0
\(196\) −6.36396 6.36396i −0.454569 0.454569i
\(197\) −11.0866 + 4.59220i −0.789884 + 0.327181i −0.740897 0.671619i \(-0.765599\pi\)
−0.0489872 + 0.998799i \(0.515599\pi\)
\(198\) 2.29610 + 5.54328i 0.163177 + 0.393944i
\(199\) −14.7821 6.12293i −1.04787 0.434043i −0.208741 0.977971i \(-0.566937\pi\)
−0.839132 + 0.543928i \(0.816937\pi\)
\(200\) 5.00000i 0.353553i
\(201\) −6.12293 + 14.7821i −0.431879 + 1.04265i
\(202\) 12.7279 12.7279i 0.895533 0.895533i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 11.3137 11.3137i 0.788263 0.788263i
\(207\) 0 0
\(208\) 2.00000i 0.138675i
\(209\) 22.1731 + 9.18440i 1.53375 + 0.635298i
\(210\) 0 0
\(211\) 9.23880 3.82683i 0.636025 0.263450i −0.0412856 0.999147i \(-0.513145\pi\)
0.677311 + 0.735697i \(0.263145\pi\)
\(212\) −4.24264 4.24264i −0.291386 0.291386i
\(213\) 0 0
\(214\) −5.54328 + 2.29610i −0.378931 + 0.156958i
\(215\) 0 0
\(216\) 3.69552 + 1.53073i 0.251448 + 0.104153i
\(217\) 16.0000i 1.08615i
\(218\) −6.12293 + 14.7821i −0.414697 + 1.00117i
\(219\) −2.82843 + 2.82843i −0.191127 + 0.191127i
\(220\) 0 0
\(221\) 0 0
\(222\) 8.00000 0.536925
\(223\) −5.65685 + 5.65685i −0.378811 + 0.378811i −0.870673 0.491862i \(-0.836316\pi\)
0.491862 + 0.870673i \(0.336316\pi\)
\(224\) 1.53073 3.69552i 0.102276 0.246917i
\(225\) 5.00000i 0.333333i
\(226\) 5.54328 + 2.29610i 0.368733 + 0.152734i
\(227\) 2.29610 + 5.54328i 0.152398 + 0.367920i 0.981578 0.191060i \(-0.0611926\pi\)
−0.829181 + 0.558981i \(0.811193\pi\)
\(228\) −7.39104 + 3.06147i −0.489483 + 0.202751i
\(229\) 9.89949 + 9.89949i 0.654177 + 0.654177i 0.953996 0.299819i \(-0.0969263\pi\)
−0.299819 + 0.953996i \(0.596926\pi\)
\(230\) 0 0
\(231\) 44.3462 18.3688i 2.91777 1.20858i
\(232\) 0 0
\(233\) 16.6298 + 6.88830i 1.08946 + 0.451268i 0.853817 0.520573i \(-0.174282\pi\)
0.235639 + 0.971841i \(0.424282\pi\)
\(234\) 2.00000i 0.130744i
\(235\) 0 0
\(236\) 0 0
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 3.82683 9.23880i 0.246508 0.595123i −0.751395 0.659853i \(-0.770619\pi\)
0.997903 + 0.0647298i \(0.0206186\pi\)
\(242\) 25.0000i 1.60706i
\(243\) −9.23880 3.82683i −0.592669 0.245492i
\(244\) 1.53073 + 3.69552i 0.0979952 + 0.236581i
\(245\) 0 0
\(246\) −8.48528 8.48528i −0.541002 0.541002i
\(247\) 5.65685 + 5.65685i 0.359937 + 0.359937i
\(248\) −3.69552 + 1.53073i −0.234666 + 0.0972017i
\(249\) 0 0
\(250\) 0 0
\(251\) 24.0000i 1.51487i −0.652913 0.757433i \(-0.726453\pi\)
0.652913 0.757433i \(-0.273547\pi\)
\(252\) −1.53073 + 3.69552i −0.0964272 + 0.232796i
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −4.24264 + 4.24264i −0.264649 + 0.264649i −0.826940 0.562291i \(-0.809920\pi\)
0.562291 + 0.826940i \(0.309920\pi\)
\(258\) 6.12293 14.7821i 0.381197 0.920292i
\(259\) 16.0000i 0.994192i
\(260\) 0 0
\(261\) 0 0
\(262\) 5.54328 2.29610i 0.342465 0.141854i
\(263\) 16.9706 + 16.9706i 1.04645 + 1.04645i 0.998867 + 0.0475824i \(0.0151517\pi\)
0.0475824 + 0.998867i \(0.484848\pi\)
\(264\) 8.48528 + 8.48528i 0.522233 + 0.522233i
\(265\) 0 0
\(266\) 6.12293 + 14.7821i 0.375421 + 0.906347i
\(267\) 11.0866 + 4.59220i 0.678486 + 0.281038i
\(268\) 8.00000i 0.488678i
\(269\) −9.18440 + 22.1731i −0.559983 + 1.35192i 0.349796 + 0.936826i \(0.386251\pi\)
−0.909779 + 0.415093i \(0.863749\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 16.0000 0.968364
\(274\) −4.24264 + 4.24264i −0.256307 + 0.256307i
\(275\) 11.4805 27.7164i 0.692300 1.67136i
\(276\) 0 0
\(277\) −7.39104 3.06147i −0.444084 0.183946i 0.149425 0.988773i \(-0.452258\pi\)
−0.593509 + 0.804827i \(0.702258\pi\)
\(278\) −0.765367 1.84776i −0.0459037 0.110821i
\(279\) 3.69552 1.53073i 0.221245 0.0916426i
\(280\) 0 0
\(281\) −4.24264 4.24264i −0.253095 0.253095i 0.569143 0.822238i \(-0.307275\pi\)
−0.822238 + 0.569143i \(0.807275\pi\)
\(282\) 0 0
\(283\) 5.35757 + 12.9343i 0.318474 + 0.768865i 0.999335 + 0.0364525i \(0.0116058\pi\)
−0.680861 + 0.732413i \(0.738394\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 4.59220 11.0866i 0.271543 0.655562i
\(287\) −16.9706 + 16.9706i −1.00174 + 1.00174i
\(288\) −1.00000 −0.0589256
\(289\) 0 0
\(290\) 0 0
\(291\) 19.7990 19.7990i 1.16064 1.16064i
\(292\) −0.765367 + 1.84776i −0.0447897 + 0.108132i
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 16.6298 + 6.88830i 0.969871 + 0.401734i
\(295\) 0 0
\(296\) 3.69552 1.53073i 0.214798 0.0889721i
\(297\) 16.9706 + 16.9706i 0.984732 + 0.984732i
\(298\) −4.24264 4.24264i −0.245770 0.245770i
\(299\) 0 0
\(300\) 3.82683 + 9.23880i 0.220942 + 0.533402i
\(301\) −29.5641 12.2459i −1.70405 0.705840i
