Properties

Label 572.2.n.b.313.5
Level $572$
Weight $2$
Character 572.313
Analytic conductor $4.567$
Analytic rank $0$
Dimension $28$
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] = [572,2,Mod(53,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 313.5
Character \(\chi\) \(=\) 572.313
Dual form 572.2.n.b.53.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.178116 + 0.129409i) q^{3} +(1.35047 - 4.15632i) q^{5} +(-3.13912 + 2.28071i) q^{7} +(-0.912072 - 2.80707i) q^{9} +O(q^{10})\) \(q+(0.178116 + 0.129409i) q^{3} +(1.35047 - 4.15632i) q^{5} +(-3.13912 + 2.28071i) q^{7} +(-0.912072 - 2.80707i) q^{9} +(3.23144 + 0.746877i) q^{11} +(-0.309017 - 0.951057i) q^{13} +(0.778406 - 0.565545i) q^{15} +(0.502635 - 1.54695i) q^{17} +(-3.94112 - 2.86339i) q^{19} -0.854274 q^{21} -4.01571 q^{23} +(-11.4061 - 8.28703i) q^{25} +(0.404909 - 1.24618i) q^{27} +(4.63739 - 3.36926i) q^{29} +(0.353067 + 1.08663i) q^{31} +(0.478919 + 0.551209i) q^{33} +(5.24005 + 16.1272i) q^{35} +(2.50562 - 1.82044i) q^{37} +(0.0680344 - 0.209388i) q^{39} +(4.51654 + 3.28146i) q^{41} +2.48077 q^{43} -12.8988 q^{45} +(-8.04252 - 5.84323i) q^{47} +(2.48935 - 7.66143i) q^{49} +(0.289718 - 0.210492i) q^{51} +(2.96619 + 9.12900i) q^{53} +(7.46821 - 12.4222i) q^{55} +(-0.331430 - 1.02004i) q^{57} +(7.89282 - 5.73447i) q^{59} +(-1.38357 + 4.25820i) q^{61} +(9.26521 + 6.73157i) q^{63} -4.37021 q^{65} +2.89186 q^{67} +(-0.715265 - 0.519670i) q^{69} +(3.96928 - 12.2162i) q^{71} +(3.66478 - 2.66262i) q^{73} +(-0.959199 - 2.95211i) q^{75} +(-11.8473 + 5.02542i) q^{77} +(2.14428 + 6.59941i) q^{79} +(-6.93012 + 5.03503i) q^{81} +(0.949480 - 2.92220i) q^{83} +(-5.75083 - 4.17822i) q^{85} +1.26201 q^{87} +16.3403 q^{89} +(3.13912 + 2.28071i) q^{91} +(-0.0777326 + 0.239236i) q^{93} +(-17.2235 + 12.5136i) q^{95} +(1.34446 + 4.13784i) q^{97} +(-0.850767 - 9.75207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.178116 + 0.129409i 0.102836 + 0.0747144i 0.638015 0.770024i \(-0.279756\pi\)
−0.535179 + 0.844739i \(0.679756\pi\)
\(4\) 0 0
\(5\) 1.35047 4.15632i 0.603948 1.85876i 0.100082 0.994979i \(-0.468089\pi\)
0.503866 0.863782i \(-0.331911\pi\)
\(6\) 0 0
\(7\) −3.13912 + 2.28071i −1.18648 + 0.862026i −0.992887 0.119057i \(-0.962013\pi\)
−0.193589 + 0.981083i \(0.562013\pi\)
\(8\) 0 0
\(9\) −0.912072 2.80707i −0.304024 0.935690i
\(10\) 0 0
\(11\) 3.23144 + 0.746877i 0.974314 + 0.225192i
\(12\) 0 0
\(13\) −0.309017 0.951057i −0.0857059 0.263776i
\(14\) 0 0
\(15\) 0.778406 0.565545i 0.200984 0.146023i
\(16\) 0 0
\(17\) 0.502635 1.54695i 0.121907 0.375191i −0.871418 0.490541i \(-0.836799\pi\)
0.993325 + 0.115350i \(0.0367991\pi\)
\(18\) 0 0
\(19\) −3.94112 2.86339i −0.904156 0.656908i 0.0353742 0.999374i \(-0.488738\pi\)
−0.939530 + 0.342466i \(0.888738\pi\)
\(20\) 0 0
\(21\) −0.854274 −0.186418
\(22\) 0 0
\(23\) −4.01571 −0.837334 −0.418667 0.908140i \(-0.637503\pi\)
−0.418667 + 0.908140i \(0.637503\pi\)
\(24\) 0 0
\(25\) −11.4061 8.28703i −2.28122 1.65741i
\(26\) 0 0
\(27\) 0.404909 1.24618i 0.0779248 0.239828i
\(28\) 0 0
\(29\) 4.63739 3.36926i 0.861142 0.625656i −0.0670538 0.997749i \(-0.521360\pi\)
0.928195 + 0.372093i \(0.121360\pi\)
\(30\) 0 0
\(31\) 0.353067 + 1.08663i 0.0634127 + 0.195164i 0.977743 0.209804i \(-0.0672826\pi\)
−0.914331 + 0.404968i \(0.867283\pi\)
\(32\) 0 0
\(33\) 0.478919 + 0.551209i 0.0833691 + 0.0959531i
\(34\) 0 0
\(35\) 5.24005 + 16.1272i 0.885730 + 2.72600i
\(36\) 0 0
\(37\) 2.50562 1.82044i 0.411922 0.299278i −0.362458 0.932000i \(-0.618062\pi\)
0.774379 + 0.632722i \(0.218062\pi\)
\(38\) 0 0
\(39\) 0.0680344 0.209388i 0.0108942 0.0335290i
\(40\) 0 0
\(41\) 4.51654 + 3.28146i 0.705365 + 0.512478i 0.881675 0.471857i \(-0.156416\pi\)
−0.176310 + 0.984335i \(0.556416\pi\)
\(42\) 0 0
\(43\) 2.48077 0.378314 0.189157 0.981947i \(-0.439424\pi\)
0.189157 + 0.981947i \(0.439424\pi\)
\(44\) 0 0
\(45\) −12.8988 −1.92284
\(46\) 0 0
\(47\) −8.04252 5.84323i −1.17312 0.852323i −0.181743 0.983346i \(-0.558174\pi\)
−0.991379 + 0.131023i \(0.958174\pi\)
\(48\) 0 0
\(49\) 2.48935 7.66143i 0.355621 1.09449i
\(50\) 0 0
\(51\) 0.289718 0.210492i 0.0405686 0.0294748i
\(52\) 0 0
\(53\) 2.96619 + 9.12900i 0.407438 + 1.25396i 0.918843 + 0.394624i \(0.129125\pi\)
−0.511405 + 0.859340i \(0.670875\pi\)
\(54\) 0 0
\(55\) 7.46821 12.4222i 1.00701 1.67501i
\(56\) 0 0
\(57\) −0.331430 1.02004i −0.0438989 0.135107i
\(58\) 0 0
\(59\) 7.89282 5.73447i 1.02756 0.746564i 0.0597391 0.998214i \(-0.480973\pi\)
0.967818 + 0.251650i \(0.0809731\pi\)
\(60\) 0 0
\(61\) −1.38357 + 4.25820i −0.177148 + 0.545206i −0.999725 0.0234476i \(-0.992536\pi\)
