Properties

Label 460.2.m.a.301.3
Level $460$
Weight $2$
Character 460.301
Analytic conductor $3.673$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(41,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 301.3
Character \(\chi\) \(=\) 460.301
Dual form 460.2.m.a.81.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.241946 + 1.68277i) q^{3} +(-0.959493 - 0.281733i) q^{5} +(2.58157 - 2.97929i) q^{7} +(0.105306 - 0.0309206i) q^{9} +O(q^{10})\) \(q+(0.241946 + 1.68277i) q^{3} +(-0.959493 - 0.281733i) q^{5} +(2.58157 - 2.97929i) q^{7} +(0.105306 - 0.0309206i) q^{9} +(1.84361 - 1.18481i) q^{11} +(2.08288 + 2.40377i) q^{13} +(0.241946 - 1.68277i) q^{15} +(0.820281 - 1.79617i) q^{17} +(0.904027 + 1.97954i) q^{19} +(5.63805 + 3.62336i) q^{21} +(-3.74040 + 3.00157i) q^{23} +(0.841254 + 0.540641i) q^{25} +(2.19622 + 4.80905i) q^{27} +(0.693399 - 1.51833i) q^{29} +(0.122568 - 0.852481i) q^{31} +(2.43982 + 2.81570i) q^{33} +(-3.31636 + 2.13129i) q^{35} +(1.64535 - 0.483119i) q^{37} +(-3.54104 + 4.08658i) q^{39} +(-1.93728 - 0.568838i) q^{41} +(1.39884 + 9.72914i) q^{43} -0.109752 q^{45} -6.47457 q^{47} +(-1.21546 - 8.45371i) q^{49} +(3.22099 + 0.945769i) q^{51} +(6.84462 - 7.89911i) q^{53} +(-2.10273 + 0.617417i) q^{55} +(-3.11239 + 2.00021i) q^{57} +(-8.37319 - 9.66318i) q^{59} +(1.26755 - 8.81598i) q^{61} +(0.179733 - 0.393561i) q^{63} +(-1.32129 - 2.89321i) q^{65} +(11.5834 + 7.44419i) q^{67} +(-5.95592 - 5.56801i) q^{69} +(2.28434 + 1.46806i) q^{71} +(0.192036 + 0.420501i) q^{73} +(-0.706236 + 1.54644i) q^{75} +(1.22949 - 8.55131i) q^{77} +(-6.61761 - 7.63713i) q^{79} +(-7.28416 + 4.68125i) q^{81} +(-7.69481 + 2.25940i) q^{83} +(-1.29309 + 1.49231i) q^{85} +(2.72277 + 0.799477i) q^{87} +(-0.0222007 - 0.154409i) q^{89} +12.5386 q^{91} +1.46418 q^{93} +(-0.309706 - 2.15405i) q^{95} +(-11.4900 - 3.37375i) q^{97} +(0.157508 - 0.181774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.241946 + 1.68277i 0.139687 + 0.971547i 0.932265 + 0.361776i \(0.117829\pi\)
−0.792578 + 0.609771i \(0.791261\pi\)
\(4\) 0 0
\(5\) −0.959493 0.281733i −0.429098 0.125995i
\(6\) 0 0
\(7\) 2.58157 2.97929i 0.975741 1.12606i −0.0162644 0.999868i \(-0.505177\pi\)
0.992005 0.126197i \(-0.0402772\pi\)
\(8\) 0 0
\(9\) 0.105306 0.0309206i 0.0351020 0.0103069i
\(10\) 0 0
\(11\) 1.84361 1.18481i 0.555868 0.357235i −0.232348 0.972633i \(-0.574641\pi\)
0.788217 + 0.615398i \(0.211005\pi\)
\(12\) 0 0
\(13\) 2.08288 + 2.40377i 0.577686 + 0.666685i 0.967106 0.254376i \(-0.0818699\pi\)
−0.389420 + 0.921060i \(0.627324\pi\)
\(14\) 0 0
\(15\) 0.241946 1.68277i 0.0624701 0.434489i
\(16\) 0 0
\(17\) 0.820281 1.79617i 0.198947 0.435634i −0.783695 0.621146i \(-0.786667\pi\)
0.982642 + 0.185512i \(0.0593945\pi\)
\(18\) 0 0
\(19\) 0.904027 + 1.97954i 0.207398 + 0.454138i 0.984534 0.175195i \(-0.0560555\pi\)
−0.777136 + 0.629333i \(0.783328\pi\)
\(20\) 0 0
\(21\) 5.63805 + 3.62336i 1.23032 + 0.790681i
\(22\) 0 0
\(23\) −3.74040 + 3.00157i −0.779927 + 0.625871i
\(24\) 0 0
\(25\) 0.841254 + 0.540641i 0.168251 + 0.108128i
\(26\) 0 0
\(27\) 2.19622 + 4.80905i 0.422662 + 0.925502i
\(28\) 0 0
\(29\) 0.693399 1.51833i 0.128761 0.281947i −0.834261 0.551370i \(-0.814105\pi\)
0.963022 + 0.269422i \(0.0868327\pi\)
\(30\) 0 0
\(31\) 0.122568 0.852481i 0.0220139 0.153110i −0.975850 0.218444i \(-0.929902\pi\)
0.997863 + 0.0653335i \(0.0208111\pi\)
\(32\) 0 0
\(33\) 2.43982 + 2.81570i 0.424718 + 0.490151i
\(34\) 0 0
\(35\) −3.31636 + 2.13129i −0.560567 + 0.360254i
\(36\) 0 0
\(37\) 1.64535 0.483119i 0.270494 0.0794243i −0.143673 0.989625i \(-0.545891\pi\)
0.414167 + 0.910201i \(0.364073\pi\)
\(38\) 0 0
\(39\) −3.54104 + 4.08658i −0.567020 + 0.654376i
\(40\) 0 0
\(41\) −1.93728 0.568838i −0.302553 0.0888376i 0.126932 0.991911i \(-0.459487\pi\)
−0.429485 + 0.903074i \(0.641305\pi\)
\(42\) 0 0
\(43\) 1.39884 + 9.72914i 0.213321 + 1.48368i 0.761962 + 0.647622i \(0.224236\pi\)
−0.548640 + 0.836058i \(0.684854\pi\)
\(44\) 0 0
\(45\) −0.109752 −0.0163608
\(46\) 0 0
\(47\) −6.47457 −0.944413 −0.472206 0.881488i \(-0.656542\pi\)
−0.472206 + 0.881488i \(0.656542\pi\)
\(48\) 0 0
\(49\) −1.21546 8.45371i −0.173637 1.20767i
\(50\) 0 0
\(51\) 3.22099 + 0.945769i 0.451029 + 0.132434i
\(52\) 0 0
\(53\) 6.84462 7.89911i 0.940181 1.08503i −0.0560624 0.998427i \(-0.517855\pi\)
0.996243 0.0865993i \(-0.0276000\pi\)
\(54\) 0 0
\(55\) −2.10273 + 0.617417i −0.283532 + 0.0832525i
\(56\) 0 0
\(57\) −3.11239 + 2.00021i −0.412246 + 0.264934i
\(58\) 0 0
\(59\) −8.37319 9.66318i −1.09010 1.25804i −0.963966 0.266025i \(-0.914290\pi\)
−0.126130 0.992014i \(-0.540256\pi\)
\(60\) 0 0
\(61\) 1.26755 8.81598i 0.162293 1.12877i −0.732005 0.681299i \(-0.761415\pi\)
0.894298 0.447472i \(-0.147675\pi\)
\(62\) 0 0
\(63\) 0.179733 0.393561i 0.0226442 0.0495840i
\(64\) 0 0
\(65\) −1.32129 2.89321i −0.163885 0.358859i
\(66\) 0 0
\(67\) 11.5834 + 7.44419i 1.41514 + 0.909453i 1.00000 0.000305859i \(-9.73578e-5\pi\)
0.415137 + 0.909759i \(0.363734\pi\)
\(68\) 0 0
\(69\) −5.95592 5.56801i −0.717009 0.670309i
\(70\) 0 0
\(71\) 2.28434 + 1.46806i 0.271101 + 0.174226i 0.669127 0.743148i \(-0.266668\pi\)
−0.398026 + 0.917374i \(0.630305\pi\)
\(72\) 0 0
\(73\) 0.192036 + 0.420501i 0.0224761 + 0.0492159i 0.920537 0.390655i \(-0.127751\pi\)
−0.898061 + 0.439871i \(0.855024\pi\)
\(74\) 0 0
\(75\) −0.706236 + 1.54644i −0.0815491 + 0.178568i
\(76\) 0 0
\(77\) 1.22949 8.55131i 0.140114 0.974513i
\(78\) 0 0