\(302\) 16.0000i 0.920697i
\(303\) −13.7766 + 33.2597i −0.791445 + 1.91072i
\(304\) −2.82843 + 2.82843i −0.162221 + 0.162221i
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 16.9706 16.9706i 0.966988 0.966988i
\(309\) −12.2459 + 29.5641i −0.696643 + 1.68185i
\(310\) 0 0
\(311\) −11.0866 4.59220i −0.628661 0.260400i 0.0455232 0.998963i \(-0.485505\pi\)
−0.674184 + 0.738563i \(0.735505\pi\)
\(312\) 1.53073 + 3.69552i 0.0866607 + 0.209218i
\(313\) 31.4119 13.0112i 1.77551 0.735439i 0.781785 0.623548i \(-0.214309\pi\)
0.993721 0.111891i \(-0.0356907\pi\)
\(314\) 9.89949 + 9.89949i 0.558661 + 0.558661i
\(315\) 0 0
\(316\) 7.39104 3.06147i 0.415778 0.172221i
\(317\) −4.59220 11.0866i −0.257924 0.622683i 0.740877 0.671641i \(-0.234410\pi\)
−0.998801 + 0.0489576i \(0.984410\pi\)
\(318\) 11.0866 + 4.59220i 0.621703 + 0.257518i
\(319\) 0 0
\(320\) 0 0
\(321\) 8.48528 8.48528i 0.473602 0.473602i
\(322\) 0 0
\(323\) 0 0
\(324\) −11.0000 −0.611111
\(325\) 7.07107 7.07107i 0.392232 0.392232i
\(326\) −0.765367 + 1.84776i −0.0423898 + 0.102338i
\(327\) 32.0000i 1.76960i
\(328\) −5.54328 2.29610i −0.306076 0.126781i
\(329\) 0 0
\(330\) 0 0
\(331\) −11.3137 11.3137i −0.621858 0.621858i 0.324149 0.946006i \(-0.394922\pi\)
−0.946006 + 0.324149i \(0.894922\pi\)
\(332\) 0 0
\(333\) −3.69552 + 1.53073i −0.202513 + 0.0838837i
\(334\) 4.59220 + 11.0866i 0.251274 + 0.606629i
\(335\) 0 0
\(336\) 8.00000i 0.436436i
\(337\) −8.41904 + 20.3253i −0.458614 + 1.10719i 0.510345 + 0.859970i \(0.329518\pi\)
−0.968959 + 0.247222i \(0.920482\pi\)
\(338\) −6.36396 + 6.36396i −0.346154 + 0.346154i
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 2.82843 2.82843i 0.152944 0.152944i
\(343\) 3.06147 7.39104i 0.165304 0.399078i
\(344\) 8.00000i 0.431331i
\(345\) 0 0
\(346\) −9.18440 22.1731i −0.493757 1.19203i
\(347\) −16.6298 + 6.88830i −0.892736 + 0.369783i −0.781423 0.624002i \(-0.785506\pi\)
−0.111313 + 0.993785i \(0.535506\pi\)
\(348\) 0 0
\(349\) −18.3848 18.3848i −0.984115 0.984115i 0.0157613 0.999876i \(-0.494983\pi\)
−0.999876 + 0.0157613i \(0.994983\pi\)
\(350\) 18.4776 7.65367i 0.987669 0.409106i
\(351\) 3.06147 + 7.39104i 0.163409 + 0.394504i
\(352\) 5.54328 + 2.29610i 0.295458 + 0.122383i
\(353\) 6.00000i 0.319348i 0.987170 + 0.159674i \(0.0510443\pi\)
−0.987170 + 0.159674i \(0.948956\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −16.9706 + 16.9706i −0.895672 + 0.895672i −0.995050 0.0993777i \(-0.968315\pi\)
0.0993777 + 0.995050i \(0.468315\pi\)
\(360\) 0 0
\(361\) 3.00000i 0.157895i
\(362\) 3.69552 + 1.53073i 0.194232 + 0.0804536i
\(363\) 19.1342 + 46.1940i 1.00428 + 2.42455i
\(364\) 7.39104 3.06147i 0.387396 0.160464i
\(365\) 0 0
\(366\) −5.65685 5.65685i −0.295689 0.295689i
\(367\) −14.7821 + 6.12293i −0.771618 + 0.319615i −0.733528 0.679660i \(-0.762127\pi\)
−0.0380903 + 0.999274i \(0.512127\pi\)
\(368\) 0 0
\(369\) 5.54328 + 2.29610i 0.288571 + 0.119530i
\(370\) 0 0
\(371\) 9.18440 22.1731i 0.476830 1.15117i
\(372\) 5.65685 5.65685i 0.293294 0.293294i
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 16.0000i 0.822951i
\(379\) −12.9343 5.35757i −0.664391 0.275200i 0.0248939 0.999690i \(-0.492075\pi\)
−0.689285 + 0.724490i \(0.742075\pi\)
\(380\) 0 0
\(381\) −29.5641 + 12.2459i −1.51462 + 0.627375i
\(382\) −16.9706 16.9706i −0.868290 0.868290i
\(383\) 16.9706 + 16.9706i 0.867155 + 0.867155i 0.992157 0.125001i \(-0.0398935\pi\)
−0.125001 + 0.992157i \(0.539894\pi\)
\(384\) −1.84776 + 0.765367i −0.0942931 + 0.0390575i
\(385\) 0 0
\(386\) −9.23880 3.82683i −0.470242 0.194781i
\(387\) 8.00000i 0.406663i
\(388\) 5.35757 12.9343i 0.271989 0.656640i
\(389\) 21.2132 21.2132i 1.07555 1.07555i 0.0786498 0.996902i \(-0.474939\pi\)
0.996902 0.0786498i \(-0.0250609\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 9.00000 0.454569
\(393\) −8.48528 + 8.48528i −0.428026 + 0.428026i
\(394\) 4.59220 11.0866i 0.231352 0.558533i
\(395\) 0 0
\(396\) −5.54328 2.29610i −0.278560 0.115383i
\(397\) −7.65367 18.4776i −0.384127 0.927364i −0.991158 0.132686i \(-0.957640\pi\)
0.607032 0.794678i \(-0.292360\pi\)
\(398\) 14.7821 6.12293i 0.740958 0.306915i
\(399\) −22.6274 22.6274i −1.13279 1.13279i
\(400\) 3.53553 + 3.53553i 0.176777 + 0.176777i
\(401\) 27.7164 11.4805i 1.38409 0.573309i 0.438518 0.898722i \(-0.355503\pi\)
0.945572 + 0.325413i \(0.105503\pi\)
\(402\) −6.12293 14.7821i −0.305384 0.737263i
\(403\) −7.39104 3.06147i −0.368174 0.152503i
\(404\) 18.0000i 0.895533i
\(405\) 0 0
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) 4.59220 11.0866i 0.226517 0.546859i