0.822577 + 0.568654i \(0.192536\pi\)
\(62\) 0 0
\(63\) 9.26521 + 6.73157i 1.16731 + 0.848098i
\(64\) 0 0
\(65\) −4.37021 −0.542058
\(66\) 0 0
\(67\) 2.89186 0.353297 0.176649 0.984274i \(-0.443474\pi\)
0.176649 + 0.984274i \(0.443474\pi\)
\(68\) 0 0
\(69\) −0.715265 0.519670i −0.0861077 0.0625609i
\(70\) 0 0
\(71\) 3.96928 12.2162i 0.471067 1.44980i −0.380122 0.924936i \(-0.624118\pi\)
0.851189 0.524859i \(-0.175882\pi\)
\(72\) 0 0
\(73\) 3.66478 2.66262i 0.428930 0.311636i −0.352291 0.935890i \(-0.614597\pi\)
0.781221 + 0.624255i \(0.214597\pi\)
\(74\) 0 0
\(75\) −0.959199 2.95211i −0.110759 0.340881i
\(76\) 0 0
\(77\) −11.8473 + 5.02542i −1.35012 + 0.572699i
\(78\) 0 0
\(79\) 2.14428 + 6.59941i 0.241250 + 0.742492i 0.996231 + 0.0867444i \(0.0276464\pi\)
−0.754980 + 0.655747i \(0.772354\pi\)
\(80\) 0 0
\(81\) −6.93012 + 5.03503i −0.770013 + 0.559447i
\(82\) 0 0
\(83\) 0.949480 2.92220i 0.104219 0.320753i −0.885327 0.464968i \(-0.846066\pi\)
0.989546 + 0.144215i \(0.0460658\pi\)
\(84\) 0 0
\(85\) −5.75083 4.17822i −0.623765 0.453192i
\(86\) 0 0
\(87\) 1.26201 0.135302
\(88\) 0 0
\(89\) 16.3403 1.73206 0.866032 0.499988i \(-0.166662\pi\)
0.866032 + 0.499988i \(0.166662\pi\)
\(90\) 0 0
\(91\) 3.13912 + 2.28071i 0.329069 + 0.239083i
\(92\) 0 0
\(93\) −0.0777326 + 0.239236i −0.00806050 + 0.0248077i
\(94\) 0 0
\(95\) −17.2235 + 12.5136i −1.76710 + 1.28387i
\(96\) 0 0
\(97\) 1.34446 + 4.13784i 0.136510 + 0.420134i 0.995822 0.0913179i \(-0.0291079\pi\)
−0.859312 + 0.511452i \(0.829108\pi\)
\(98\) 0 0
\(99\) −0.850767 9.75207i −0.0855053 0.980120i
\(100\) 0 0
\(101\) 6.02948 + 18.5568i 0.599955 + 1.84647i 0.528326 + 0.849042i \(0.322820\pi\)
0.0716297 + 0.997431i \(0.477180\pi\)
\(102\) 0 0
\(103\) −2.89485 + 2.10323i −0.285238 + 0.207238i −0.721199 0.692728i \(-0.756409\pi\)
0.435961 + 0.899966i \(0.356409\pi\)
\(104\) 0 0
\(105\) −1.15367 + 3.55063i −0.112587 + 0.346506i
\(106\) 0 0
\(107\) 8.94959 + 6.50225i 0.865189 + 0.628597i 0.929292 0.369347i \(-0.120419\pi\)
−0.0641026 + 0.997943i \(0.520419\pi\)
\(108\) 0 0
\(109\) 1.70277 0.163096 0.0815480 0.996669i \(-0.474014\pi\)
0.0815480 + 0.996669i \(0.474014\pi\)
\(110\) 0 0
\(111\) 0.681874 0.0647206
\(112\) 0 0
\(113\) −8.33826 6.05810i −0.784397 0.569898i 0.121898 0.992543i \(-0.461102\pi\)
−0.906296 + 0.422645i \(0.861102\pi\)
\(114\) 0 0
\(115\) −5.42309 + 16.6906i −0.505706 + 1.55640i
\(116\) 0 0
\(117\) −2.38784 + 1.73486i −0.220756 + 0.160388i
\(118\) 0 0
\(119\) 1.95031 + 6.00244i 0.178785 + 0.550242i
\(120\) 0 0
\(121\) 9.88435 + 4.82697i 0.898577 + 0.438815i
\(122\) 0 0
\(123\) 0.379819 + 1.16896i 0.0342472 + 0.105402i
\(124\) 0 0
\(125\) −32.1692 + 23.3723i −2.87730 + 2.09048i
\(126\) 0 0
\(127\) −6.12478 + 18.8501i −0.543487 + 1.67268i 0.181074 + 0.983469i \(0.442042\pi\)
−0.724561 + 0.689211i \(0.757958\pi\)
\(128\) 0 0
\(129\) 0.441867 + 0.321035i 0.0389042 + 0.0282656i
\(130\) 0 0
\(131\) −7.46470 −0.652194 −0.326097 0.945336i \(-0.605734\pi\)
−0.326097 + 0.945336i \(0.605734\pi\)
\(132\) 0 0
\(133\) 18.9022 1.63903
\(134\) 0 0
\(135\) −4.63271 3.36586i −0.398720 0.289687i
\(136\) 0 0
\(137\) −1.89065 + 5.81883i −0.161529 + 0.497136i −0.998764 0.0497080i \(-0.984171\pi\)
0.837234 + 0.546844i \(0.184171\pi\)
\(138\) 0 0
\(139\) 15.8794 11.5371i 1.34688 0.978562i 0.347714 0.937601i \(-0.386958\pi\)
0.999161 0.0409615i \(-0.0130421\pi\)
\(140\) 0 0
\(141\) −0.676337 2.08155i −0.0569579 0.175298i
\(142\) 0 0
\(143\) −0.288246 3.30408i −0.0241044 0.276301i
\(144\) 0 0
\(145\) −7.74106 23.8245i −0.642860 1.97852i
\(146\) 0 0
\(147\) 1.43485 1.04248i 0.118345 0.0859825i
\(148\) 0 0
\(149\) 3.48572 10.7280i 0.285562 0.878868i −0.700668 0.713487i \(-0.747115\pi\)
0.986230 0.165381i \(-0.0528854\pi\)
\(150\) 0 0
\(151\) 7.89963 + 5.73942i 0.642863 + 0.467067i 0.860833 0.508888i \(-0.169943\pi\)
−0.217970 + 0.975956i \(0.569943\pi\)
\(152\) 0 0
\(153\) −4.80084 −0.388125
\(154\) 0 0
\(155\) 4.99318 0.401061
\(156\) 0 0
\(157\) 6.50663 + 4.72734i 0.519285 + 0.377283i 0.816335 0.577579i \(-0.196003\pi\)
−0.297049 + 0.954862i \(0.596003\pi\)
\(158\) 0 0
\(159\) −0.653049 + 2.00988i −0.0517901 + 0.159394i
\(160\) 0 0
\(161\) 12.6058 9.15866i 0.993477 0.721803i
\(162\) 0 0
\(163\) 2.74508 + 8.44847i 0.215011 + 0.661735i 0.999153 + 0.0411540i \(0.0131034\pi\)
−0.784142 + 0.620582i \(0.786897\pi\)
\(164\) 0 0
\(165\) 2.93776 1.24615i 0.228705 0.0970126i
\(166\) 0 0
\(167\) −2.98840 9.19734i −0.231249 0.711712i −0.997597 0.0692856i \(-0.977928\pi\)
0.766348 0.642426i \(-0.222072\pi\)