\(79\) −6.61761 7.63713i −0.744540 0.859245i 0.249487 0.968378i \(-0.419738\pi\)
−0.994027 + 0.109133i \(0.965192\pi\)
\(80\) 0 0
\(81\) −7.28416 + 4.68125i −0.809351 + 0.520138i
\(82\) 0 0
\(83\) −7.69481 + 2.25940i −0.844616 + 0.248001i −0.675284 0.737558i \(-0.735979\pi\)
−0.169331 + 0.985559i \(0.554161\pi\)
\(84\) 0 0
\(85\) −1.29309 + 1.49231i −0.140256 + 0.161864i
\(86\) 0 0
\(87\) 2.72277 + 0.799477i 0.291911 + 0.0857129i
\(88\) 0 0
\(89\) −0.0222007 0.154409i −0.00235327 0.0163673i 0.988611 0.150494i \(-0.0480863\pi\)
−0.990964 + 0.134126i \(0.957177\pi\)
\(90\) 0 0
\(91\) 12.5386 1.31440
\(92\) 0 0
\(93\) 1.46418 0.151829
\(94\) 0 0
\(95\) −0.309706 2.15405i −0.0317751 0.221001i
\(96\) 0 0
\(97\) −11.4900 3.37375i −1.16663 0.342553i −0.359623 0.933098i \(-0.617095\pi\)
−0.807005 + 0.590545i \(0.798913\pi\)
\(98\) 0 0
\(99\) 0.157508 0.181774i 0.0158301 0.0182689i
\(100\) 0 0
\(101\) −7.01280 + 2.05914i −0.697800 + 0.204893i −0.611346 0.791363i \(-0.709372\pi\)
−0.0864538 + 0.996256i \(0.527554\pi\)
\(102\) 0 0
\(103\) 0.320351 0.205877i 0.0315652 0.0202857i −0.524763 0.851248i \(-0.675846\pi\)
0.556328 + 0.830963i \(0.312210\pi\)
\(104\) 0 0
\(105\) −4.38885 5.06501i −0.428308 0.494294i
\(106\) 0 0
\(107\) −1.71641 + 11.9379i −0.165932 + 1.15408i 0.721255 + 0.692669i \(0.243565\pi\)
−0.887187 + 0.461410i \(0.847344\pi\)
\(108\) 0 0
\(109\) 5.14715 11.2707i 0.493008 1.07954i −0.485672 0.874141i \(-0.661425\pi\)
0.978679 0.205395i \(-0.0658478\pi\)
\(110\) 0 0
\(111\) 1.21106 + 2.65186i 0.114949 + 0.251703i
\(112\) 0 0
\(113\) 4.84902 + 3.11628i 0.456158 + 0.293155i 0.748471 0.663168i \(-0.230789\pi\)
−0.292313 + 0.956323i \(0.594425\pi\)
\(114\) 0 0
\(115\) 4.43453 1.82619i 0.413522 0.170293i
\(116\) 0 0
\(117\) 0.293665 + 0.188727i 0.0271494 + 0.0174478i
\(118\) 0 0
\(119\) −3.23368 7.08077i −0.296431 0.649094i
\(120\) 0 0
\(121\) −2.57446 + 5.63729i −0.234042 + 0.512481i
\(122\) 0 0
\(123\) 0.488505 3.39763i 0.0440470 0.306354i
\(124\) 0 0
\(125\) −0.654861 0.755750i −0.0585725 0.0675963i
\(126\) 0 0
\(127\) −8.09131 + 5.19997i −0.717988 + 0.461423i −0.847936 0.530098i \(-0.822155\pi\)
0.129949 + 0.991521i \(0.458519\pi\)
\(128\) 0 0
\(129\) −16.0335 + 4.70785i −1.41167 + 0.414503i
\(130\) 0 0
\(131\) −7.25086 + 8.36794i −0.633511 + 0.731110i −0.978213 0.207602i \(-0.933434\pi\)
0.344703 + 0.938712i \(0.387980\pi\)
\(132\) 0 0
\(133\) 8.23143 + 2.41697i 0.713756 + 0.209578i
\(134\) 0 0
\(135\) −0.752391 5.23299i −0.0647555 0.450384i
\(136\) 0 0
\(137\) −14.4697 −1.23623 −0.618114 0.786088i \(-0.712103\pi\)
−0.618114 + 0.786088i \(0.712103\pi\)
\(138\) 0 0
\(139\) −17.1539 −1.45498 −0.727489 0.686119i \(-0.759313\pi\)
−0.727489 + 0.686119i \(0.759313\pi\)
\(140\) 0 0
\(141\) −1.56649 10.8952i −0.131923 0.917542i
\(142\) 0 0
\(143\) 6.68802 + 1.96378i 0.559280 + 0.164220i
\(144\) 0 0
\(145\) −1.09308 + 1.26148i −0.0907750 + 0.104760i
\(146\) 0 0
\(147\) 13.9316 4.09068i 1.14906 0.337393i
\(148\) 0 0
\(149\) −8.68795 + 5.58341i −0.711745 + 0.457411i −0.845756 0.533569i \(-0.820850\pi\)
0.134012 + 0.990980i \(0.457214\pi\)
\(150\) 0 0
\(151\) −10.0556 11.6047i −0.818310 0.944380i 0.180925 0.983497i \(-0.442091\pi\)
−0.999235 + 0.0391173i \(0.987545\pi\)
\(152\) 0 0
\(153\) 0.0308420 0.214511i 0.00249343 0.0173422i
\(154\) 0 0
\(155\) −0.357775 + 0.783419i −0.0287372 + 0.0629257i
\(156\) 0 0
\(157\) −7.26939 15.9177i −0.580160 1.27037i −0.941208 0.337827i \(-0.890308\pi\)
0.361048 0.932547i \(-0.382419\pi\)
\(158\) 0 0
\(159\) 14.9484 + 9.60676i 1.18549 + 0.761865i
\(160\) 0 0
\(161\) −0.713551 + 18.8925i −0.0562357 + 1.48894i
\(162\) 0 0
\(163\) 16.6127 + 10.6764i 1.30121 + 0.836237i 0.993343 0.115193i \(-0.0367485\pi\)
0.307867 + 0.951429i \(0.400385\pi\)
\(164\) 0 0
\(165\) −1.54772 3.38903i −0.120490 0.263835i
\(166\) 0 0
\(167\) −1.97673 + 4.32843i −0.152964 + 0.334944i −0.970564 0.240842i \(-0.922577\pi\)
0.817600 + 0.575786i \(0.195304\pi\)
\(168\) 0 0
\(169\) 0.410370 2.85419i 0.0315669 0.219553i
\(170\) 0 0
\(171\) 0.156408 + 0.180505i 0.0119608 + 0.0138035i
\(172\) 0 0
\(173\) −0.520223 + 0.334327i −0.0395518 + 0.0254184i −0.560267 0.828312i \(-0.689302\pi\)
0.520716 + 0.853730i \(0.325665\pi\)
\(174\) 0 0
\(175\) 3.78248 1.11064i 0.285928 0.0839562i
\(176\) 0 0
\(177\) 14.2350 16.4281i 1.06997 1.23481i
\(178\) 0 0
\(179\) −16.2201 4.76264i −1.21234 0.355976i −0.387784 0.921750i \(-0.626759\pi\)
−0.824560 + 0.565774i \(0.808577\pi\)
\(180\) 0 0
\(181\) 2.95827 + 20.5752i 0.219886 + 1.52934i 0.738452 + 0.674306i \(0.235557\pi\)
−0.518566 + 0.855038i \(0.673534\pi\)
\(182\) 0 0
\(183\) 15.1419 1.11932
\(184\) 0 0
\(185\) −1.71481 −0.126076
\(186\) 0 0
\(187\) −0.615846 4.28330i −0.0450351 0.313226i
\(188\) 0 0
\(189\) 19.9972 + 5.87171i 1.45458 + 0.427104i
\(190\) 0 0
\(191\) 8.29242 9.56996i 0.600019 0.692458i −0.371767 0.928326i \(-0.621248\pi\)
0.971785 + 0.235868i \(0.0757933\pi\)
\(192\) 0 0
\(193\) 9.03665 2.65340i 0.650472 0.190996i 0.0601827 0.998187i \(-0.480832\pi\)
0.590290 + 0.807191i \(0.299013\pi\)
\(194\) 0 0
\(195\) 4.54893 2.92342i 0.325755 0.209350i
\(196\) 0 0
\(197\) 9.60682 + 11.0869i 0.684458 + 0.789906i 0.986565 0.163367i \(-0.0522356\pi\)
−0.302107 + 0.953274i \(0.597690\pi\)
\(198\) 0 0
\(199\) −3.39975 + 23.6458i −0.241002 + 1.67621i 0.406120 + 0.913820i \(0.366881\pi\)
−0.647122 + 0.762386i \(0.724028\pi\)
\(200\) 0 0
\(201\) −9.72431 + 21.2933i −0.685900 + 1.50191i