\(412\) 16.0000i 0.788263i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 1.41421 + 1.41421i 0.0693375 + 0.0693375i
\(417\) 2.82843 + 2.82843i 0.138509 + 0.138509i
\(418\) −22.1731 + 9.18440i −1.08452 + 0.449224i
\(419\) −11.4805 27.7164i −0.560859 1.35403i −0.909080 0.416622i \(-0.863214\pi\)
0.348221 0.937413i \(-0.386786\pi\)
\(420\) 0 0
\(421\) 2.00000i 0.0974740i 0.998812 + 0.0487370i \(0.0155196\pi\)
−0.998812 + 0.0487370i \(0.984480\pi\)
\(422\) −3.82683 + 9.23880i −0.186287 + 0.449738i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) −11.3137 + 11.3137i −0.547509 + 0.547509i
\(428\) 2.29610 5.54328i 0.110986 0.267944i
\(429\) 24.0000i 1.15873i
\(430\) 0 0
\(431\) −9.18440 22.1731i −0.442397 1.06804i −0.975105 0.221742i \(-0.928826\pi\)
0.532708 0.846299i \(-0.321174\pi\)
\(432\) −3.69552 + 1.53073i −0.177801 + 0.0736475i
\(433\) 1.41421 + 1.41421i 0.0679628 + 0.0679628i 0.740271 0.672308i \(-0.234697\pi\)
−0.672308 + 0.740271i \(0.734697\pi\)
\(434\) −11.3137 11.3137i −0.543075 0.543075i
\(435\) 0 0
\(436\) −6.12293 14.7821i −0.293235 0.707933i
\(437\) 0 0
\(438\) 4.00000i 0.191127i
\(439\) 3.06147 7.39104i 0.146116 0.352755i −0.833829 0.552022i \(-0.813856\pi\)
0.979945 + 0.199268i \(0.0638563\pi\)
\(440\) 0 0
\(441\) −9.00000 −0.428571
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −5.65685 + 5.65685i −0.268462 + 0.268462i
\(445\) 0 0
\(446\) 8.00000i 0.378811i
\(447\) 11.0866 + 4.59220i 0.524376 + 0.217204i
\(448\) 1.53073 + 3.69552i 0.0723204 + 0.174597i
\(449\) 16.6298 6.88830i 0.784810 0.325079i 0.0459553 0.998943i \(-0.485367\pi\)
0.738855 + 0.673864i \(0.235367\pi\)
\(450\) −3.53553 3.53553i −0.166667 0.166667i
\(451\) −25.4558 25.4558i −1.19867 1.19867i
\(452\) −5.54328 + 2.29610i −0.260734 + 0.107999i
\(453\) 12.2459 + 29.5641i 0.575361 + 1.38904i
\(454\) −5.54328 2.29610i −0.260159 0.107761i
\(455\) 0 0
\(456\) 3.06147 7.39104i 0.143366 0.346117i
\(457\) 18.3848 18.3848i 0.860004 0.860004i −0.131335 0.991338i \(-0.541926\pi\)
0.991338 + 0.131335i \(0.0419262\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) 4.24264 4.24264i 0.197599 0.197599i −0.601371 0.798970i \(-0.705378\pi\)
0.798970 + 0.601371i \(0.205378\pi\)
\(462\) −18.3688 + 44.3462i −0.854594 + 2.06317i
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −16.6298 + 6.88830i −0.770362 + 0.319094i
\(467\) 8.48528 + 8.48528i 0.392652 + 0.392652i 0.875632 0.482980i \(-0.160445\pi\)
−0.482980 + 0.875632i \(0.660445\pi\)
\(468\) −1.41421 1.41421i −0.0653720 0.0653720i
\(469\) −29.5641 + 12.2459i −1.36515 + 0.565462i
\(470\) 0 0
\(471\) −25.8686 10.7151i −1.19196 0.493727i
\(472\) 0 0
\(473\) 18.3688 44.3462i 0.844599 2.03904i
\(474\) −11.3137 + 11.3137i −0.519656 + 0.519656i
\(475\) −20.0000 −0.917663
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) −16.9706 + 16.9706i −0.776215 + 0.776215i
\(479\) −9.18440 + 22.1731i −0.419646 + 1.01312i 0.562804 + 0.826590i \(0.309723\pi\)
−0.982450 + 0.186525i \(0.940277\pi\)
\(480\) 0 0
\(481\) 7.39104 + 3.06147i 0.337002 + 0.139591i
\(482\) 3.82683 + 9.23880i 0.174308 + 0.420816i
\(483\) 0 0
\(484\) 17.6777 + 17.6777i 0.803530 + 0.803530i
\(485\) 0 0
\(486\) 9.23880 3.82683i 0.419080 0.173589i
\(487\) 3.06147 + 7.39104i 0.138728 + 0.334920i 0.977940 0.208885i \(-0.0669833\pi\)
−0.839212 + 0.543804i \(0.816983\pi\)
\(488\) −3.69552 1.53073i −0.167288 0.0692931i
\(489\) 4.00000i 0.180886i
\(490\) 0 0
\(491\) −8.48528 + 8.48528i −0.382935 + 0.382935i −0.872159 0.489223i \(-0.837280\pi\)
0.489223 + 0.872159i \(0.337280\pi\)
\(492\) 12.0000 0.541002
\(493\) 0 0
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) 1.53073 3.69552i 0.0687320 0.165934i
\(497\) 0 0
\(498\) 0 0
\(499\) −5.35757 12.9343i −0.239838 0.579019i 0.757428 0.652919i \(-0.226456\pi\)
−0.997266 + 0.0738993i \(0.976456\pi\)
\(500\) 0 0
\(501\) −16.9706 16.9706i −0.758189 0.758189i
\(502\) 16.9706 + 16.9706i 0.757433 + 0.757433i
\(503\) −22.1731 + 9.18440i −0.988650 + 0.409512i −0.817623 0.575754i \(-0.804709\pi\)
−0.171027 + 0.985266i \(0.554709\pi\)
\(504\) −1.53073 3.69552i −0.0681843 0.164611i
\(505\) 0 0
\(506\) 0 0
\(507\) 6.88830 16.6298i 0.305920 0.738557i
\(508\) −11.3137 + 11.3137i −0.501965 + 0.501965i
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 6.12293 14.7821i 0.270334 0.652644i
\(514\) 6.00000i 0.264649i
\(515\) 0 0
\(516\) 6.12293 + 14.7821i 0.269547 + 0.650744i
\(517\) 0 0
\(518\) 11.3137 + 11.3137i 0.497096 + 0.497096i
\(519\) 33.9411 + 33.9411i 1.48985 + 1.48985i
\(520\) 0 0
\(521\) −6.88830 16.6298i −0.301782 0.728566i −0.999921 0.0126035i \(-0.995988\pi\)