\(168\) 0 0
\(169\) −0.809017 + 0.587785i −0.0622321 + 0.0452143i
\(170\) 0 0
\(171\) −4.44316 + 13.6746i −0.339777 + 1.04573i
\(172\) 0 0
\(173\) −9.91019 7.20017i −0.753458 0.547419i 0.143439 0.989659i \(-0.454184\pi\)
−0.896897 + 0.442240i \(0.854184\pi\)
\(174\) 0 0
\(175\) 54.7055 4.13534
\(176\) 0 0
\(177\) 2.14793 0.161449
\(178\) 0 0
\(179\) −1.30205 0.945993i −0.0973196 0.0707068i 0.538061 0.842906i \(-0.319157\pi\)
−0.635381 + 0.772199i \(0.719157\pi\)
\(180\) 0 0
\(181\) 2.86293 8.81118i 0.212800 0.654930i −0.786503 0.617587i \(-0.788110\pi\)
0.999302 0.0373434i \(-0.0118895\pi\)
\(182\) 0 0
\(183\) −0.797487 + 0.579408i −0.0589520 + 0.0428311i
\(184\) 0 0
\(185\) −4.18256 12.8726i −0.307508 0.946412i
\(186\) 0 0
\(187\) 2.77962 4.62347i 0.203266 0.338102i
\(188\) 0 0
\(189\) 1.57111 + 4.83539i 0.114282 + 0.351723i
\(190\) 0 0
\(191\) −4.60854 + 3.34830i −0.333462 + 0.242275i −0.741898 0.670512i \(-0.766074\pi\)
0.408436 + 0.912787i \(0.366074\pi\)
\(192\) 0 0
\(193\) 4.07478 12.5409i 0.293309 0.902712i −0.690475 0.723356i \(-0.742599\pi\)
0.983784 0.179356i \(-0.0574014\pi\)
\(194\) 0 0
\(195\) −0.778406 0.565545i −0.0557428 0.0404995i
\(196\) 0 0
\(197\) −14.2046 −1.01204 −0.506018 0.862523i \(-0.668883\pi\)
−0.506018 + 0.862523i \(0.668883\pi\)
\(198\) 0 0
\(199\) −4.23611 −0.300290 −0.150145 0.988664i \(-0.547974\pi\)
−0.150145 + 0.988664i \(0.547974\pi\)
\(200\) 0 0
\(201\) 0.515088 + 0.374234i 0.0363315 + 0.0263964i
\(202\) 0 0
\(203\) −6.87304 + 21.1530i −0.482393 + 1.48465i
\(204\) 0 0
\(205\) 19.7382 14.3407i 1.37858 1.00160i
\(206\) 0 0
\(207\) 3.66262 + 11.2724i 0.254570 + 0.783485i
\(208\) 0 0
\(209\) −10.5969 12.1964i −0.733002 0.843643i
\(210\) 0 0
\(211\) −2.66961 8.21622i −0.183784 0.565628i 0.816142 0.577852i \(-0.196109\pi\)
−0.999925 + 0.0122241i \(0.996109\pi\)
\(212\) 0 0
\(213\) 2.28788 1.66224i 0.156763 0.113895i
\(214\) 0 0
\(215\) 3.35021 10.3109i 0.228482 0.703196i
\(216\) 0 0
\(217\) −3.58660 2.60582i −0.243474 0.176894i
\(218\) 0 0
\(219\) 0.997324 0.0673929
\(220\) 0 0
\(221\) −1.62656 −0.109414
\(222\) 0 0
\(223\) 10.5688 + 7.67870i 0.707741 + 0.514204i 0.882444 0.470417i \(-0.155897\pi\)
−0.174703 + 0.984621i \(0.555897\pi\)
\(224\) 0 0
\(225\) −12.8591 + 39.5761i −0.857271 + 2.63841i
\(226\) 0 0
\(227\) 4.73587 3.44081i 0.314331 0.228375i −0.419422 0.907791i \(-0.637767\pi\)
0.733752 + 0.679417i \(0.237767\pi\)
\(228\) 0 0
\(229\) −3.97376 12.2300i −0.262593 0.808179i −0.992238 0.124353i \(-0.960315\pi\)
0.729645 0.683826i \(-0.239685\pi\)
\(230\) 0 0
\(231\) −2.76053 0.638037i −0.181630 0.0419798i
\(232\) 0 0
\(233\) 8.56654 + 26.3651i 0.561213 + 1.72723i 0.678945 + 0.734189i \(0.262438\pi\)
−0.117732 + 0.993045i \(0.537562\pi\)
\(234\) 0 0
\(235\) −35.1475 + 25.5362i −2.29277 + 1.66580i
\(236\) 0 0
\(237\) −0.472093 + 1.45295i −0.0306657 + 0.0943795i
\(238\) 0 0
\(239\) −1.51759 1.10259i −0.0981648 0.0713209i 0.537620 0.843187i \(-0.319323\pi\)
−0.635785 + 0.771866i \(0.719323\pi\)
\(240\) 0 0
\(241\) −17.3205 −1.11571 −0.557856 0.829938i \(-0.688376\pi\)
−0.557856 + 0.829938i \(0.688376\pi\)
\(242\) 0 0
\(243\) −5.81689 −0.373153
\(244\) 0 0
\(245\) −28.4815 20.6931i −1.81962 1.32203i
\(246\) 0 0
\(247\) −1.50538 + 4.63307i −0.0957847 + 0.294795i
\(248\) 0 0
\(249\) 0.547277 0.397620i 0.0346823 0.0251982i
\(250\) 0 0
\(251\) −7.56947 23.2964i −0.477781 1.47046i −0.842170 0.539212i \(-0.818722\pi\)
0.364389 0.931247i \(-0.381278\pi\)
\(252\) 0 0
\(253\) −12.9765 2.99924i −0.815826 0.188561i
\(254\) 0 0
\(255\) −0.483617 1.48842i −0.0302853 0.0932085i
\(256\) 0 0
\(257\) 21.3955 15.5448i 1.33462 0.969655i 0.334993 0.942221i \(-0.391266\pi\)
0.999624 0.0274347i \(-0.00873383\pi\)
\(258\) 0 0
\(259\) −3.71356 + 11.4292i −0.230749 + 0.710174i
\(260\) 0 0
\(261\) −13.6874 9.94447i −0.847228 0.615547i
\(262\) 0 0
\(263\) −15.5302 −0.957634 −0.478817 0.877915i \(-0.658934\pi\)
−0.478817 + 0.877915i \(0.658934\pi\)
\(264\) 0 0
\(265\) 41.9487 2.57689
\(266\) 0 0
\(267\) 2.91047 + 2.11458i 0.178118 + 0.129410i
\(268\) 0 0
\(269\) −4.16145 + 12.8076i −0.253728 + 0.780895i 0.740349 + 0.672222i \(0.234660\pi\)
−0.994078 + 0.108673i \(0.965340\pi\)
\(270\) 0 0
\(271\) 1.68125 1.22150i 0.102129 0.0742009i −0.535549 0.844504i \(-0.679895\pi\)
0.637678 + 0.770303i \(0.279895\pi\)
\(272\) 0 0
\(273\) 0.263985 + 0.812463i 0.0159771 + 0.0491725i
\(274\) 0 0
\(275\) −30.6687 35.2980i −1.84939 2.12855i
\(276\) 0 0
\(277\) 0.325836 + 1.00282i 0.0195776 + 0.0602536i 0.960368 0.278735i \(-0.0899151\pi\)
−0.940790 + 0.338989i \(0.889915\pi\)