\(202\) 0 0
\(203\) −2.73349 5.98551i −0.191854 0.420101i
\(204\) 0 0
\(205\) 1.69855 + 1.09159i 0.118632 + 0.0762401i
\(206\) 0 0
\(207\) −0.301076 + 0.431739i −0.0209262 + 0.0300079i
\(208\) 0 0
\(209\) 4.01206 + 2.57840i 0.277520 + 0.178351i
\(210\) 0 0
\(211\) −2.26444 4.95842i −0.155890 0.341352i 0.815531 0.578713i \(-0.196445\pi\)
−0.971421 + 0.237361i \(0.923718\pi\)
\(212\) 0 0
\(213\) −1.91771 + 4.19920i −0.131400 + 0.287725i
\(214\) 0 0
\(215\) 1.39884 9.72914i 0.0954001 0.663522i
\(216\) 0 0
\(217\) −2.22337 2.56590i −0.150932 0.174185i
\(218\) 0 0
\(219\) −0.661143 + 0.424891i −0.0446759 + 0.0287115i
\(220\) 0 0
\(221\) 6.02610 1.76942i 0.405360 0.119024i
\(222\) 0 0
\(223\) 3.60267 4.15771i 0.241253 0.278421i −0.622191 0.782865i \(-0.713757\pi\)
0.863444 + 0.504445i \(0.168303\pi\)
\(224\) 0 0
\(225\) 0.105306 + 0.0309206i 0.00702040 + 0.00206138i
\(226\) 0 0
\(227\) 3.29987 + 22.9511i 0.219020 + 1.52332i 0.741666 + 0.670769i \(0.234036\pi\)
−0.522646 + 0.852550i \(0.675055\pi\)
\(228\) 0 0
\(229\) 14.2193 0.939635 0.469818 0.882764i \(-0.344320\pi\)
0.469818 + 0.882764i \(0.344320\pi\)
\(230\) 0 0
\(231\) 14.6874 0.966357
\(232\) 0 0
\(233\) −3.59061 24.9732i −0.235229 1.63605i −0.674912 0.737898i \(-0.735818\pi\)
0.439683 0.898153i \(-0.355091\pi\)
\(234\) 0 0
\(235\) 6.21230 + 1.82410i 0.405246 + 0.118991i
\(236\) 0 0
\(237\) 11.2504 12.9837i 0.730794 0.843381i
\(238\) 0 0
\(239\) 12.5795 3.69366i 0.813697 0.238923i 0.151697 0.988427i \(-0.451526\pi\)
0.662000 + 0.749504i \(0.269708\pi\)
\(240\) 0 0
\(241\) 21.6963 13.9434i 1.39758 0.898171i 0.397767 0.917486i \(-0.369785\pi\)
0.999813 + 0.0193156i \(0.00614872\pi\)
\(242\) 0 0
\(243\) 0.746537 + 0.861550i 0.0478904 + 0.0552685i
\(244\) 0 0
\(245\) −1.21546 + 8.45371i −0.0776529 + 0.540088i
\(246\) 0 0
\(247\) −2.87538 + 6.29621i −0.182956 + 0.400618i
\(248\) 0 0
\(249\) −5.66378 12.4019i −0.358927 0.785941i
\(250\) 0 0
\(251\) −19.1427 12.3023i −1.20828 0.776512i −0.227907 0.973683i \(-0.573188\pi\)
−0.980369 + 0.197171i \(0.936825\pi\)
\(252\) 0 0
\(253\) −3.33952 + 9.96539i −0.209954 + 0.626519i
\(254\) 0 0
\(255\) −2.82407 1.81492i −0.176850 0.113655i
\(256\) 0 0
\(257\) −0.309807 0.678382i −0.0193252 0.0423163i 0.899723 0.436461i \(-0.143768\pi\)
−0.919048 + 0.394144i \(0.871041\pi\)
\(258\) 0 0
\(259\) 2.80824 6.14918i 0.174495 0.382092i
\(260\) 0 0
\(261\) 0.0260713 0.181330i 0.00161377 0.0112240i
\(262\) 0 0
\(263\) −11.3480 13.0963i −0.699750 0.807554i 0.288969 0.957338i \(-0.406688\pi\)
−0.988719 + 0.149784i \(0.952142\pi\)
\(264\) 0 0
\(265\) −8.79280 + 5.65079i −0.540138 + 0.347125i
\(266\) 0 0
\(267\) 0.254464 0.0747173i 0.0155729 0.00457262i
\(268\) 0 0
\(269\) 16.9178 19.5242i 1.03150 1.19041i 0.0500373 0.998747i \(-0.484066\pi\)
0.981460 0.191665i \(-0.0613886\pi\)
\(270\) 0 0
\(271\) 4.83679 + 1.42021i 0.293814 + 0.0862717i 0.425318 0.905044i \(-0.360162\pi\)
−0.131504 + 0.991316i \(0.541980\pi\)
\(272\) 0 0
\(273\) 3.03366 + 21.0996i 0.183605 + 1.27700i
\(274\) 0 0
\(275\) 2.19150 0.132152
\(276\) 0 0
\(277\) −13.2268 −0.794720 −0.397360 0.917663i \(-0.630074\pi\)
−0.397360 + 0.917663i \(0.630074\pi\)
\(278\) 0 0
\(279\) −0.0134521 0.0935613i −0.000805355 0.00560137i
\(280\) 0 0
\(281\) −2.06162 0.605346i −0.122986 0.0361119i 0.219660 0.975576i \(-0.429505\pi\)
−0.342646 + 0.939464i \(0.611323\pi\)
\(282\) 0 0
\(283\) −4.09886 + 4.73034i −0.243652 + 0.281189i −0.864383 0.502834i \(-0.832291\pi\)
0.620731 + 0.784024i \(0.286836\pi\)
\(284\) 0 0
\(285\) 3.54984 1.04233i 0.210274 0.0617421i
\(286\) 0 0
\(287\) −6.69596 + 4.30323i −0.395250 + 0.254012i
\(288\) 0 0
\(289\) 8.57928 + 9.90102i 0.504664 + 0.582413i
\(290\) 0 0
\(291\) 2.89731 20.1512i 0.169843 1.18128i
\(292\) 0 0
\(293\) −5.19288 + 11.3708i −0.303371 + 0.664290i −0.998509 0.0545862i \(-0.982616\pi\)
0.695138 + 0.718876i \(0.255343\pi\)
\(294\) 0 0
\(295\) 5.31159 + 11.6307i 0.309252 + 0.677168i
\(296\) 0 0
\(297\) 9.74679 + 6.26388i 0.565566 + 0.363467i
\(298\) 0 0
\(299\) −15.0059 2.73915i −0.867811 0.158409i
\(300\) 0 0
\(301\) 32.5971 + 20.9489i 1.87887 + 1.20747i
\(302\) 0 0
\(303\) −5.16178 11.3027i −0.296537 0.649325i
\(304\) 0 0
\(305\) −3.69995 + 8.10176i −0.211859 + 0.463905i
\(306\) 0 0
\(307\) −1.86343 + 12.9604i −0.106352 + 0.739691i 0.864953 + 0.501853i \(0.167348\pi\)
−0.971305 + 0.237839i \(0.923561\pi\)
\(308\) 0 0
\(309\) 0.423951 + 0.489266i 0.0241178 + 0.0278334i
\(310\) 0 0
\(311\) −23.6964 + 15.2287i −1.34370 + 0.863543i −0.997220 0.0745144i \(-0.976259\pi\)
−0.346479 + 0.938058i \(0.612623\pi\)
\(312\) 0 0
\(313\) 0.0686569 0.0201595i 0.00388072 0.00113948i −0.279792 0.960061i \(-0.590265\pi\)
0.283672 + 0.958921i \(0.408447\pi\)
\(314\) 0 0
\(315\) −0.283332 + 0.326982i −0.0159639 + 0.0184233i
\(316\) 0 0
\(317\) 14.5984 + 4.28647i 0.819926 + 0.240752i 0.664684 0.747125i \(-0.268566\pi\)
0.155242 + 0.987877i \(0.450384\pi\)
\(318\) 0 0
\(319\) −0.520586 3.62076i −0.0291472 0.202724i
\(320\) 0 0
\(321\) −20.5040 −1.14442
\(322\) 0 0
\(323\) 4.29714 0.239099
\(324\) 0 0
\(325\) 0.452652 + 3.14826i 0.0251086 + 0.174634i
\(326\) 0 0
\(327\) 20.2113 + 5.93457i 1.11769 + 0.328182i
\(328\) 0 0
\(329\) −16.7145 + 19.2896i −0.921502 + 1.06347i
\(330\) 0 0
\(331\) 14.1847 4.16499i 0.779659 0.228929i 0.132398 0.991197i \(-0.457732\pi\)
0.647261 + 0.762268i \(0.275914\pi\)
\(332\) 0 0
\(333\) 0.158327 0.101751i 0.00867628 0.00557590i