0.698139 0.715963i \(-0.254012\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) −2.29610 + 5.54328i −0.100306 + 0.242159i
\(525\) −28.2843 + 28.2843i −1.23443 + 1.23443i
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) −12.0000 −0.522233
\(529\) 16.2635 16.2635i 0.707107 0.707107i
\(530\) 0 0
\(531\) 0 0
\(532\) −14.7821 6.12293i −0.640884 0.265463i
\(533\) −4.59220 11.0866i −0.198910 0.480212i
\(534\) −11.0866 + 4.59220i −0.479762 + 0.198724i
\(535\) 0 0
\(536\) −5.65685 5.65685i −0.244339 0.244339i
\(537\) −22.1731 + 9.18440i −0.956840 + 0.396336i
\(538\) −9.18440 22.1731i −0.395968 0.955951i
\(539\) 49.8895 + 20.6649i 2.14889 + 0.890100i
\(540\) 0 0
\(541\) 7.65367 18.4776i 0.329057 0.794414i −0.669606 0.742717i \(-0.733537\pi\)
0.998663 0.0516971i \(-0.0164630\pi\)
\(542\) 5.65685 5.65685i 0.242983 0.242983i
\(543\) −8.00000 −0.343313
\(544\) 0 0
\(545\) 0 0
\(546\) −11.3137 + 11.3137i −0.484182 + 0.484182i
\(547\) −0.765367 + 1.84776i −0.0327247 + 0.0790045i −0.939397 0.342831i \(-0.888614\pi\)
0.906672 + 0.421836i \(0.138614\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 3.69552 + 1.53073i 0.157721 + 0.0653301i
\(550\) 11.4805 + 27.7164i 0.489530 + 1.18183i
\(551\) 0 0
\(552\) 0 0
\(553\) 22.6274 + 22.6274i 0.962216 + 0.962216i
\(554\) 7.39104 3.06147i 0.314015 0.130069i
\(555\) 0 0
\(556\) 1.84776 + 0.765367i 0.0783624 + 0.0324588i
\(557\) 30.0000i 1.27114i −0.772043 0.635570i \(-0.780765\pi\)
0.772043 0.635570i \(-0.219235\pi\)
\(558\) −1.53073 + 3.69552i −0.0648011 + 0.156444i
\(559\) 11.3137 11.3137i 0.478519 0.478519i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 16.9706 16.9706i 0.715224 0.715224i −0.252399 0.967623i \(-0.581220\pi\)
0.967623 + 0.252399i \(0.0812196\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −12.9343 5.35757i −0.543670 0.225195i
\(567\) −16.8381 40.6507i −0.707133 1.70717i
\(568\) 0 0
\(569\) −21.2132 21.2132i −0.889304 0.889304i 0.105152 0.994456i \(-0.466467\pi\)
−0.994456 + 0.105152i \(0.966467\pi\)
\(570\) 0 0
\(571\) 24.0209 9.94977i 1.00524 0.416385i 0.181525 0.983386i \(-0.441897\pi\)
0.823717 + 0.567001i \(0.191897\pi\)
\(572\) 4.59220 + 11.0866i 0.192010 + 0.463552i
\(573\) 44.3462 + 18.3688i 1.85259 + 0.767368i
\(574\) 24.0000i 1.00174i
\(575\) 0 0
\(576\) 0.707107 0.707107i 0.0294628 0.0294628i
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 0 0
\(579\) 20.0000 0.831172
\(580\) 0 0
\(581\) 0 0
\(582\) 28.0000i 1.16064i
\(583\) 33.2597 + 13.7766i 1.37747 + 0.570569i
\(584\) −0.765367 1.84776i −0.0316711 0.0764608i
\(585\) 0 0
\(586\) 4.24264 + 4.24264i 0.175262 + 0.175262i
\(587\) −8.48528 8.48528i −0.350225 0.350225i 0.509968 0.860193i \(-0.329657\pi\)
−0.860193 + 0.509968i \(0.829657\pi\)
\(588\) −16.6298 + 6.88830i −0.685803 + 0.284069i
\(589\) 6.12293 + 14.7821i 0.252291 + 0.609085i
\(590\) 0 0
\(591\) 24.0000i 0.987228i
\(592\) −1.53073 + 3.69552i −0.0629128 + 0.151885i
\(593\) −21.2132 + 21.2132i −0.871122 + 0.871122i −0.992595 0.121473i \(-0.961238\pi\)
0.121473 + 0.992595i \(0.461238\pi\)
\(594\) −24.0000 −0.984732
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) −22.6274 + 22.6274i −0.926079 + 0.926079i
\(598\) 0 0
\(599\) 24.0000i 0.980613i 0.871550 + 0.490307i \(0.163115\pi\)
−0.871550 + 0.490307i \(0.836885\pi\)
\(600\) −9.23880 3.82683i −0.377172 0.156230i
\(601\) 17.6034 + 42.4985i 0.718059 + 1.73355i 0.678804 + 0.734319i \(0.262498\pi\)
0.0392547 + 0.999229i \(0.487502\pi\)
\(602\) 29.5641 12.2459i 1.20494 0.499104i
\(603\) 5.65685 + 5.65685i 0.230365 + 0.230365i
\(604\) 11.3137 + 11.3137i 0.460348 + 0.460348i
\(605\) 0 0
\(606\) −13.7766 33.2597i −0.559636 1.35108i
\(607\) 18.4776 + 7.65367i 0.749982 + 0.310653i 0.724734 0.689028i \(-0.241962\pi\)
0.0252479 + 0.999681i \(0.491962\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) −14.1421 + 14.1421i −0.570730 + 0.570730i
\(615\) 0 0
\(616\) 24.0000i 0.966988i
\(617\) 27.7164 + 11.4805i 1.11582 + 0.462188i 0.862938 0.505310i \(-0.168622\pi\)
0.252882 + 0.967497i \(0.418622\pi\)
\(618\) −12.2459 29.5641i −0.492601 1.18924i
\(619\) −24.0209 + 9.94977i −0.965480 + 0.399915i −0.809028 0.587770i \(-0.800006\pi\)
−0.156452 + 0.987685i \(0.550006\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 11.0866 4.59220i 0.444530 0.184130i
\(623\) 9.18440 + 22.1731i 0.367965 + 0.888347i
\(624\) −3.69552 1.53073i −0.147939 0.0612784i
\(625\) 25.0000i 1.00000i
\(626\) −13.0112 + 31.4119i −0.520034 + 1.25547i
\(627\) 33.9411 33.9411i 1.35548 1.35548i
\(628\) −14.0000 −0.558661
\(629\) 0 0