\(278\) 0 0
\(279\) 2.72822 1.98217i 0.163334 0.118669i
\(280\) 0 0
\(281\) 0.631654 1.94403i 0.0376813 0.115971i −0.930447 0.366428i \(-0.880581\pi\)
0.968128 + 0.250457i \(0.0805807\pi\)
\(282\) 0 0
\(283\) −17.3319 12.5923i −1.03027 0.748536i −0.0619088 0.998082i \(-0.519719\pi\)
−0.968363 + 0.249545i \(0.919719\pi\)
\(284\) 0 0
\(285\) −4.68718 −0.277644
\(286\) 0 0
\(287\) −21.6620 −1.27867
\(288\) 0 0
\(289\) 11.6129 + 8.43724i 0.683110 + 0.496308i
\(290\) 0 0
\(291\) −0.296003 + 0.911003i −0.0173520 + 0.0534040i
\(292\) 0 0
\(293\) 17.7679 12.9091i 1.03801 0.754159i 0.0681149 0.997677i \(-0.478302\pi\)
0.969896 + 0.243518i \(0.0783016\pi\)
\(294\) 0 0
\(295\) −13.1753 40.5493i −0.767093 2.36087i
\(296\) 0 0
\(297\) 2.23918 3.72454i 0.129930 0.216120i
\(298\) 0 0
\(299\) 1.24092 + 3.81917i 0.0717644 + 0.220868i
\(300\) 0 0
\(301\) −7.78745 + 5.65792i −0.448861 + 0.326117i
\(302\) 0 0
\(303\) −1.32747 + 4.08555i −0.0762614 + 0.234709i
\(304\) 0 0
\(305\) 15.8299 + 11.5011i 0.906420 + 0.658553i
\(306\) 0 0
\(307\) 16.9551 0.967681 0.483841 0.875156i \(-0.339241\pi\)
0.483841 + 0.875156i \(0.339241\pi\)
\(308\) 0 0
\(309\) −0.787799 −0.0448163
\(310\) 0 0
\(311\) 14.0619 + 10.2166i 0.797380 + 0.579330i 0.910144 0.414292i \(-0.135971\pi\)
−0.112765 + 0.993622i \(0.535971\pi\)
\(312\) 0 0
\(313\) 4.64033 14.2815i 0.262287 0.807237i −0.730019 0.683427i \(-0.760489\pi\)
0.992306 0.123810i \(-0.0395113\pi\)
\(314\) 0 0
\(315\) 40.4909 29.4184i 2.28140 1.65754i
\(316\) 0 0
\(317\) −2.20255 6.77874i −0.123707 0.380732i 0.869956 0.493129i \(-0.164147\pi\)
−0.993663 + 0.112397i \(0.964147\pi\)
\(318\) 0 0
\(319\) 17.5018 7.42399i 0.979915 0.415664i
\(320\) 0 0
\(321\) 0.752617 + 2.31632i 0.0420070 + 0.129284i
\(322\) 0 0
\(323\) −6.41048 + 4.65749i −0.356689 + 0.259150i
\(324\) 0 0
\(325\) −4.35675 + 13.4087i −0.241669 + 0.743780i
\(326\) 0 0
\(327\) 0.303292 + 0.220354i 0.0167721 + 0.0121856i
\(328\) 0 0
\(329\) 38.5732 2.12661
\(330\) 0 0
\(331\) 27.8163 1.52892 0.764462 0.644669i \(-0.223005\pi\)
0.764462 + 0.644669i \(0.223005\pi\)
\(332\) 0 0
\(333\) −7.39541 5.37308i −0.405266 0.294443i
\(334\) 0 0
\(335\) 3.90537 12.0195i 0.213373 0.656695i
\(336\) 0 0
\(337\) 21.2896 15.4678i 1.15972 0.842586i 0.169977 0.985448i \(-0.445631\pi\)
0.989743 + 0.142862i \(0.0456306\pi\)
\(338\) 0 0
\(339\) −0.701208 2.15809i −0.0380844 0.117212i
\(340\) 0 0
\(341\) 0.329335 + 3.77507i 0.0178345 + 0.204431i
\(342\) 0 0
\(343\) 1.26583 + 3.89583i 0.0683485 + 0.210355i
\(344\) 0 0
\(345\) −3.12586 + 2.27107i −0.168290 + 0.122270i
\(346\) 0 0
\(347\) −4.14525 + 12.7578i −0.222529 + 0.684873i 0.776004 + 0.630727i \(0.217243\pi\)
−0.998533 + 0.0541453i \(0.982757\pi\)
\(348\) 0 0
\(349\) −27.1416 19.7195i −1.45286 1.05556i −0.985154 0.171676i \(-0.945082\pi\)
−0.467702 0.883886i \(-0.654918\pi\)
\(350\) 0 0
\(351\) −1.31031 −0.0699393
\(352\) 0 0
\(353\) 24.2306 1.28966 0.644832 0.764324i \(-0.276927\pi\)
0.644832 + 0.764324i \(0.276927\pi\)
\(354\) 0 0
\(355\) −45.4140 32.9952i −2.41032 1.75120i
\(356\) 0 0
\(357\) −0.429388 + 1.32152i −0.0227256 + 0.0699423i
\(358\) 0 0
\(359\) −17.8799 + 12.9905i −0.943664 + 0.685612i −0.949300 0.314372i \(-0.898206\pi\)
0.00563601 + 0.999984i \(0.498206\pi\)
\(360\) 0 0
\(361\) 1.46211 + 4.49991i 0.0769531 + 0.236837i
\(362\) 0 0
\(363\) 1.13591 + 2.13889i 0.0596199 + 0.112263i
\(364\) 0 0
\(365\) −6.11751 18.8277i −0.320205 0.985489i
\(366\) 0 0
\(367\) 19.5328 14.1914i 1.01960 0.740784i 0.0534009 0.998573i \(-0.482994\pi\)
0.966201 + 0.257789i \(0.0829939\pi\)
\(368\) 0 0
\(369\) 5.09187 15.6712i 0.265072 0.815808i
\(370\) 0 0
\(371\) −30.1318 21.8920i −1.56436 1.13658i
\(372\) 0 0
\(373\) −36.4461 −1.88711 −0.943555 0.331216i \(-0.892541\pi\)
−0.943555 + 0.331216i \(0.892541\pi\)
\(374\) 0 0
\(375\) −8.75446 −0.452079
\(376\) 0 0
\(377\) −4.63739 3.36926i −0.238838 0.173526i
\(378\) 0 0
\(379\) 3.32922 10.2463i 0.171011 0.526317i −0.828418 0.560110i \(-0.810759\pi\)
0.999429 + 0.0337933i \(0.0107588\pi\)
\(380\) 0 0
\(381\) −3.53031 + 2.56492i −0.180863 + 0.131405i
\(382\) 0 0
\(383\) 2.84080 + 8.74308i 0.145158 + 0.446750i 0.997031 0.0769976i \(-0.0245334\pi\)
−0.851873 + 0.523748i \(0.824533\pi\)
\(384\) 0 0
\(385\) 4.88783 + 56.0277i 0.249107 + 2.85544i
\(386\) 0 0
\(387\) −2.26265 6.96371i −0.115017 0.353985i
\(388\) 0 0
\(389\) −9.29887 + 6.75602i −0.471471 + 0.342544i −0.798014 0.602638i \(-0.794116\pi\)
0.326543 + 0.945182i \(0.394116\pi\)
\(390\) 0 0
\(391\) −2.01844 + 6.21212i −0.102077 + 0.314160i
\(392\) 0 0
\(393\) −1.32959 0.966001i −0.0670687 0.0487283i