\(334\) 0 0
\(335\) −9.01691 10.4061i −0.492647 0.568544i
\(336\) 0 0
\(337\) −3.72179 + 25.8856i −0.202739 + 1.41008i 0.593371 + 0.804929i \(0.297797\pi\)
−0.796110 + 0.605152i \(0.793112\pi\)
\(338\) 0 0
\(339\) −4.07077 + 8.91375i −0.221094 + 0.484129i
\(340\) 0 0
\(341\) −0.784064 1.71686i −0.0424595 0.0929733i
\(342\) 0 0
\(343\) −5.10933 3.28357i −0.275878 0.177296i
\(344\) 0 0
\(345\) 4.14597 + 7.02044i 0.223212 + 0.377968i
\(346\) 0 0
\(347\) −26.1914 16.8322i −1.40603 0.903600i −0.406082 0.913837i \(-0.633105\pi\)
−0.999948 + 0.0102365i \(0.996742\pi\)
\(348\) 0 0
\(349\) −6.90520 15.1203i −0.369627 0.809370i −0.999467 0.0326449i \(-0.989607\pi\)
0.629840 0.776725i \(-0.283120\pi\)
\(350\) 0 0
\(351\) −6.98538 + 15.2958i −0.372852 + 0.816432i
\(352\) 0 0
\(353\) −2.82843 + 19.6722i −0.150542 + 1.04704i 0.764771 + 0.644302i \(0.222852\pi\)
−0.915313 + 0.402742i \(0.868057\pi\)
\(354\) 0 0
\(355\) −1.77821 2.05216i −0.0943775 0.108917i
\(356\) 0 0
\(357\) 11.1329 7.15470i 0.589217 0.378667i
\(358\) 0 0
\(359\) 17.5829 5.16279i 0.927987 0.272482i 0.217394 0.976084i \(-0.430245\pi\)
0.710594 + 0.703602i \(0.248426\pi\)
\(360\) 0 0
\(361\) 9.34103 10.7801i 0.491633 0.567375i
\(362\) 0 0
\(363\) −10.1091 2.96831i −0.530592 0.155796i
\(364\) 0 0
\(365\) −0.0657887 0.457570i −0.00344354 0.0239503i
\(366\) 0 0
\(367\) −16.9068 −0.882525 −0.441263 0.897378i \(-0.645469\pi\)
−0.441263 + 0.897378i \(0.645469\pi\)
\(368\) 0 0
\(369\) −0.221597 −0.0115359
\(370\) 0 0
\(371\) −5.86388 40.7842i −0.304437 2.11741i
\(372\) 0 0
\(373\) −22.2975 6.54715i −1.15452 0.338999i −0.352221 0.935917i \(-0.614573\pi\)
−0.802302 + 0.596918i \(0.796392\pi\)
\(374\) 0 0
\(375\) 1.11331 1.28483i 0.0574911 0.0663483i
\(376\) 0 0
\(377\) 5.09398 1.49573i 0.262353 0.0770339i
\(378\) 0 0
\(379\) 12.6620 8.13739i 0.650405 0.417990i −0.173409 0.984850i \(-0.555478\pi\)
0.823814 + 0.566860i \(0.191842\pi\)
\(380\) 0 0
\(381\) −10.7080 12.3577i −0.548588 0.633104i
\(382\) 0 0
\(383\) 2.13807 14.8706i 0.109250 0.759851i −0.859379 0.511339i \(-0.829150\pi\)
0.968629 0.248511i \(-0.0799413\pi\)
\(384\) 0 0
\(385\) −3.58887 + 7.85854i −0.182906 + 0.400508i
\(386\) 0 0
\(387\) 0.448138 + 0.981285i 0.0227801 + 0.0498815i
\(388\) 0 0
\(389\) 21.3885 + 13.7455i 1.08444 + 0.696927i 0.955579 0.294736i \(-0.0952318\pi\)
0.128860 + 0.991663i \(0.458868\pi\)
\(390\) 0 0
\(391\) 2.32314 + 9.18050i 0.117486 + 0.464278i
\(392\) 0 0
\(393\) −15.8356 10.1769i −0.798801 0.513359i
\(394\) 0 0
\(395\) 4.19792 + 9.19217i 0.211221 + 0.462508i
\(396\) 0 0
\(397\) 4.50490 9.86435i 0.226094 0.495078i −0.762256 0.647276i \(-0.775908\pi\)
0.988350 + 0.152199i \(0.0486353\pi\)
\(398\) 0 0
\(399\) −2.07564 + 14.4364i −0.103912 + 0.722723i
\(400\) 0 0
\(401\) −5.98123 6.90270i −0.298688 0.344705i 0.586490 0.809956i \(-0.300509\pi\)
−0.885178 + 0.465252i \(0.845964\pi\)
\(402\) 0 0
\(403\) 2.30446 1.48099i 0.114793 0.0737732i
\(404\) 0 0
\(405\) 8.30796 2.43944i 0.412826 0.121217i
\(406\) 0 0
\(407\) 2.46098 2.84012i 0.121986 0.140779i
\(408\) 0 0
\(409\) −9.78041 2.87179i −0.483610 0.142001i 0.0308343 0.999525i \(-0.490184\pi\)
−0.514444 + 0.857524i \(0.672002\pi\)
\(410\) 0 0
\(411\) −3.50088 24.3491i −0.172686 1.20105i
\(412\) 0 0
\(413\) −50.4053 −2.48028
\(414\) 0 0
\(415\) 8.01967 0.393670
\(416\) 0 0
\(417\) −4.15032 28.8661i −0.203242 1.41358i
\(418\) 0 0
\(419\) 31.7234 + 9.31484i 1.54979 + 0.455060i 0.941038 0.338301i \(-0.109852\pi\)
0.608752 + 0.793360i \(0.291670\pi\)
\(420\) 0 0
\(421\) −21.4295 + 24.7310i −1.04441 + 1.20531i −0.0661771 + 0.997808i \(0.521080\pi\)
−0.978234 + 0.207506i \(0.933465\pi\)
\(422\) 0 0
\(423\) −0.681811 + 0.200198i −0.0331508 + 0.00973395i
\(424\) 0 0
\(425\) 1.66114 1.06755i 0.0805773 0.0517839i
\(426\) 0 0
\(427\) −22.9931 26.5354i −1.11271 1.28414i
\(428\) 0 0
\(429\) −1.68645 + 11.7295i −0.0814226 + 0.566307i
\(430\) 0 0
\(431\) 4.62218 10.1212i 0.222643 0.487519i −0.765041 0.643981i \(-0.777282\pi\)
0.987684 + 0.156462i \(0.0500088\pi\)
\(432\) 0 0
\(433\) −12.5951 27.5793i −0.605280 1.32538i −0.925756 0.378121i \(-0.876570\pi\)
0.320476 0.947256i \(-0.396157\pi\)
\(434\) 0 0
\(435\) −2.38724 1.53418i −0.114459 0.0735585i
\(436\) 0 0
\(437\) −9.32316 4.69078i −0.445987 0.224390i
\(438\) 0 0
\(439\) 1.95931 + 1.25917i 0.0935128 + 0.0600970i 0.586562 0.809905i \(-0.300481\pi\)
−0.493049 + 0.870002i \(0.664118\pi\)
\(440\) 0 0
\(441\) −0.389390 0.852644i −0.0185424 0.0406021i
\(442\) 0 0
\(443\) −8.86811 + 19.4184i −0.421337 + 0.922598i 0.573317 + 0.819333i \(0.305656\pi\)
−0.994654 + 0.103265i \(0.967071\pi\)
\(444\) 0 0
\(445\) −0.0222007 + 0.154409i −0.00105241 + 0.00731970i
\(446\) 0 0
\(447\) −11.4976 13.2689i −0.543818 0.627599i
\(448\) 0 0
\(449\) −32.2929 + 20.7534i −1.52400 + 0.979413i −0.532913 + 0.846170i \(0.678903\pi\)
−0.991083 + 0.133243i \(0.957461\pi\)
\(450\) 0 0
\(451\) −4.24556 + 1.24661i −0.199916 + 0.0587005i
\(452\) 0 0
\(453\) 17.0952 19.7289i 0.803202 0.926944i
\(454\) 0 0
\(455\) −12.0307 3.53253i −0.564008 0.165608i
\(456\) 0 0
\(457\) 3.89954 + 27.1219i 0.182413 + 1.26871i 0.851036 + 0.525107i \(0.175975\pi\)
−0.668623 + 0.743601i \(0.733116\pi\)
\(458\) 0 0
\(459\) 10.4394 0.487268
\(460\) 0 0
\(461\) −17.0131 −0.792381 −0.396190 0.918168i \(-0.629668\pi\)
−0.396190 + 0.918168i \(0.629668\pi\)
\(462\) 0 0
\(463\) −2.64651 18.4069i −0.122994 0.855441i −0.954134 0.299378i \(-0.903221\pi\)