\(630\) 0 0
\(631\) −5.65685 + 5.65685i −0.225196 + 0.225196i −0.810682 0.585486i \(-0.800904\pi\)
0.585486 + 0.810682i \(0.300904\pi\)
\(632\) −3.06147 + 7.39104i −0.121779 + 0.294000i
\(633\) 20.0000i 0.794929i
\(634\) 11.0866 + 4.59220i 0.440303 + 0.182380i
\(635\) 0 0
\(636\) −11.0866 + 4.59220i −0.439610 + 0.182093i
\(637\) 12.7279 + 12.7279i 0.504299 + 0.504299i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.6298 6.88830i −0.656839 0.272072i 0.0292688 0.999572i \(-0.490682\pi\)
−0.686108 + 0.727500i \(0.740682\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 5.35757 12.9343i 0.211282 0.510080i −0.782339 0.622853i \(-0.785973\pi\)
0.993621 + 0.112774i \(0.0359734\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −48.0000 −1.88707 −0.943537 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) 7.77817 7.77817i 0.305556 0.305556i
\(649\) 0 0
\(650\) 10.0000i 0.392232i
\(651\) 29.5641 + 12.2459i 1.15871 + 0.479953i
\(652\) −0.765367 1.84776i −0.0299741 0.0723638i
\(653\) −22.1731 + 9.18440i −0.867701 + 0.359413i −0.771714 0.635969i \(-0.780601\pi\)
−0.0959864 + 0.995383i \(0.530601\pi\)
\(654\) 22.6274 + 22.6274i 0.884802 + 0.884802i
\(655\) 0 0
\(656\) 5.54328 2.29610i 0.216429 0.0896477i
\(657\) 0.765367 + 1.84776i 0.0298598 + 0.0720879i
\(658\) 0 0
\(659\) 12.0000i 0.467454i −0.972302 0.233727i \(-0.924908\pi\)
0.972302 0.233727i \(-0.0750921\pi\)
\(660\) 0 0
\(661\) −32.5269 + 32.5269i −1.26515 + 1.26515i −0.316587 + 0.948564i \(0.602537\pi\)
−0.948564 + 0.316587i \(0.897463\pi\)
\(662\) 16.0000 0.621858
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.53073 3.69552i 0.0593147 0.143198i
\(667\) 0 0
\(668\) −11.0866 4.59220i −0.428952 0.177678i
\(669\) 6.12293 + 14.7821i 0.236726 + 0.571508i
\(670\) 0 0
\(671\) −16.9706 16.9706i −0.655141 0.655141i
\(672\) −5.65685 5.65685i −0.218218 0.218218i
\(673\) 35.1074 14.5420i 1.35329 0.560552i 0.416085 0.909326i \(-0.363402\pi\)
0.937207 + 0.348774i \(0.113402\pi\)
\(674\) −8.41904 20.3253i −0.324289 0.782903i
\(675\) −18.4776 7.65367i −0.711203 0.294590i
\(676\) 9.00000i 0.346154i
\(677\) −4.59220 + 11.0866i −0.176493 + 0.426091i −0.987226 0.159324i \(-0.949068\pi\)
0.810734 + 0.585415i \(0.199068\pi\)
\(678\) 8.48528 8.48528i 0.325875 0.325875i
\(679\) 56.0000 2.14908
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 16.9706 16.9706i 0.649836 0.649836i
\(683\) −11.4805 + 27.7164i −0.439289 + 1.06054i 0.536906 + 0.843642i \(0.319593\pi\)
−0.976195 + 0.216896i \(0.930407\pi\)
\(684\) 4.00000i 0.152944i
\(685\) 0 0
\(686\) 3.06147 + 7.39104i 0.116887 + 0.282191i
\(687\) 25.8686 10.7151i 0.986950 0.408808i
\(688\) 5.65685 + 5.65685i 0.215666 + 0.215666i
\(689\) 8.48528 + 8.48528i 0.323263 + 0.323263i
\(690\) 0 0
\(691\) −3.82683 9.23880i −0.145580 0.351460i 0.834223 0.551427i \(-0.185917\pi\)
−0.979803 + 0.199967i \(0.935917\pi\)
\(692\) 22.1731 + 9.18440i 0.842895 + 0.349139i
\(693\) 24.0000i 0.911685i
\(694\) 6.88830 16.6298i 0.261476 0.631260i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 26.0000 0.984115
\(699\) 25.4558 25.4558i 0.962828 0.962828i
\(700\) −7.65367 + 18.4776i −0.289281 + 0.698387i
\(701\) 18.0000i 0.679851i −0.940452 0.339925i \(-0.889598\pi\)
0.940452 0.339925i \(-0.110402\pi\)
\(702\) −7.39104 3.06147i −0.278957 0.115548i
\(703\) −6.12293 14.7821i −0.230931 0.557516i
\(704\) −5.54328 + 2.29610i −0.208920 + 0.0865375i
\(705\) 0 0
\(706\) −4.24264 4.24264i −0.159674 0.159674i
\(707\) −66.5193 + 27.5532i −2.50172 + 1.03625i
\(708\) 0 0
\(709\) −14.7821 6.12293i −0.555152 0.229952i 0.0874268 0.996171i \(-0.472136\pi\)
−0.642579 + 0.766219i \(0.722136\pi\)
\(710\) 0 0
\(711\) 3.06147 7.39104i 0.114814 0.277186i
\(712\) −4.24264 + 4.24264i −0.159000 + 0.159000i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −8.48528 + 8.48528i −0.317110 + 0.317110i
\(717\) 18.3688 44.3462i 0.685996 1.65614i
\(718\) 24.0000i 0.895672i
\(719\) −44.3462 18.3688i −1.65383 0.685041i −0.656253 0.754541i \(-0.727860\pi\)
−0.997582 + 0.0695002i \(0.977860\pi\)
\(720\) 0 0
\(721\) −59.1283 + 24.4917i −2.20205 + 0.912120i
\(722\) −2.12132 2.12132i −0.0789474 0.0789474i
\(723\) −14.1421 14.1421i −0.525952 0.525952i
\(724\) −3.69552 + 1.53073i −0.137343 + 0.0568893i
\(725\) 0 0
\(726\) −46.1940 19.1342i −1.71442 0.710136i
\(727\) 8.00000i 0.296704i 0.988935 + 0.148352i \(0.0473968\pi\)
−0.988935 + 0.148352i \(0.952603\pi\)
\(728\) −3.06147 + 7.39104i −0.113466 + 0.273930i
\(729\) 9.19239 9.19239i 0.340459 0.340459i
\(730\) 0 0
\(731\) 0 0
\(732\) 8.00000 0.295689