\(394\) 0 0
\(395\) 30.3250 1.52582
\(396\) 0 0
\(397\) 15.3434 0.770062 0.385031 0.922904i \(-0.374191\pi\)
0.385031 + 0.922904i \(0.374191\pi\)
\(398\) 0 0
\(399\) 3.36680 + 2.44612i 0.168551 + 0.122459i
\(400\) 0 0
\(401\) −2.17675 + 6.69936i −0.108702 + 0.334550i −0.990581 0.136925i \(-0.956278\pi\)
0.881880 + 0.471475i \(0.156278\pi\)
\(402\) 0 0
\(403\) 0.924341 0.671573i 0.0460447 0.0334534i
\(404\) 0 0
\(405\) 11.5683 + 35.6034i 0.574831 + 1.76915i
\(406\) 0 0
\(407\) 9.45640 4.01124i 0.468736 0.198830i
\(408\) 0 0
\(409\) 0.990253 + 3.04769i 0.0489649 + 0.150698i 0.972549 0.232696i \(-0.0747549\pi\)
−0.923585 + 0.383395i \(0.874755\pi\)
\(410\) 0 0
\(411\) −1.08977 + 0.791762i −0.0537542 + 0.0390547i
\(412\) 0 0
\(413\) −11.6979 + 36.0024i −0.575615 + 1.77156i
\(414\) 0 0
\(415\) −10.8633 7.89268i −0.533260 0.387436i
\(416\) 0 0
\(417\) 4.32139 0.211619
\(418\) 0 0
\(419\) −18.9448 −0.925514 −0.462757 0.886485i \(-0.653140\pi\)
−0.462757 + 0.886485i \(0.653140\pi\)
\(420\) 0 0
\(421\) 15.8451 + 11.5121i 0.772241 + 0.561066i 0.902640 0.430395i \(-0.141626\pi\)
−0.130399 + 0.991462i \(0.541626\pi\)
\(422\) 0 0
\(423\) −9.06700 + 27.9054i −0.440853 + 1.35681i
\(424\) 0 0
\(425\) −18.5528 + 13.4794i −0.899941 + 0.653845i
\(426\) 0 0
\(427\) −5.36849 16.5225i −0.259800 0.799581i
\(428\) 0 0
\(429\) 0.376236 0.625812i 0.0181649 0.0302145i
\(430\) 0 0
\(431\) 10.0198 + 30.8376i 0.482634 + 1.48540i 0.835378 + 0.549676i \(0.185249\pi\)
−0.352743 + 0.935720i \(0.614751\pi\)
\(432\) 0 0
\(433\) −21.7793 + 15.8236i −1.04665 + 0.760433i −0.971572 0.236745i \(-0.923920\pi\)
−0.0750747 + 0.997178i \(0.523920\pi\)
\(434\) 0 0
\(435\) 1.70430 5.24531i 0.0817151 0.251493i
\(436\) 0 0
\(437\) 15.8264 + 11.4986i 0.757080 + 0.550051i
\(438\) 0 0
\(439\) −39.5595 −1.88807 −0.944037 0.329841i \(-0.893005\pi\)
−0.944037 + 0.329841i \(0.893005\pi\)
\(440\) 0 0
\(441\) −23.7766 −1.13222
\(442\) 0 0
\(443\) 6.29026 + 4.57014i 0.298859 + 0.217134i 0.727102 0.686530i \(-0.240867\pi\)
−0.428242 + 0.903664i \(0.640867\pi\)
\(444\) 0 0
\(445\) 22.0670 67.9153i 1.04608 3.21949i
\(446\) 0 0
\(447\) 2.00916 1.45974i 0.0950301 0.0690434i
\(448\) 0 0
\(449\) −1.86611 5.74328i −0.0880670 0.271042i 0.897318 0.441385i \(-0.145513\pi\)
−0.985385 + 0.170343i \(0.945513\pi\)
\(450\) 0 0
\(451\) 12.1441 + 13.9771i 0.571841 + 0.658157i
\(452\) 0 0
\(453\) 0.664321 + 2.04457i 0.0312125 + 0.0960623i
\(454\) 0 0
\(455\) 13.7186 9.96716i 0.643139 0.467268i
\(456\) 0 0
\(457\) −11.5474 + 35.5391i −0.540163 + 1.66245i 0.192059 + 0.981383i \(0.438483\pi\)
−0.732222 + 0.681066i \(0.761517\pi\)
\(458\) 0 0
\(459\) −1.72426 1.25275i −0.0804816 0.0584733i
\(460\) 0 0
\(461\) 3.25906 0.151789 0.0758947 0.997116i \(-0.475819\pi\)
0.0758947 + 0.997116i \(0.475819\pi\)
\(462\) 0 0
\(463\) −21.7618 −1.01136 −0.505678 0.862722i \(-0.668758\pi\)
−0.505678 + 0.862722i \(0.668758\pi\)
\(464\) 0 0
\(465\) 0.889367 + 0.646163i 0.0412434 + 0.0299651i
\(466\) 0 0
\(467\) −3.96156 + 12.1924i −0.183319 + 0.564198i −0.999915 0.0130112i \(-0.995858\pi\)
0.816596 + 0.577209i \(0.195858\pi\)
\(468\) 0 0
\(469\) −9.07791 + 6.59549i −0.419179 + 0.304551i
\(470\) 0 0
\(471\) 0.547176 + 1.68404i 0.0252125 + 0.0775962i
\(472\) 0 0
\(473\) 8.01646 + 1.85283i 0.368597 + 0.0851933i
\(474\) 0 0
\(475\) 21.2239 + 65.3204i 0.973819 + 2.99711i
\(476\) 0 0
\(477\) 22.9203 16.6526i 1.04945 0.762471i
\(478\) 0 0
\(479\) 11.0246 33.9303i 0.503728 1.55032i −0.299169 0.954200i \(-0.596710\pi\)
0.802898 0.596117i \(-0.203290\pi\)
\(480\) 0 0
\(481\) −2.50562 1.82044i −0.114246 0.0830049i
\(482\) 0 0
\(483\) 3.43052 0.156094
\(484\) 0 0
\(485\) 19.0138 0.863373
\(486\) 0 0
\(487\) −30.1986 21.9405i −1.36843 0.994220i −0.997858 0.0654154i \(-0.979163\pi\)
−0.370569 0.928805i \(-0.620837\pi\)
\(488\) 0 0
\(489\) −0.604367 + 1.86005i −0.0273304 + 0.0841144i
\(490\) 0 0
\(491\) 1.74156 1.26532i 0.0785956 0.0571030i −0.547794 0.836614i \(-0.684532\pi\)
0.626389 + 0.779510i \(0.284532\pi\)
\(492\) 0 0
\(493\) −2.88117 8.86733i −0.129761 0.399364i
\(494\) 0 0
\(495\) −41.6816 9.63381i −1.87345 0.433008i
\(496\) 0 0
\(497\) 15.4015 + 47.4009i 0.690851 + 2.12622i
\(498\) 0 0
\(499\) 12.6994 9.22666i 0.568504 0.413042i −0.266058 0.963957i \(-0.585721\pi\)
0.834561 + 0.550915i \(0.185721\pi\)
\(500\) 0 0
\(501\) 0.657938 2.02492i 0.0293945 0.0904669i
\(502\) 0 0
\(503\) 25.4031 + 18.4564i 1.13267 + 0.822930i 0.986081 0.166268i \(-0.0531717\pi\)
0.146585 + 0.989198i \(0.453172\pi\)
\(504\) 0 0
\(505\) 85.2707 3.79449
\(506\) 0 0