0.831141 0.556062i \(-0.187688\pi\)
\(464\) 0 0
\(465\) −1.40487 0.412508i −0.0651495 0.0191296i
\(466\) 0 0
\(467\) 11.9296 13.7675i 0.552038 0.637086i −0.409319 0.912391i \(-0.634234\pi\)
0.961357 + 0.275306i \(0.0887791\pi\)
\(468\) 0 0
\(469\) 52.0817 15.2926i 2.40491 0.706145i
\(470\) 0 0
\(471\) 25.0271 16.0839i 1.15319 0.741108i
\(472\) 0 0
\(473\) 14.1061 + 16.2794i 0.648601 + 0.748526i
\(474\) 0 0
\(475\) −0.309706 + 2.15405i −0.0142103 + 0.0988347i
\(476\) 0 0
\(477\) 0.476534 1.04346i 0.0218190 0.0477769i
\(478\) 0 0
\(479\) 6.76936 + 14.8228i 0.309300 + 0.677273i 0.998899 0.0469191i \(-0.0149403\pi\)
−0.689599 + 0.724192i \(0.742213\pi\)
\(480\) 0 0
\(481\) 4.58837 + 2.94877i 0.209212 + 0.134452i
\(482\) 0 0
\(483\) −31.9643 + 3.37021i −1.45443 + 0.153350i
\(484\) 0 0
\(485\) 10.0740 + 6.47419i 0.457438 + 0.293978i
\(486\) 0 0
\(487\) −12.3960 27.1434i −0.561715 1.22998i −0.951092 0.308906i \(-0.900037\pi\)
0.389377 0.921078i \(-0.372690\pi\)
\(488\) 0 0
\(489\) −13.9465 + 30.5385i −0.630681 + 1.38100i
\(490\) 0 0
\(491\) 3.29656 22.9281i 0.148772 1.03473i −0.769463 0.638692i \(-0.779476\pi\)
0.918234 0.396038i \(-0.129615\pi\)
\(492\) 0 0
\(493\) −2.15839 2.49092i −0.0972092 0.112185i
\(494\) 0 0
\(495\) −0.202339 + 0.130035i −0.00909447 + 0.00584466i
\(496\) 0 0
\(497\) 10.2709 3.01582i 0.460714 0.135278i
\(498\) 0 0
\(499\) −11.0505 + 12.7529i −0.494688 + 0.570900i −0.947112 0.320903i \(-0.896014\pi\)
0.452425 + 0.891803i \(0.350559\pi\)
\(500\) 0 0
\(501\) −7.76202 2.27913i −0.346781 0.101824i
\(502\) 0 0
\(503\) 1.00237 + 6.97162i 0.0446933 + 0.310849i 0.999889 + 0.0148751i \(0.00473507\pi\)
−0.955196 + 0.295974i \(0.904356\pi\)
\(504\) 0 0
\(505\) 7.30886 0.325240
\(506\) 0 0
\(507\) 4.90223 0.217715
\(508\) 0 0
\(509\) 3.72507 + 25.9085i 0.165111 + 1.14837i 0.888816 + 0.458263i \(0.151528\pi\)
−0.723705 + 0.690109i \(0.757563\pi\)
\(510\) 0 0
\(511\) 1.74855 + 0.513420i 0.0773511 + 0.0227123i
\(512\) 0 0
\(513\) −7.53427 + 8.69502i −0.332646 + 0.383894i
\(514\) 0 0
\(515\) −0.365377 + 0.107284i −0.0161004 + 0.00472752i
\(516\) 0 0
\(517\) −11.9366 + 7.67116i −0.524969 + 0.337377i
\(518\) 0 0
\(519\) −0.688461 0.794526i −0.0302201 0.0348758i
\(520\) 0 0
\(521\) 0.217375 1.51188i 0.00952337 0.0662365i −0.984506 0.175353i \(-0.943893\pi\)
0.994029 + 0.109117i \(0.0348023\pi\)
\(522\) 0 0
\(523\) −4.46561 + 9.77833i −0.195268 + 0.427577i −0.981786 0.189990i \(-0.939154\pi\)
0.786518 + 0.617567i \(0.211882\pi\)
\(524\) 0 0
\(525\) 2.78410 + 6.09632i 0.121508 + 0.266065i
\(526\) 0 0
\(527\) −1.43066 0.919427i −0.0623204 0.0400509i
\(528\) 0 0
\(529\) 4.98116 22.4541i 0.216572 0.976267i
\(530\) 0 0
\(531\) −1.18054 0.758686i −0.0512310 0.0329242i
\(532\) 0 0
\(533\) −2.66777 5.84160i −0.115554 0.253028i
\(534\) 0 0
\(535\) 5.01017 10.9708i 0.216609 0.474307i
\(536\) 0 0
\(537\) 4.09005 28.4469i 0.176499 1.22757i
\(538\) 0 0
\(539\) −12.2569 14.1452i −0.527943 0.609278i
\(540\) 0 0
\(541\) 12.5230 8.04805i 0.538406 0.346013i −0.243009 0.970024i \(-0.578134\pi\)
0.781415 + 0.624011i \(0.214498\pi\)
\(542\) 0 0
\(543\) −33.9076 + 9.95617i −1.45511 + 0.427260i
\(544\) 0 0
\(545\) −8.11397 + 9.36402i −0.347564 + 0.401111i
\(546\) 0 0
\(547\) 31.4688 + 9.24007i 1.34551 + 0.395077i 0.873632 0.486588i \(-0.161759\pi\)
0.471877 + 0.881665i \(0.343577\pi\)
\(548\) 0 0
\(549\) −0.139115 0.967569i −0.00593730 0.0412948i
\(550\) 0 0
\(551\) 3.63246 0.154748
\(552\) 0 0
\(553\) −39.8370 −1.69404
\(554\) 0 0
\(555\) −0.414892 2.88564i −0.0176112 0.122488i
\(556\) 0 0
\(557\) 35.0586 + 10.2941i 1.48548 + 0.436177i 0.921097 0.389334i \(-0.127295\pi\)
0.564386 + 0.825511i \(0.309113\pi\)
\(558\) 0 0
\(559\) −20.4730 + 23.6271i −0.865915 + 0.999319i
\(560\) 0 0
\(561\) 7.05881 2.07265i 0.298023 0.0875075i
\(562\) 0 0
\(563\) 30.3853 19.5275i 1.28059 0.822985i 0.289629 0.957139i \(-0.406468\pi\)
0.990960 + 0.134154i \(0.0428318\pi\)
\(564\) 0 0
\(565\) −3.77465 4.35617i −0.158801 0.183266i
\(566\) 0 0
\(567\) −4.85777 + 33.7866i −0.204007 + 1.41890i
\(568\) 0 0
\(569\) 3.65977 8.01378i 0.153426 0.335955i −0.817275 0.576248i \(-0.804516\pi\)
0.970700 + 0.240293i \(0.0772435\pi\)
\(570\) 0 0
\(571\) −0.710988 1.55685i −0.0297539 0.0651520i 0.894172 0.447725i \(-0.147765\pi\)
−0.923925 + 0.382573i \(0.875038\pi\)
\(572\) 0 0
\(573\) 18.1104 + 11.6388i 0.756571 + 0.486219i
\(574\) 0 0
\(575\) −4.76939 + 0.502869i −0.198897 + 0.0209711i
\(576\) 0 0
\(577\) −33.1398 21.2977i −1.37963 0.886634i −0.380359 0.924839i \(-0.624200\pi\)
−0.999270 + 0.0382050i \(0.987836\pi\)
\(578\) 0 0
\(579\) 6.65144 + 14.5646i 0.276424 + 0.605285i
\(580\) 0 0
\(581\) −13.1333 + 28.7579i −0.544860 + 1.19308i
\(582\) 0 0
\(583\) 3.25981 22.6725i 0.135007 0.938998i
\(584\) 0 0
\(585\) −0.228599 0.263818i −0.00945141 0.0109075i
\(586\) 0 0
\(587\) 11.4489 7.35776i 0.472546 0.303687i −0.282606 0.959236i \(-0.591199\pi\)
0.755153 + 0.655549i \(0.227563\pi\)
\(588\) 0 0
\(589\) 1.79833 0.528037i 0.0740988 0.0217574i
\(590\) 0 0
\(591\) −16.3323 + 18.8485i −0.671821 + 0.775323i
\(592\) 0 0
\(593\) 38.6668 + 11.3536i 1.58785 + 0.466236i 0.952133 0.305684i \(-0.0988850\pi\)
0.635720 + 0.771919i \(0.280703\pi\)
\(594\) 0 0
\(595\) 1.10781 + 7.70499i 0.0454158 + 0.315874i
\(596\) 0 0
\(597\) −40.6130 −1.66218
\(598\) 0 0
\(599\) 48.4251 1.97859 0.989297 0.145914i \(-0.0466124\pi\)
0.989297 + 0.145914i \(0.0466124\pi\)
\(600\) 0 0