\(733\) 15.5563 15.5563i 0.574587 0.574587i −0.358820 0.933407i \(-0.616821\pi\)
0.933407 + 0.358820i \(0.116821\pi\)
\(734\) 6.12293 14.7821i 0.226002 0.545616i
\(735\) 0 0
\(736\) 0 0
\(737\) −18.3688 44.3462i −0.676624 1.63351i
\(738\) −5.54328 + 2.29610i −0.204051 + 0.0845206i
\(739\) 14.1421 + 14.1421i 0.520227 + 0.520227i 0.917640 0.397413i \(-0.130092\pi\)
−0.397413 + 0.917640i \(0.630092\pi\)
\(740\) 0 0
\(741\) 14.7821 6.12293i 0.543033 0.224932i
\(742\) 9.18440 + 22.1731i 0.337170 + 0.814000i
\(743\) −33.2597 13.7766i −1.22018 0.505415i −0.322712 0.946497i \(-0.604595\pi\)
−0.897467 + 0.441083i \(0.854595\pi\)
\(744\) 8.00000i 0.293294i
\(745\) 0 0
\(746\) −15.5563 + 15.5563i −0.569558 + 0.569558i
\(747\) 0 0
\(748\) 0 0
\(749\) 24.0000 0.876941
\(750\) 0 0
\(751\) −3.06147 + 7.39104i −0.111715 + 0.269703i −0.969842 0.243734i \(-0.921628\pi\)
0.858128 + 0.513436i \(0.171628\pi\)
\(752\) 0 0
\(753\) −44.3462 18.3688i −1.61607 0.669396i
\(754\) 0 0
\(755\) 0 0
\(756\) −11.3137 11.3137i −0.411476 0.411476i
\(757\) 7.07107 + 7.07107i 0.257002 + 0.257002i 0.823834 0.566831i \(-0.191831\pi\)
−0.566831 + 0.823834i \(0.691831\pi\)
\(758\) 12.9343 5.35757i 0.469795 0.194596i
\(759\) 0 0
\(760\) 0 0
\(761\) 6.00000i 0.217500i 0.994069 + 0.108750i \(0.0346848\pi\)
−0.994069 + 0.108750i \(0.965315\pi\)
\(762\) 12.2459 29.5641i 0.443621 1.07100i
\(763\) 45.2548 45.2548i 1.63833 1.63833i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) 0.765367 1.84776i 0.0276178 0.0666753i
\(769\) 14.0000i 0.504853i −0.967616 0.252426i \(-0.918771\pi\)
0.967616 0.252426i \(-0.0812286\pi\)
\(770\) 0 0
\(771\) 4.59220 + 11.0866i 0.165384 + 0.399273i
\(772\) 9.23880 3.82683i 0.332512 0.137731i
\(773\) −29.6985 29.6985i −1.06818 1.06818i −0.997499 0.0706813i \(-0.977483\pi\)
−0.0706813 0.997499i \(-0.522517\pi\)
\(774\) −5.65685 5.65685i −0.203331 0.203331i
\(775\) 18.4776 7.65367i 0.663735 0.274928i
\(776\) 5.35757 + 12.9343i 0.192325 + 0.464315i
\(777\) −29.5641 12.2459i −1.06061 0.439318i
\(778\) 30.0000i 1.07555i
\(779\) −9.18440 + 22.1731i −0.329065 + 0.794434i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −6.36396 + 6.36396i −0.227284 + 0.227284i
\(785\) 0 0
\(786\) 12.0000i 0.428026i
\(787\) 42.4985 + 17.6034i 1.51491 + 0.627495i 0.976563 0.215231i \(-0.0690504\pi\)
0.538343 + 0.842726i \(0.319050\pi\)
\(788\) 4.59220 + 11.0866i 0.163590 + 0.394942i
\(789\) 44.3462 18.3688i 1.57877 0.653947i
\(790\) 0 0
\(791\) −16.9706 16.9706i −0.603404 0.603404i
\(792\) 5.54328 2.29610i 0.196972 0.0815884i
\(793\) −3.06147 7.39104i −0.108716 0.262463i
\(794\) 18.4776 + 7.65367i 0.655745 + 0.271619i
\(795\) 0 0
\(796\) −6.12293 + 14.7821i −0.217022 + 0.523937i
\(797\) 29.6985 29.6985i 1.05197 1.05197i 0.0534012 0.998573i \(-0.482994\pi\)
0.998573 0.0534012i \(-0.0170062\pi\)
\(798\) 32.0000 1.13279
\(799\) 0 0
\(800\) −5.00000 −0.176777
\(801\) 4.24264 4.24264i 0.149906 0.149906i
\(802\) −11.4805 + 27.7164i −0.405391 + 0.978700i
\(803\) 12.0000i 0.423471i
\(804\) 14.7821 + 6.12293i 0.521324 + 0.215939i
\(805\) 0 0
\(806\) 7.39104 3.06147i 0.260338 0.107836i
\(807\) 33.9411 + 33.9411i 1.19478 + 1.19478i
\(808\) −12.7279 12.7279i −0.447767 0.447767i
\(809\) 27.7164 11.4805i 0.974456 0.403633i 0.162087 0.986776i \(-0.448177\pi\)
0.812369 + 0.583143i \(0.198177\pi\)
\(810\) 0 0
\(811\) 35.1074 + 14.5420i 1.23279 + 0.510638i 0.901454 0.432876i \(-0.142501\pi\)
0.331335 + 0.943513i \(0.392501\pi\)
\(812\) 0 0
\(813\) −6.12293 + 14.7821i −0.214741 + 0.518430i
\(814\) −16.9706 + 16.9706i −0.594818 + 0.594818i
\(815\) 0 0
\(816\) 0 0
\(817\) −32.0000 −1.11954
\(818\) 7.07107 7.07107i 0.247234 0.247234i
\(819\) 3.06147 7.39104i 0.106976 0.258264i
\(820\) 0 0
\(821\) −33.2597 13.7766i −1.16077 0.480807i −0.282639 0.959226i \(-0.591210\pi\)
−0.878131 + 0.478420i \(0.841210\pi\)
\(822\) 4.59220 + 11.0866i 0.160171 + 0.386688i
\(823\) 14.7821 6.12293i 0.515271 0.213432i −0.109867 0.993946i \(-0.535043\pi\)
0.625138 + 0.780514i \(0.285043\pi\)
\(824\) −11.3137 11.3137i −0.394132 0.394132i
\(825\) −42.4264 42.4264i −1.47710 1.47710i
\(826\) 0 0
\(827\) 2.29610 + 5.54328i 0.0798432 + 0.192759i 0.958760 0.284216i \(-0.0917333\pi\)
−0.878917 + 0.476975i \(0.841733\pi\)
\(828\) 0 0
\(829\) 10.0000i 0.347314i −0.984806 0.173657i \(-0.944442\pi\)
0.984806 0.173657i \(-0.0555585\pi\)
\(830\) 0 0
\(831\) −11.3137 + 11.3137i −0.392468 + 0.392468i
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) −4.00000 −0.138509
\(835\) 0 0
\(836\) 9.18440 22.1731i 0.317649 0.766873i
\(837\) 16.0000i 0.553041i