\(507\) −0.220164 −0.00977783
\(508\) 0 0
\(509\) −3.17106 2.30391i −0.140555 0.102119i 0.515286 0.857018i \(-0.327686\pi\)
−0.655841 + 0.754899i \(0.727686\pi\)
\(510\) 0 0
\(511\) −5.43154 + 16.7165i −0.240277 + 0.739497i
\(512\) 0 0
\(513\) −5.16410 + 3.75194i −0.228001 + 0.165652i
\(514\) 0 0
\(515\) 4.83230 + 14.8723i 0.212936 + 0.655351i
\(516\) 0 0
\(517\) −21.6247 24.8888i −0.951054 1.09461i
\(518\) 0 0
\(519\) −0.833399 2.56494i −0.0365822 0.112588i
\(520\) 0 0
\(521\) −25.1394 + 18.2648i −1.10137 + 0.800196i −0.981284 0.192567i \(-0.938319\pi\)
−0.120091 + 0.992763i \(0.538319\pi\)
\(522\) 0 0
\(523\) 4.87093 14.9912i 0.212991 0.655519i −0.786299 0.617846i \(-0.788006\pi\)
0.999290 0.0376729i \(-0.0119945\pi\)
\(524\) 0 0
\(525\) 9.74394 + 7.07939i 0.425261 + 0.308970i
\(526\) 0 0
\(527\) 1.85843 0.0809543
\(528\) 0 0
\(529\) −6.87406 −0.298872
\(530\) 0 0
\(531\) −23.2959 16.9254i −1.01095 0.734502i
\(532\) 0 0
\(533\) 1.72516 5.30951i 0.0747252 0.229980i
\(534\) 0 0
\(535\) 39.1116 28.4162i 1.69094 1.22854i
\(536\) 0 0
\(537\) −0.109496 0.336994i −0.00472510 0.0145424i
\(538\) 0 0
\(539\) 13.7663 22.8982i 0.592957 0.986295i
\(540\) 0 0
\(541\) −5.05933 15.5710i −0.217518 0.669450i −0.998965 0.0454794i \(-0.985518\pi\)
0.781448 0.623971i \(-0.214482\pi\)
\(542\) 0 0
\(543\) 1.65018 1.19893i 0.0708161 0.0514509i
\(544\) 0 0
\(545\) 2.29954 7.07726i 0.0985015 0.303156i
\(546\) 0 0
\(547\) 24.0023 + 17.4387i 1.02627 + 0.745626i 0.967558 0.252649i \(-0.0813019\pi\)
0.0587081 + 0.998275i \(0.481302\pi\)
\(548\) 0 0
\(549\) 13.2150 0.564002
\(550\) 0 0
\(551\) −27.9240 −1.18960
\(552\) 0 0
\(553\) −21.7825 15.8259i −0.926285 0.672985i
\(554\) 0 0
\(555\) 0.920850 2.83408i 0.0390879 0.120300i
\(556\) 0 0
\(557\) −29.6170 + 21.5180i −1.25491 + 0.911747i −0.998496 0.0548193i \(-0.982542\pi\)
−0.256416 + 0.966567i \(0.582542\pi\)
\(558\) 0 0
\(559\) −0.766601 2.35936i −0.0324238 0.0997901i
\(560\) 0 0
\(561\) 1.09342 0.463808i 0.0461640 0.0195820i
\(562\) 0 0
\(563\) 11.6585 + 35.8810i 0.491345 + 1.51221i 0.822576 + 0.568655i \(0.192536\pi\)
−0.331231 + 0.943550i \(0.607464\pi\)
\(564\) 0 0
\(565\) −36.4399 + 26.4752i −1.53304 + 1.11382i
\(566\) 0 0
\(567\) 10.2711 31.6111i 0.431345 1.32754i
\(568\) 0 0
\(569\) 21.2091 + 15.4093i 0.889133 + 0.645993i 0.935652 0.352924i \(-0.114813\pi\)
−0.0465186 + 0.998917i \(0.514813\pi\)
\(570\) 0 0
\(571\) −35.1634 −1.47154 −0.735771 0.677230i \(-0.763180\pi\)
−0.735771 + 0.677230i \(0.763180\pi\)
\(572\) 0 0
\(573\) −1.25416 −0.0523932
\(574\) 0 0
\(575\) 45.8037 + 33.2783i 1.91014 + 1.38780i
\(576\) 0 0
\(577\) 0.468294 1.44126i 0.0194953 0.0600004i −0.940836 0.338863i \(-0.889958\pi\)
0.960331 + 0.278863i \(0.0899575\pi\)
\(578\) 0 0
\(579\) 2.34869 1.70642i 0.0976082 0.0709165i
\(580\) 0 0
\(581\) 3.68414 + 11.3386i 0.152844 + 0.470405i
\(582\) 0 0
\(583\) 2.76682 + 31.7151i 0.114590 + 1.31351i
\(584\) 0 0
\(585\) 3.98595 + 12.2675i 0.164799 + 0.507198i
\(586\) 0 0
\(587\) 4.68673 3.40511i 0.193442 0.140544i −0.486849 0.873486i \(-0.661854\pi\)
0.680290 + 0.732943i \(0.261854\pi\)
\(588\) 0 0
\(589\) 1.71996 5.29350i 0.0708699 0.218115i
\(590\) 0 0
\(591\) −2.53007 1.83821i −0.104073 0.0756137i
\(592\) 0 0
\(593\) 10.2331 0.420224 0.210112 0.977677i \(-0.432617\pi\)
0.210112 + 0.977677i \(0.432617\pi\)
\(594\) 0 0
\(595\) 27.5819 1.13075
\(596\) 0 0
\(597\) −0.754521 0.548192i −0.0308805 0.0224360i
\(598\) 0 0
\(599\) 8.36804 25.7542i 0.341909 1.05229i −0.621309 0.783566i \(-0.713399\pi\)
0.963218 0.268722i \(-0.0866012\pi\)
\(600\) 0 0
\(601\) −14.3261 + 10.4085i −0.584374 + 0.424572i −0.840298 0.542124i \(-0.817620\pi\)
0.255924 + 0.966697i \(0.417620\pi\)
\(602\) 0 0
\(603\) −2.63759 8.11766i −0.107411 0.330577i
\(604\) 0 0
\(605\) 33.4109 34.5638i 1.35835 1.40522i
\(606\) 0 0
\(607\) −8.03558 24.7310i −0.326154 1.00380i −0.970917 0.239417i \(-0.923044\pi\)
0.644763 0.764383i \(-0.276956\pi\)
\(608\) 0 0
\(609\) −3.96160 + 2.87827i −0.160532 + 0.116633i
\(610\) 0 0
\(611\) −3.07197 + 9.45455i −0.124279 + 0.382490i
\(612\) 0 0
\(613\) −14.9294 10.8468i −0.602992 0.438099i 0.243948 0.969788i \(-0.421557\pi\)
−0.846939 + 0.531689i \(0.821557\pi\)
\(614\) 0 0
\(615\) 5.37152 0.216600
\(616\) 0 0
\(617\) 19.7587 0.795454 0.397727 0.917504i \(-0.369799\pi\)
0.397727 + 0.917504i \(0.369799\pi\)
\(618\) 0 0
\(619\) −21.4843 15.6093i −0.863527 0.627389i 0.0653152 0.997865i \(-0.479195\pi\)
−0.928842 + 0.370476i \(0.879195\pi\)
\(620\) 0 0
\(621\) −1.62600 + 5.00431i −0.0652490 + 0.200816i
\(622\) 0 0
\(623\) −51.2941 + 37.2673i −2.05505 + 1.49308i