\(601\) 5.48857 + 38.1739i 0.223883 + 1.55714i 0.723147 + 0.690694i \(0.242695\pi\)
−0.499264 + 0.866450i \(0.666396\pi\)
\(602\) 0 0
\(603\) 1.44998 + 0.425753i 0.0590478 + 0.0173380i
\(604\) 0 0
\(605\) 4.05839 4.68363i 0.164997 0.190417i
\(606\) 0 0
\(607\) −19.3731 + 5.68846i −0.786330 + 0.230887i −0.650159 0.759798i \(-0.725298\pi\)
−0.136171 + 0.990685i \(0.543480\pi\)
\(608\) 0 0
\(609\) 9.41088 6.04800i 0.381348 0.245078i
\(610\) 0 0
\(611\) −13.4857 15.5634i −0.545574 0.629626i
\(612\) 0 0
\(613\) 6.73249 46.8255i 0.271923 1.89126i −0.156489 0.987680i \(-0.550017\pi\)
0.428411 0.903584i \(-0.359073\pi\)
\(614\) 0 0
\(615\) −1.42594 + 3.12237i −0.0574994 + 0.125906i
\(616\) 0 0
\(617\) 13.3727 + 29.2822i 0.538366 + 1.17886i 0.962007 + 0.273026i \(0.0880245\pi\)
−0.423641 + 0.905830i \(0.639248\pi\)
\(618\) 0 0
\(619\) 36.3012 + 23.3294i 1.45907 + 0.937687i 0.998753 + 0.0499315i \(0.0159003\pi\)
0.460316 + 0.887755i \(0.347736\pi\)
\(620\) 0 0
\(621\) −22.6494 11.3956i −0.908890 0.457292i
\(622\) 0 0
\(623\) −0.517342 0.332476i −0.0207269 0.0133203i
\(624\) 0 0
\(625\) 0.415415 + 0.909632i 0.0166166 + 0.0363853i
\(626\) 0 0
\(627\) −3.36814 + 7.37520i −0.134511 + 0.294537i
\(628\) 0 0
\(629\) 0.481890 3.35162i 0.0192142 0.133638i
\(630\) 0 0
\(631\) 8.02835 + 9.26521i 0.319603 + 0.368842i 0.892704 0.450643i \(-0.148805\pi\)
−0.573101 + 0.819485i \(0.694260\pi\)
\(632\) 0 0
\(633\) 7.79601 5.01019i 0.309863 0.199137i
\(634\) 0 0
\(635\) 9.22856 2.70975i 0.366224 0.107533i
\(636\) 0 0
\(637\) 17.7891 20.5297i 0.704830 0.813417i
\(638\) 0 0
\(639\) 0.285948 + 0.0839619i 0.0113119 + 0.00332148i
\(640\) 0 0
\(641\) 1.69343 + 11.7781i 0.0668864 + 0.465205i 0.995546 + 0.0942731i \(0.0300527\pi\)
−0.928660 + 0.370932i \(0.879038\pi\)
\(642\) 0 0
\(643\) −12.1095 −0.477552 −0.238776 0.971075i \(-0.576746\pi\)
−0.238776 + 0.971075i \(0.576746\pi\)
\(644\) 0 0
\(645\) 16.7103 0.657969
\(646\) 0 0
\(647\) 5.94441 + 41.3443i 0.233699 + 1.62541i 0.681877 + 0.731467i \(0.261164\pi\)
−0.448178 + 0.893944i \(0.647927\pi\)
\(648\) 0 0
\(649\) −26.8859 7.89443i −1.05537 0.309883i
\(650\) 0 0
\(651\) 3.77989 4.36223i 0.148146 0.170969i
\(652\) 0 0
\(653\) 19.1230 5.61501i 0.748340 0.219732i 0.114742 0.993395i \(-0.463396\pi\)
0.633597 + 0.773663i \(0.281578\pi\)
\(654\) 0 0
\(655\) 9.31467 5.98618i 0.363954 0.233899i
\(656\) 0 0
\(657\) 0.0332247 + 0.0383434i 0.00129622 + 0.00149592i
\(658\) 0 0
\(659\) 1.99431 13.8708i 0.0776875 0.540328i −0.913395 0.407075i \(-0.866549\pi\)
0.991082 0.133253i \(-0.0425423\pi\)
\(660\) 0 0
\(661\) −9.79773 + 21.4540i −0.381087 + 0.834465i 0.617755 + 0.786370i \(0.288042\pi\)
−0.998843 + 0.0480947i \(0.984685\pi\)
\(662\) 0 0
\(663\) 4.43552 + 9.71244i 0.172261 + 0.377200i
\(664\) 0 0
\(665\) −7.21707 4.63813i −0.279866 0.179859i
\(666\) 0 0
\(667\) 1.96379 + 7.76045i 0.0760383 + 0.300486i
\(668\) 0 0
\(669\) 7.86811 + 5.05653i 0.304199 + 0.195497i
\(670\) 0 0
\(671\) −8.10844 17.7550i −0.313023 0.685424i
\(672\) 0 0
\(673\) 4.83473 10.5866i 0.186365 0.408083i −0.793270 0.608871i \(-0.791623\pi\)
0.979635 + 0.200788i \(0.0643501\pi\)
\(674\) 0 0
\(675\) −0.752391 + 5.23299i −0.0289595 + 0.201418i
\(676\) 0 0
\(677\) −8.06822 9.31122i −0.310087 0.357859i 0.579219 0.815172i \(-0.303358\pi\)
−0.889306 + 0.457313i \(0.848812\pi\)
\(678\) 0 0
\(679\) −39.7135 + 25.5223i −1.52406 + 0.979456i
\(680\) 0 0
\(681\) −37.8230 + 11.1058i −1.44938 + 0.425577i
\(682\) 0 0
\(683\) −2.40269 + 2.77285i −0.0919364 + 0.106100i −0.799854 0.600195i \(-0.795090\pi\)
0.707917 + 0.706295i \(0.249635\pi\)
\(684\) 0 0
\(685\) 13.8836 + 4.07658i 0.530464 + 0.155758i
\(686\) 0 0
\(687\) 3.44029 + 23.9277i 0.131255 + 0.912900i
\(688\) 0 0
\(689\) 33.2441 1.26650
\(690\) 0 0
\(691\) 40.9110 1.55633 0.778164 0.628061i \(-0.216151\pi\)
0.778164 + 0.628061i \(0.216151\pi\)
\(692\) 0 0
\(693\) −0.134939 0.938522i −0.00512591 0.0356515i
\(694\) 0 0
\(695\) 16.4591 + 4.83282i 0.624329 + 0.183319i
\(696\) 0 0
\(697\) −2.61084 + 3.01307i −0.0988928 + 0.114128i
\(698\) 0 0
\(699\) 41.1555 12.0843i 1.55664 0.457071i
\(700\) 0 0
\(701\) 3.73723 2.40177i 0.141153 0.0907136i −0.468158 0.883645i \(-0.655082\pi\)
0.609311 + 0.792931i \(0.291446\pi\)
\(702\) 0 0
\(703\) 2.44380 + 2.82029i 0.0921696 + 0.106369i
\(704\) 0 0
\(705\) −1.56649 + 10.8952i −0.0589976 + 0.410337i
\(706\) 0 0
\(707\) −11.9692 + 26.2090i −0.450150 + 0.985690i
\(708\) 0 0
\(709\) −14.9124 32.6537i −0.560048 1.22633i −0.951929 0.306319i \(-0.900903\pi\)
0.391881 0.920016i \(-0.371825\pi\)
\(710\) 0 0
\(711\) −0.933020 0.599615i −0.0349910 0.0224873i
\(712\) 0 0
\(713\) 2.10033 + 3.55652i 0.0786579 + 0.133193i
\(714\) 0 0
\(715\) −5.86385 3.76847i −0.219295 0.140933i
\(716\) 0 0
\(717\) 9.25912 + 20.2746i 0.345788 + 0.757170i
\(718\) 0 0
\(719\) 15.5751 34.1048i 0.580854 1.27189i −0.359959 0.932968i \(-0.617209\pi\)
0.940813 0.338925i \(-0.110063\pi\)
\(720\) 0 0
\(721\) 0.213641 1.48590i 0.00795640 0.0553380i
\(722\) 0 0
\(723\) 28.7128 + 33.1363i 1.06784 + 1.23235i
\(724\) 0 0
\(725\) 1.40420 0.902423i 0.0521506 0.0335151i
\(726\) 0 0
\(727\) 2.38744 0.701015i 0.0885452 0.0259992i −0.237160 0.971471i \(-0.576217\pi\)
0.325705 + 0.945471i \(0.394398\pi\)
\(728\) 0 0
\(729\) −18.2799 + 21.0961i −0.677033 + 0.781338i
\(730\) 0 0
\(731\) 18.6226 + 5.46809i 0.688781 + 0.202244i
\(732\) 0 0
\(733\) 0.0854324 + 0.594196i 0.00315552 + 0.0219471i 0.991338 0.131333i \(-0.0419256\pi\)