\(838\) 27.7164 + 11.4805i 0.957447 + 0.396587i
\(839\) 13.7766 + 33.2597i 0.475621 + 1.14825i 0.961643 + 0.274304i \(0.0884476\pi\)
−0.486022 + 0.873947i \(0.661552\pi\)
\(840\) 0 0
\(841\) −20.5061 20.5061i −0.707107 0.707107i
\(842\) −1.41421 1.41421i −0.0487370 0.0487370i
\(843\) −11.0866 + 4.59220i −0.381841 + 0.158164i
\(844\) −3.82683 9.23880i −0.131725 0.318012i
\(845\) 0 0
\(846\) 0 0
\(847\) −38.2683 + 92.3880i −1.31492 + 3.17449i
\(848\) −4.24264 + 4.24264i −0.145693 + 0.145693i
\(849\) 28.0000 0.960958
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 15.3073 36.9552i 0.524113 1.26532i −0.411214 0.911539i \(-0.634895\pi\)
0.935328 0.353783i \(-0.115105\pi\)
\(854\) 16.0000i 0.547509i
\(855\) 0 0
\(856\) 2.29610 + 5.54328i 0.0784791 + 0.189465i
\(857\) 16.6298 6.88830i 0.568064 0.235300i −0.0801177 0.996785i \(-0.525530\pi\)
0.648182 + 0.761486i \(0.275530\pi\)
\(858\) −16.9706 16.9706i −0.579365 0.579365i
\(859\) 11.3137 + 11.3137i 0.386019 + 0.386019i 0.873265 0.487246i \(-0.161998\pi\)
−0.487246 + 0.873265i \(0.661998\pi\)
\(860\) 0 0
\(861\) 18.3688 + 44.3462i 0.626007 + 1.51132i
\(862\) 22.1731 + 9.18440i 0.755219 + 0.312822i
\(863\) 48.0000i 1.63394i 0.576681 + 0.816970i \(0.304348\pi\)
−0.576681 + 0.816970i \(0.695652\pi\)
\(864\) 1.53073 3.69552i 0.0520766 0.125724i
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) 0 0
\(868\) 16.0000 0.543075
\(869\) −33.9411 + 33.9411i −1.15137 + 1.15137i
\(870\) 0 0
\(871\) 16.0000i 0.542139i
\(872\) 14.7821 + 6.12293i 0.500584 + 0.207349i
\(873\) −5.35757 12.9343i −0.181326 0.437760i
\(874\) 0 0
\(875\) 0 0
\(876\) 2.82843 + 2.82843i 0.0955637 + 0.0955637i
\(877\) 29.5641 12.2459i 0.998310 0.413514i 0.177133 0.984187i \(-0.443318\pi\)
0.821177 + 0.570673i \(0.193318\pi\)
\(878\) 3.06147 + 7.39104i 0.103320 + 0.249435i
\(879\) −11.0866 4.59220i −0.373940 0.154891i
\(880\) 0 0
\(881\) 6.88830 16.6298i 0.232073 0.560273i −0.764348 0.644804i \(-0.776939\pi\)
0.996421 + 0.0845306i \(0.0269391\pi\)
\(882\) 6.36396 6.36396i 0.214286 0.214286i
\(883\) 16.0000 0.538443 0.269221 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 16.9706 16.9706i 0.570137 0.570137i
\(887\) −9.18440 + 22.1731i −0.308382 + 0.744500i 0.691376 + 0.722495i \(0.257005\pi\)
−0.999758 + 0.0220048i \(0.992995\pi\)
\(888\) 8.00000i 0.268462i
\(889\) −59.1283 24.4917i −1.98310 0.821427i
\(890\) 0 0
\(891\) 60.9760 25.2571i 2.04277 0.846145i
\(892\) 5.65685 + 5.65685i 0.189405 + 0.189405i
\(893\) 0 0
\(894\) −11.0866 + 4.59220i −0.370790 + 0.153586i
\(895\) 0 0
\(896\) −3.69552 1.53073i −0.123459 0.0511382i
\(897\) 0 0
\(898\) −6.88830 + 16.6298i −0.229866 + 0.554945i
\(899\) 0 0
\(900\) 5.00000 0.166667
\(901\) 0 0
\(902\) 36.0000 1.19867
\(903\) −45.2548 + 45.2548i −1.50599 + 1.50599i
\(904\) 2.29610 5.54328i 0.0763672 0.184367i
\(905\) 0 0
\(906\) −29.5641 12.2459i −0.982203 0.406842i
\(907\) 22.1956 + 53.5850i 0.736994 + 1.77926i 0.617717 + 0.786400i \(0.288058\pi\)
0.119277 + 0.992861i \(0.461942\pi\)
\(908\) 5.54328 2.29610i 0.183960 0.0761988i
\(909\) 12.7279 + 12.7279i 0.422159 + 0.422159i
\(910\) 0 0
\(911\) 11.0866 4.59220i 0.367314 0.152146i −0.191389 0.981514i \(-0.561299\pi\)
0.558703 + 0.829368i \(0.311299\pi\)
\(912\) 3.06147 + 7.39104i 0.101375 + 0.244742i
\(913\) 0 0
\(914\) 26.0000i 0.860004i
\(915\) 0 0
\(916\) 9.89949 9.89949i 0.327089 0.327089i
\(917\) −24.0000 −0.792550
\(918\) 0 0
\(919\) 56.0000 1.84727 0.923635 0.383274i \(-0.125203\pi\)
0.923635 + 0.383274i \(0.125203\pi\)
\(920\) 0 0
\(921\) 15.3073 36.9552i 0.504394 1.21771i
\(922\) 6.00000i 0.197599i
\(923\) 0 0
\(924\) −18.3688 44.3462i −0.604289 1.45888i
\(925\) −18.4776 + 7.65367i −0.607539 + 0.251651i
\(926\) −11.3137 11.3137i −0.371792 0.371792i
\(927\) 11.3137 + 11.3137i 0.371591 + 0.371591i
\(928\) 0 0
\(929\) −6.88830 16.6298i −0.225998 0.545607i 0.769685 0.638423i \(-0.220413\pi\)
−0.995683 + 0.0928163i \(0.970413\pi\)
\(930\) 0 0
\(931\) 36.0000i 1.17985i
\(932\) 6.88830 16.6298i 0.225634 0.544728i
\(933\) −16.9706 + 16.9706i −0.555591 + 0.555591i
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 2.00000 0.0653720
\(937\) 41.0122 41.0122i 1.33981 1.33981i 0.443570 0.896240i \(-0.353712\pi\)
0.896240 0.443570i \(-0.146288\pi\)
\(938\) 12.2459 29.5641i 0.399842 0.965304i
\(939\) 68.0000i 2.21910i
\(940\) 0 0
\(941\) 13.7766 + 33.2597i 0.449104 + 1.08423i 0.972658 + 0.232241i \(0.0746059\pi\)
−0.523554 + 0.851993i \(0.675394\pi\)
\(942\) 25.8686 10.7151i 0.842845 0.349118i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 18.3688 + 44.3462i 0.597221 + 1.44182i