\(624\) 0 0
\(625\) 31.9155 + 98.2257i 1.27662 + 3.92903i
\(626\) 0 0
\(627\) −0.309152 3.54372i −0.0123464 0.141522i
\(628\) 0 0
\(629\) −1.55672 4.79109i −0.0620705 0.191033i
\(630\) 0 0
\(631\) 1.39803 1.01573i 0.0556547 0.0404355i −0.559610 0.828756i \(-0.689049\pi\)
0.615265 + 0.788321i \(0.289049\pi\)
\(632\) 0 0
\(633\) 0.587752 1.80892i 0.0233611 0.0718979i
\(634\) 0 0
\(635\) 70.0758 + 50.9131i 2.78087 + 2.02042i
\(636\) 0 0
\(637\) −8.05571 −0.319179
\(638\) 0 0
\(639\) −37.9120 −1.49977
\(640\) 0 0
\(641\) −22.8151 16.5762i −0.901144 0.654719i 0.0376157 0.999292i \(-0.488024\pi\)
−0.938760 + 0.344573i \(0.888024\pi\)
\(642\) 0 0
\(643\) −7.96651 + 24.5184i −0.314168 + 0.966911i 0.661927 + 0.749568i \(0.269739\pi\)
−0.976095 + 0.217342i \(0.930261\pi\)
\(644\) 0 0
\(645\) 1.93105 1.40299i 0.0760350 0.0552427i
\(646\) 0 0
\(647\) −1.43222 4.40791i −0.0563063 0.173293i 0.918948 0.394378i \(-0.129040\pi\)
−0.975254 + 0.221085i \(0.929040\pi\)
\(648\) 0 0
\(649\) 29.7881 12.6356i 1.16928 0.495991i
\(650\) 0 0
\(651\) −0.301616 0.928278i −0.0118213 0.0363821i
\(652\) 0 0
\(653\) 0.880712 0.639875i 0.0344649 0.0250402i −0.570419 0.821354i \(-0.693219\pi\)
0.604884 + 0.796313i \(0.293219\pi\)
\(654\) 0 0
\(655\) −10.0808 + 31.0257i −0.393891 + 1.21227i
\(656\) 0 0
\(657\) −10.8167 7.85878i −0.421999 0.306600i
\(658\) 0 0
\(659\) −31.1662 −1.21406 −0.607031 0.794678i \(-0.707640\pi\)
−0.607031 + 0.794678i \(0.707640\pi\)
\(660\) 0 0
\(661\) 38.8239 1.51007 0.755037 0.655683i \(-0.227619\pi\)
0.755037 + 0.655683i \(0.227619\pi\)
\(662\) 0 0
\(663\) −0.289718 0.210492i −0.0112517 0.00817484i
\(664\) 0 0
\(665\) 25.5269 78.5636i 0.989890 3.04657i
\(666\) 0 0
\(667\) −18.6224 + 13.5300i −0.721063 + 0.523883i
\(668\) 0 0
\(669\) 0.888787 + 2.73541i 0.0343625 + 0.105757i
\(670\) 0 0
\(671\) −7.65128 + 12.7267i −0.295374 + 0.491310i
\(672\) 0 0
\(673\) −2.99761 9.22568i −0.115549 0.355624i 0.876512 0.481380i \(-0.159864\pi\)
−0.992061 + 0.125756i \(0.959864\pi\)
\(674\) 0 0
\(675\) −14.9456 + 10.8586i −0.575255 + 0.417948i
\(676\) 0 0
\(677\) −8.26447 + 25.4354i −0.317629 + 0.977562i 0.657029 + 0.753865i \(0.271813\pi\)
−0.974659 + 0.223697i \(0.928187\pi\)
\(678\) 0 0
\(679\) −13.6576 9.92285i −0.524132 0.380804i
\(680\) 0 0
\(681\) 1.28881 0.0493872
\(682\) 0 0
\(683\) −11.4814 −0.439324 −0.219662 0.975576i \(-0.570495\pi\)
−0.219662 + 0.975576i \(0.570495\pi\)
\(684\) 0 0
\(685\) 21.6316 + 15.7163i 0.826502 + 0.600489i
\(686\) 0 0
\(687\) 0.874879 2.69260i 0.0333787 0.102729i
\(688\) 0 0
\(689\) 7.76559 5.64203i 0.295845 0.214944i
\(690\) 0 0
\(691\) 9.96760 + 30.6771i 0.379185 + 1.16701i 0.940611 + 0.339486i \(0.110253\pi\)
−0.561426 + 0.827527i \(0.689747\pi\)
\(692\) 0 0
\(693\) 24.9123 + 28.6726i 0.946339 + 1.08918i
\(694\) 0 0
\(695\) −26.5071 81.5804i −1.00547 3.09452i
\(696\) 0 0
\(697\) 7.34643 5.33749i 0.278266 0.202172i
\(698\) 0 0
\(699\) −1.88604 + 5.80465i −0.0713367 + 0.219552i
\(700\) 0 0
\(701\) 13.6700 + 9.93181i 0.516307 + 0.375119i 0.815211 0.579164i \(-0.196621\pi\)
−0.298904 + 0.954283i \(0.596621\pi\)
\(702\) 0 0
\(703\) −15.0876 −0.569040
\(704\) 0 0
\(705\) −9.56496 −0.360237
\(706\) 0 0
\(707\) −61.2499 44.5007i −2.30354 1.67362i
\(708\) 0 0
\(709\) 12.5136 38.5130i 0.469959 1.44638i −0.382679 0.923881i \(-0.624998\pi\)
0.852638 0.522503i \(-0.175002\pi\)
\(710\) 0 0
\(711\) 16.5693 12.0383i 0.621396 0.451471i
\(712\) 0 0
\(713\) −1.41781 4.36359i −0.0530976 0.163418i
\(714\) 0 0
\(715\) −14.1220 3.26401i −0.528135 0.122067i
\(716\) 0 0
\(717\) −0.127622 0.392780i −0.00476613 0.0146687i
\(718\) 0 0
\(719\) 3.00851 2.18581i 0.112198 0.0815170i −0.530271 0.847828i \(-0.677910\pi\)
0.642470 + 0.766311i \(0.277910\pi\)
\(720\) 0 0
\(721\) 4.29044 13.2046i 0.159784 0.491766i
\(722\) 0 0
\(723\) −3.08507 2.24143i −0.114735 0.0833598i
\(724\) 0 0
\(725\) −80.8157 −3.00142
\(726\) 0 0
\(727\) 6.51503 0.241629 0.120814 0.992675i \(-0.461449\pi\)
0.120814 + 0.992675i \(0.461449\pi\)
\(728\) 0 0
\(729\) 19.7543 + 14.3523i 0.731640 + 0.531567i
\(730\) 0 0
\(731\) 1.24692 3.83764i 0.0461192 0.141940i
\(732\) 0 0
\(733\) −17.1364 + 12.4503i −0.632946 + 0.459862i −0.857419 0.514618i \(-0.827934\pi\)
0.224474 + 0.974480i \(0.427934\pi\)
\(734\) 0 0
\(735\) −2.39516 7.37155i −0.0883468 0.271904i
\(736\) 0 0
\(737\) 9.34486 + 2.15986i 0.344223 + 0.0795596i
\(738\) 0 0
\(739\) −1.07916 3.32131i −0.0396975 0.122176i 0.929244 0.369467i \(-0.120460\pi\)
−0.968941 + 0.247291i \(0.920460\pi\)
\(740\) 0 0
\(741\) −0.867694 + 0.630417i −0.0318755 + 0.0231589i