−0.988183 + 0.153280i \(0.951016\pi\)
\(734\) 0 0
\(735\) −14.5197 −0.535568
\(736\) 0 0
\(737\) 30.1752 1.11152
\(738\) 0 0
\(739\) 2.68046 + 18.6430i 0.0986025 + 0.685795i 0.977831 + 0.209395i \(0.0671495\pi\)
−0.879229 + 0.476400i \(0.841941\pi\)
\(740\) 0 0
\(741\) −11.2908 3.31526i −0.414776 0.121789i
\(742\) 0 0
\(743\) 10.2057 11.7780i 0.374411 0.432093i −0.537005 0.843579i \(-0.680444\pi\)
0.911416 + 0.411485i \(0.134990\pi\)
\(744\) 0 0
\(745\) 9.90906 2.90956i 0.363040 0.106598i
\(746\) 0 0
\(747\) −0.740448 + 0.475857i −0.0270916 + 0.0174107i
\(748\) 0 0
\(749\) 31.1354 + 35.9321i 1.13766 + 1.31293i
\(750\) 0 0
\(751\) 2.95266 20.5362i 0.107744 0.749377i −0.862291 0.506413i \(-0.830971\pi\)
0.970035 0.242964i \(-0.0781198\pi\)
\(752\) 0 0
\(753\) 16.0704 35.1892i 0.585637 1.28237i
\(754\) 0 0
\(755\) 6.37881 + 13.9676i 0.232148 + 0.508334i
\(756\) 0 0
\(757\) 3.53742 + 2.27336i 0.128570 + 0.0826268i 0.603345 0.797480i \(-0.293834\pi\)
−0.474775 + 0.880107i \(0.657471\pi\)
\(758\) 0 0
\(759\) −17.5774 3.20856i −0.638020 0.116463i
\(760\) 0 0
\(761\) −16.1522 10.3804i −0.585516 0.376288i 0.214090 0.976814i \(-0.431322\pi\)
−0.799605 + 0.600526i \(0.794958\pi\)
\(762\) 0 0
\(763\) −20.2909 44.4309i −0.734580 1.60851i
\(764\) 0 0
\(765\) −0.0900273 + 0.197132i −0.00325494 + 0.00712733i
\(766\) 0 0
\(767\) 5.78771 40.2544i 0.208982 1.45350i
\(768\) 0 0
\(769\) −23.8002 27.4669i −0.858257 0.990481i −1.00000 0.000577919i \(-0.999816\pi\)
0.141743 0.989904i \(-0.454729\pi\)
\(770\) 0 0
\(771\) 1.06660 0.685464i 0.0384128 0.0246864i
\(772\) 0 0
\(773\) 6.18512 1.81612i 0.222463 0.0653211i −0.168601 0.985684i \(-0.553925\pi\)
0.391065 + 0.920363i \(0.372107\pi\)
\(774\) 0 0
\(775\) 0.563997 0.650888i 0.0202594 0.0233806i
\(776\) 0 0
\(777\) 11.0271 + 3.23785i 0.395595 + 0.116157i
\(778\) 0 0
\(779\) −0.625318 4.34918i −0.0224043 0.155826i
\(780\) 0 0
\(781\) 5.95080 0.212936
\(782\) 0 0
\(783\) 8.82459 0.315365
\(784\) 0 0
\(785\) 2.49038 + 17.3210i 0.0888855 + 0.618212i
\(786\) 0 0
\(787\) −40.6562 11.9377i −1.44924 0.425535i −0.539948 0.841698i \(-0.681556\pi\)
−0.909290 + 0.416163i \(0.863374\pi\)
\(788\) 0 0
\(789\) 19.2925 22.2647i 0.686830 0.792645i
\(790\) 0 0
\(791\) 21.8024 6.40175i 0.775203 0.227620i
\(792\) 0 0
\(793\) 23.8317 15.3157i 0.846288 0.543876i
\(794\) 0 0
\(795\) −11.6364 13.4291i −0.412699 0.476280i
\(796\) 0 0
\(797\) 3.24659 22.5805i 0.115000 0.799843i −0.847933 0.530103i \(-0.822153\pi\)
0.962933 0.269740i \(-0.0869377\pi\)
\(798\) 0 0
\(799\) −5.31097 + 11.6294i −0.187889 + 0.411418i
\(800\) 0 0
\(801\) −0.00711230 0.0155738i −0.000251301 0.000550272i
\(802\) 0 0
\(803\) 0.852254 + 0.547711i 0.0300754 + 0.0193283i
\(804\) 0 0
\(805\) 6.00727 17.9262i 0.211729 0.631814i
\(806\) 0 0
\(807\) 36.9479 + 23.7450i 1.30063 + 0.835863i
\(808\) 0 0
\(809\) −13.0483 28.5719i −0.458755 1.00453i −0.987770 0.155921i \(-0.950166\pi\)
0.529015 0.848613i \(-0.322562\pi\)
\(810\) 0 0
\(811\) −12.9852 + 28.4337i −0.455973 + 0.998442i 0.532414 + 0.846484i \(0.321285\pi\)
−0.988387 + 0.151958i \(0.951442\pi\)
\(812\) 0 0
\(813\) −1.21965 + 8.48282i −0.0427748 + 0.297505i
\(814\) 0 0
\(815\) −12.9319 14.9242i −0.452986 0.522773i
\(816\) 0 0
\(817\) −17.9947 + 11.5645i −0.629554 + 0.404590i
\(818\) 0 0
\(819\) 1.32039 0.387701i 0.0461381 0.0135474i
\(820\) 0 0
\(821\) 1.50719 1.73939i 0.0526014 0.0607052i −0.728839 0.684685i \(-0.759940\pi\)
0.781441 + 0.623980i \(0.214485\pi\)
\(822\) 0 0
\(823\) 30.7835 + 9.03884i 1.07304 + 0.315074i 0.770093 0.637932i \(-0.220210\pi\)
0.302951 + 0.953006i \(0.402028\pi\)
\(824\) 0 0
\(825\) 0.530224 + 3.68779i 0.0184600 + 0.128392i
\(826\) 0 0
\(827\) −16.9699 −0.590101 −0.295051 0.955482i \(-0.595337\pi\)
−0.295051 + 0.955482i \(0.595337\pi\)
\(828\) 0 0
\(829\) −22.0617 −0.766236 −0.383118 0.923699i \(-0.625150\pi\)
−0.383118 + 0.923699i \(0.625150\pi\)
\(830\) 0 0
\(831\) −3.20016 22.2576i −0.111012 0.772108i
\(832\) 0 0
\(833\) −16.1813 4.75125i −0.560648 0.164621i
\(834\) 0 0
\(835\) 3.11612 3.59619i 0.107838 0.124451i
\(836\) 0 0
\(837\) 4.36881 1.28280i 0.151008 0.0443400i
\(838\) 0 0
\(839\) 4.84240 3.11202i 0.167178 0.107439i −0.454376 0.890810i \(-0.650138\pi\)
0.621555 + 0.783371i \(0.286501\pi\)
\(840\) 0 0
\(841\) 17.1664 + 19.8111i 0.591946 + 0.683142i
\(842\) 0 0
\(843\) 0.519858 3.61569i 0.0179049 0.124531i
\(844\) 0 0
\(845\) −1.19786 + 2.62296i −0.0412078 + 0.0902325i
\(846\) 0 0
\(847\) 10.1490 + 22.2231i 0.348722 + 0.763595i
\(848\) 0 0
\(849\) −8.95176 5.75295i −0.307224 0.197441i
\(850\) 0 0
\(851\) −4.70416 + 6.74570i −0.161256 + 0.231240i
\(852\) 0 0
\(853\) 13.8543 + 8.90360i 0.474361 + 0.304854i 0.755889 0.654699i \(-0.227205\pi\)
−0.281528 + 0.959553i \(0.590841\pi\)
\(854\) 0 0
\(855\) −0.0992185 0.217258i −0.00339320 0.00743008i
\(856\) 0 0
\(857\) 2.68383 5.87678i 0.0916780 0.200747i −0.858238 0.513252i \(-0.828441\pi\)
0.949916 + 0.312505i \(0.101168\pi\)
\(858\) 0 0
\(859\) −2.66917 + 18.5645i −0.0910709 + 0.633412i 0.892251 + 0.451540i \(0.149125\pi\)
−0.983322 + 0.181873i \(0.941784\pi\)
\(860\) 0 0
\(861\) −8.86140 10.2266i −0.301996 0.348522i
\(862\) 0 0
\(863\) 15.6403 10.0514i 0.532402 0.342154i −0.246659 0.969102i \(-0.579333\pi\)
0.779061 + 0.626948i \(0.215696\pi\)
\(864\) 0 0
\(865\) 0.593341 0.174221i 0.0201742 0.00592368i
\(866\) 0 0
\(867\) −14.5854 + 16.8325i −0.495346 + 0.571660i