\(947\) 16.6298 + 6.88830i 0.540397 + 0.223840i 0.636150 0.771565i \(-0.280526\pi\)
−0.0957531 + 0.995405i \(0.530526\pi\)
\(948\) 16.0000i 0.519656i
\(949\) 1.53073 3.69552i 0.0496897 0.119962i
\(950\) 14.1421 14.1421i 0.458831 0.458831i
\(951\) −24.0000 −0.778253
\(952\) 0 0
\(953\) −30.0000 −0.971795 −0.485898 0.874016i \(-0.661507\pi\)
−0.485898 + 0.874016i \(0.661507\pi\)
\(954\) 4.24264 4.24264i 0.137361 0.137361i
\(955\) 0 0
\(956\) 24.0000i 0.776215i
\(957\) 0 0
\(958\) −9.18440 22.1731i −0.296735 0.716381i
\(959\) 22.1731 9.18440i 0.716007 0.296580i
\(960\) 0 0
\(961\) 10.6066 + 10.6066i 0.342148 + 0.342148i
\(962\) −7.39104 + 3.06147i −0.238297 + 0.0987057i
\(963\) −2.29610 5.54328i −0.0739908 0.178630i
\(964\) −9.23880 3.82683i −0.297562 0.123254i
\(965\) 0 0
\(966\) 0 0
\(967\) −28.2843 + 28.2843i −0.909561 + 0.909561i −0.996237 0.0866757i \(-0.972376\pi\)
0.0866757 + 0.996237i \(0.472376\pi\)
\(968\) −25.0000 −0.803530
\(969\) 0 0
\(970\) 0 0
\(971\) 16.9706 16.9706i 0.544611 0.544611i −0.380266 0.924877i \(-0.624168\pi\)
0.924877 + 0.380266i \(0.124168\pi\)
\(972\) −3.82683 + 9.23880i −0.122746 + 0.296334i
\(973\) 8.00000i 0.256468i
\(974\) −7.39104 3.06147i −0.236824 0.0980957i
\(975\) −7.65367 18.4776i −0.245114 0.591756i
\(976\) 3.69552 1.53073i 0.118291 0.0489976i
\(977\) 29.6985 + 29.6985i 0.950139 + 0.950139i 0.998815 0.0486759i \(-0.0155002\pi\)
−0.0486759 + 0.998815i \(0.515500\pi\)
\(978\) 2.82843 + 2.82843i 0.0904431 + 0.0904431i
\(979\) −33.2597 + 13.7766i −1.06298 + 0.440302i
\(980\) 0 0
\(981\) −14.7821 6.12293i −0.471955 0.195490i
\(982\) 12.0000i 0.382935i
\(983\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(984\) −8.48528 + 8.48528i −0.270501 + 0.270501i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 5.65685 5.65685i 0.179969 0.179969i
\(989\) 0 0
\(990\) 0 0
\(991\) 14.7821 + 6.12293i 0.469568 + 0.194501i 0.604904 0.796298i \(-0.293211\pi\)
−0.135336 + 0.990800i \(0.543211\pi\)
\(992\) 1.53073 + 3.69552i 0.0486008 + 0.117333i
\(993\) −29.5641 + 12.2459i −0.938190 + 0.388611i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −10.7151 25.8686i −0.339352 0.819268i −0.997778 0.0666226i \(-0.978778\pi\)
0.658426 0.752645i \(-0.271222\pi\)
\(998\) 12.9343 + 5.35757i 0.409429 + 0.169591i
\(999\) 16.0000i 0.506218i
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 578.2.d.e.399.2 8
17.2 even 8 inner 578.2.d.e.423.1 8
17.3 odd 16 578.2.c.e.327.2 4
17.4 even 4 inner 578.2.d.e.179.1 8
17.5 odd 16 578.2.c.e.251.2 4
17.6 odd 16 578.2.b.a.577.1 2
17.7 odd 16 34.2.a.a.1.1 1
17.8 even 8 inner 578.2.d.e.155.1 8
17.9 even 8 inner 578.2.d.e.155.2 8
17.10 odd 16 578.2.a.a.1.1 1
17.11 odd 16 578.2.b.a.577.2 2
17.12 odd 16 578.2.c.e.251.1 4
17.13 even 4 inner 578.2.d.e.179.2 8
17.14 odd 16 578.2.c.e.327.1 4
17.15 even 8 inner 578.2.d.e.423.2 8
17.16 even 2 inner 578.2.d.e.399.1 8
51.41 even 16 306.2.a.a.1.1 1
51.44 even 16 5202.2.a.d.1.1 1
68.7 even 16 272.2.a.d.1.1 1
68.27 even 16 4624.2.a.a.1.1 1
85.7 even 16 850.2.c.b.749.2 2
85.24 odd 16 850.2.a.e.1.1 1
85.58 even 16 850.2.c.b.749.1 2
119.41 even 16 1666.2.a.m.1.1 1
136.75 even 16 1088.2.a.d.1.1 1
136.109 odd 16 1088.2.a.l.1.1 1
187.109 even 16 4114.2.a.a.1.1 1
204.143 odd 16 2448.2.a.k.1.1 1
221.194 odd 16 5746.2.a.b.1.1 1
255.194 even 16 7650.2.a.ci.1.1 1
340.279 even 16 6800.2.a.b.1.1 1
408.245 even 16 9792.2.a.y.1.1 1
408.347 odd 16 9792.2.a.bj.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
34.2.a.a.1.1 1 17.7 odd 16
272.2.a.d.1.1 1 68.7 even 16
306.2.a.a.1.1 1 51.41 even 16
578.2.a.a.1.1 1 17.10 odd 16
578.2.b.a.577.1 2 17.6 odd 16
578.2.b.a.577.2 2 17.11 odd 16
578.2.c.e.251.1 4 17.12 odd 16
578.2.c.e.251.2 4 17.5 odd 16
578.2.c.e.327.1 4 17.14 odd 16
578.2.c.e.327.2 4 17.3 odd 16
578.2.d.e.155.1 8 17.8 even 8 inner
578.2.d.e.155.2 8 17.9 even 8 inner
578.2.d.e.179.1 8 17.4 even 4 inner
578.2.d.e.179.2 8 17.13 even 4 inner
578.2.d.e.399.1 8 17.16 even 2 inner
578.2.d.e.399.2 8 1.1 even 1 trivial
578.2.d.e.423.1 8 17.2 even 8 inner
578.2.d.e.423.2 8 17.15 even 8 inner
850.2.a.e.1.1 1 85.24 odd 16
850.2.c.b.749.1 2 85.58 even 16
850.2.c.b.749.2 2 85.7 even 16
1088.2.a.d.1.1 1 136.75 even 16
1088.2.a.l.1.1 1 136.109 odd 16
1666.2.a.m.1.1 1 119.41 even 16
2448.2.a.k.1.1 1 204.143 odd 16
4114.2.a.a.1.1 1 187.109 even 16
4624.2.a.a.1.1 1 68.27 even 16
5202.2.a.d.1.1 1 51.44 even 16
5746.2.a.b.1.1 1 221.194 odd 16
6800.2.a.b.1.1 1 340.279 even 16
7650.2.a.ci.1.1 1 255.194 even 16
9792.2.a.y.1.1 1 408.245 even 16
9792.2.a.bj.1.1 1 408.347 odd 16