\(868\) 0 0
\(869\) −21.2489 6.23923i −0.720818 0.211651i
\(870\) 0 0
\(871\) 6.23266 + 43.3491i 0.211186 + 1.46883i
\(872\) 0 0
\(873\) −1.31428 −0.0444816
\(874\) 0 0
\(875\) −3.94216 −0.133269
\(876\) 0 0
\(877\) 2.78319 + 19.3575i 0.0939816 + 0.653656i 0.981298 + 0.192495i \(0.0616580\pi\)
−0.887316 + 0.461161i \(0.847433\pi\)
\(878\) 0 0
\(879\) −20.3909 5.98729i −0.687766 0.201946i
\(880\) 0 0
\(881\) 16.4365 18.9687i 0.553758 0.639071i −0.407996 0.912984i \(-0.633772\pi\)
0.961755 + 0.273912i \(0.0883178\pi\)
\(882\) 0 0
\(883\) −32.4232 + 9.52030i −1.09113 + 0.320383i −0.777321 0.629104i \(-0.783422\pi\)
−0.313805 + 0.949488i \(0.601604\pi\)
\(884\) 0 0
\(885\) −18.2867 + 11.7522i −0.614702 + 0.395045i
\(886\) 0 0
\(887\) −25.4116 29.3266i −0.853240 0.984691i 0.146750 0.989174i \(-0.453119\pi\)
−0.999990 + 0.00448260i \(0.998573\pi\)
\(888\) 0 0
\(889\) −5.39606 + 37.5304i −0.180978 + 1.25873i
\(890\) 0 0
\(891\) −7.88272 + 17.2608i −0.264081 + 0.578257i
\(892\) 0 0
\(893\) −5.85319 12.8167i −0.195869 0.428894i
\(894\) 0 0
\(895\) 14.2212 + 9.13944i 0.475364 + 0.305498i
\(896\) 0 0
\(897\) 0.978751 25.9141i 0.0326796 0.865247i
\(898\) 0 0
\(899\) −1.20936 0.777210i −0.0403345 0.0259214i
\(900\) 0 0
\(901\) −8.57360 18.7736i −0.285628 0.625438i
\(902\) 0 0
\(903\) −27.3654 + 59.9219i −0.910664 + 1.99408i
\(904\) 0 0
\(905\) 2.95827 20.5752i 0.0983362 0.683943i
\(906\) 0 0
\(907\) −20.2992 23.4265i −0.674024 0.777865i 0.310977 0.950418i \(-0.399344\pi\)
−0.985000 + 0.172553i \(0.944798\pi\)
\(908\) 0 0
\(909\) −0.674820 + 0.433681i −0.0223824 + 0.0143843i
\(910\) 0 0
\(911\) −23.3365 + 6.85221i −0.773173 + 0.227024i −0.644439 0.764655i \(-0.722909\pi\)
−0.128733 + 0.991679i \(0.541091\pi\)
\(912\) 0 0
\(913\) −11.5092 + 13.2824i −0.380900 + 0.439582i
\(914\) 0 0
\(915\) −14.5286 4.26597i −0.480300 0.141029i
\(916\) 0 0
\(917\) 6.21191 + 43.2048i 0.205135 + 1.42675i
\(918\) 0 0
\(919\) 15.4524 0.509728 0.254864 0.966977i \(-0.417969\pi\)
0.254864 + 0.966977i \(0.417969\pi\)
\(920\) 0 0
\(921\) −22.2603 −0.733501
\(922\) 0 0
\(923\) 1.22913 + 8.54880i 0.0404573 + 0.281387i
\(924\) 0 0
\(925\) 1.64535 + 0.483119i 0.0540989 + 0.0158849i
\(926\) 0 0
\(927\) 0.0273691 0.0315856i 0.000898918 0.00103741i
\(928\) 0 0
\(929\) 19.2124 5.64127i 0.630339 0.185084i 0.0490695 0.998795i \(-0.484374\pi\)
0.581269 + 0.813711i \(0.302556\pi\)
\(930\) 0 0
\(931\) 15.6357 10.0484i 0.512439 0.329324i
\(932\) 0 0
\(933\) −31.3597 36.1910i −1.02667 1.18484i
\(934\) 0 0
\(935\) −0.615846 + 4.28330i −0.0201403 + 0.140079i
\(936\) 0 0
\(937\) 10.6321 23.2810i 0.347335 0.760557i −0.652661 0.757650i \(-0.726347\pi\)
0.999996 0.00290672i \(-0.000925239\pi\)
\(938\) 0 0
\(939\) 0.0505350 + 0.110656i 0.00164915 + 0.00361113i
\(940\) 0 0
\(941\) 18.3172 + 11.7717i 0.597123 + 0.383748i 0.804009 0.594617i \(-0.202696\pi\)
−0.206886 + 0.978365i \(0.566333\pi\)
\(942\) 0 0
\(943\) 8.95362 3.68721i 0.291570 0.120072i
\(944\) 0 0
\(945\) −17.5329 11.2677i −0.570347 0.366539i
\(946\) 0 0
\(947\) −1.73599 3.80128i −0.0564119 0.123525i 0.879327 0.476219i \(-0.157993\pi\)
−0.935739 + 0.352694i \(0.885266\pi\)
\(948\) 0 0
\(949\) −0.610798 + 1.33746i −0.0198273 + 0.0434158i
\(950\) 0 0
\(951\) −3.68112 + 25.6028i −0.119369 + 0.830226i
\(952\) 0 0
\(953\) 22.1931 + 25.6122i 0.718904 + 0.829659i 0.991175 0.132561i \(-0.0423201\pi\)
−0.272271 + 0.962221i \(0.587775\pi\)
\(954\) 0 0
\(955\) −10.6527 + 6.84607i −0.344713 + 0.221534i
\(956\) 0 0
\(957\) 5.96695 1.75205i 0.192884 0.0566358i
\(958\) 0 0
\(959\) −37.3545 + 43.1094i −1.20624 + 1.39207i
\(960\) 0 0
\(961\) 29.0326 + 8.52473i 0.936535 + 0.274991i
\(962\) 0 0
\(963\) 0.188379 + 1.31020i 0.00607043 + 0.0422207i
\(964\) 0 0
\(965\) −9.41815 −0.303181
\(966\) 0 0
\(967\) −15.4240 −0.496003 −0.248001 0.968760i \(-0.579774\pi\)
−0.248001 + 0.968760i \(0.579774\pi\)
\(968\) 0 0
\(969\) 1.03967 + 7.23110i 0.0333992 + 0.232296i
\(970\) 0 0
\(971\) −20.7349 6.08830i −0.665413 0.195383i −0.0684537 0.997654i \(-0.521807\pi\)
−0.596960 + 0.802271i \(0.703625\pi\)
\(972\) 0 0
\(973\) −44.2840 + 51.1065i −1.41968 + 1.63840i
\(974\) 0 0
\(975\) −5.18828 + 1.52342i −0.166158 + 0.0487884i
\(976\) 0 0
\(977\) 30.3593 19.5108i 0.971282 0.624205i 0.0441835 0.999023i \(-0.485931\pi\)
0.927098 + 0.374819i \(0.122295\pi\)
\(978\) 0 0
\(979\) −0.223876 0.258366i −0.00715509 0.00825742i
\(980\) 0 0
\(981\) 0.193529 1.34602i 0.00617891 0.0429753i
\(982\) 0 0
\(983\) 1.13501 2.48532i 0.0362011 0.0792694i −0.890668 0.454655i \(-0.849762\pi\)
0.926869 + 0.375386i \(0.122490\pi\)
\(984\) 0 0
\(985\) −6.09415 13.3443i −0.194176 0.425186i
\(986\) 0 0
\(987\) −36.5040 23.4597i −1.16193 0.746729i
\(988\) 0 0
\(989\) −34.4349 32.1922i −1.09497 1.02365i
\(990\) 0 0
\(991\) −6.34454 4.07739i −0.201541 0.129523i 0.435978 0.899958i \(-0.356403\pi\)
−0.637519 + 0.770435i \(0.720039\pi\)
\(992\) 0 0
\(993\) 10.4406 + 22.8618i 0.331323 + 0.725497i
\(994\) 0 0
\(995\) 9.92383 21.7302i 0.314606 0.688892i
\(996\) 0 0
\(997\) 7.67961 53.4128i 0.243216 1.69160i −0.392559 0.919727i \(-0.628410\pi\)
0.635775 0.771875i \(-0.280681\pi\)
\(998\) 0 0
\(999\) 5.93690 + 6.85154i 0.187835 + 0.216773i
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 460.2.m.a.301.3 yes 30
23.12 even 11 inner 460.2.m.a.81.3 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.m.a.81.3 30 23.12 even 11 inner
460.2.m.a.301.3 yes 30 1.1 even 1 trivial