\(742\) 0 0
\(743\) −1.53661 + 4.72921i −0.0563729 + 0.173498i −0.975278 0.220980i \(-0.929075\pi\)
0.918905 + 0.394478i \(0.129075\pi\)
\(744\) 0 0
\(745\) −39.8814 28.9755i −1.46114 1.06158i
\(746\) 0 0
\(747\) −9.06881 −0.331810
\(748\) 0 0
\(749\) −42.9236 −1.56839
\(750\) 0 0
\(751\) 35.5266 + 25.8116i 1.29638 + 0.941878i 0.999913 0.0131643i \(-0.00419043\pi\)
0.296470 + 0.955042i \(0.404190\pi\)
\(752\) 0 0
\(753\) 1.66653 5.12904i 0.0607316 0.186913i
\(754\) 0 0
\(755\) 34.5230 25.0825i 1.25642 0.912844i
\(756\) 0 0
\(757\) 5.96015 + 18.3435i 0.216625 + 0.666704i 0.999034 + 0.0439393i \(0.0139908\pi\)
−0.782409 + 0.622765i \(0.786009\pi\)
\(758\) 0 0
\(759\) −1.92320 2.21350i −0.0698078 0.0803448i
\(760\) 0 0
\(761\) −6.79630 20.9169i −0.246366 0.758236i −0.995409 0.0957147i \(-0.969486\pi\)
0.749043 0.662521i \(-0.230514\pi\)
\(762\) 0 0
\(763\) −5.34521 + 3.88352i −0.193509 + 0.140593i
\(764\) 0 0
\(765\) −6.48339 + 19.9538i −0.234407 + 0.721432i
\(766\) 0 0
\(767\) −7.89282 5.73447i −0.284993 0.207060i
\(768\) 0 0
\(769\) 25.9359 0.935273 0.467637 0.883921i \(-0.345106\pi\)
0.467637 + 0.883921i \(0.345106\pi\)
\(770\) 0 0
\(771\) 5.82253 0.209693
\(772\) 0 0
\(773\) 12.9747 + 9.42668i 0.466668 + 0.339054i 0.796141 0.605111i \(-0.206871\pi\)
−0.329473 + 0.944165i \(0.606871\pi\)
\(774\) 0 0
\(775\) 4.97779 15.3201i 0.178808 0.550313i
\(776\) 0 0
\(777\) −2.14049 + 1.55515i −0.0767895 + 0.0557908i
\(778\) 0 0
\(779\) −8.40413 25.8653i −0.301109 0.926719i
\(780\) 0 0
\(781\) 21.9505 36.5113i 0.785450 1.30648i
\(782\) 0 0
\(783\) −2.32099 7.14327i −0.0829454 0.255280i
\(784\) 0 0
\(785\) 28.4353 20.6595i 1.01490 0.737368i
\(786\) 0 0
\(787\) −7.41924 + 22.8341i −0.264467 + 0.813947i 0.727348 + 0.686268i \(0.240752\pi\)
−0.991816 + 0.127678i \(0.959248\pi\)
\(788\) 0 0
\(789\) −2.76619 2.00975i −0.0984789 0.0715491i
\(790\) 0 0
\(791\) 39.9916 1.42194
\(792\) 0 0
\(793\) 4.47733 0.158995
\(794\) 0 0
\(795\) 7.47176 + 5.42855i 0.264996 + 0.192531i
\(796\) 0 0
\(797\) −16.5136 + 50.8238i −0.584943 + 1.80027i 0.0145539 + 0.999894i \(0.495367\pi\)
−0.599497 + 0.800377i \(0.704633\pi\)
\(798\) 0 0
\(799\) −13.0817 + 9.50438i −0.462796 + 0.336241i
\(800\) 0 0
\(801\) −14.9035 45.8683i −0.526589 1.62068i
\(802\) 0 0
\(803\) 13.8311 5.86693i 0.488090 0.207040i
\(804\) 0 0
\(805\) −21.0425 64.7622i −0.741651 2.28257i
\(806\) 0 0
\(807\) −2.39865 + 1.74272i −0.0844365 + 0.0613467i
\(808\) 0 0
\(809\) 0.983037 3.02548i 0.0345617 0.106370i −0.932287 0.361718i \(-0.882190\pi\)
0.966849 + 0.255348i \(0.0821902\pi\)
\(810\) 0 0
\(811\) 17.7607 + 12.9039i 0.623662 + 0.453117i 0.854199 0.519947i \(-0.174048\pi\)
−0.230537 + 0.973064i \(0.574048\pi\)
\(812\) 0 0
\(813\) 0.457532 0.0160464
\(814\) 0 0
\(815\) 38.8217 1.35986
\(816\) 0 0
\(817\) −9.77704 7.10343i −0.342055 0.248518i
\(818\) 0 0
\(819\) 3.53899 10.8919i 0.123662 0.380594i
\(820\) 0 0
\(821\) −31.7897 + 23.0966i −1.10947 + 0.806075i −0.982580 0.185842i \(-0.940499\pi\)
−0.126888 + 0.991917i \(0.540499\pi\)
\(822\) 0 0
\(823\) 1.87643 + 5.77507i 0.0654084 + 0.201306i 0.978419 0.206628i \(-0.0662491\pi\)
−0.913011 + 0.407935i \(0.866249\pi\)
\(824\) 0 0
\(825\) −0.894726 10.2560i −0.0311504 0.357067i
\(826\) 0 0
\(827\) 5.52731 + 17.0113i 0.192203 + 0.591541i 0.999998 + 0.00207680i \(0.000661067\pi\)
−0.807795 + 0.589464i \(0.799339\pi\)
\(828\) 0 0
\(829\) 18.6924 13.5808i 0.649213 0.471681i −0.213790 0.976880i \(-0.568581\pi\)
0.863003 + 0.505199i \(0.168581\pi\)
\(830\) 0 0
\(831\) −0.0717374 + 0.220785i −0.00248854 + 0.00765894i
\(832\) 0 0
\(833\) −10.6006 7.70181i −0.367290 0.266852i
\(834\) 0 0
\(835\) −42.2628 −1.46256
\(836\) 0 0
\(837\) 1.49710 0.0517472
\(838\) 0 0
\(839\) 27.5690 + 20.0300i 0.951786 + 0.691513i 0.951229 0.308487i \(-0.0998226\pi\)
0.000557326 1.00000i \(0.499823\pi\)
\(840\) 0 0
\(841\) 1.19197 3.66850i 0.0411024 0.126500i
\(842\) 0 0
\(843\) 0.364084 0.264522i 0.0125397 0.00911063i
\(844\) 0 0
\(845\) 1.35047 + 4.15632i 0.0464575 + 0.142982i
\(846\) 0 0
\(847\) −42.0371 + 7.39085i −1.44441 + 0.253952i
\(848\) 0 0
\(849\) −1.45753 4.48580i −0.0500222 0.153952i
\(850\) 0 0
\(851\) −10.0619 + 7.31036i −0.344916 + 0.250596i
\(852\) 0 0
\(853\) 2.44016 7.51003i 0.0835494 0.257139i −0.900551 0.434750i \(-0.856837\pi\)
0.984101 + 0.177611i \(0.0568369\pi\)
\(854\) 0 0
\(855\) 50.8357 + 36.9343i 1.73855 + 1.26313i
\(856\) 0 0
\(857\) −19.5220 −0.666857 −0.333429 0.942775i \(-0.608206\pi\)
−0.333429 + 0.942775i \(0.608206\pi\)
\(858\) 0 0
\(859\) 28.6967 0.979120 0.489560 0.871970i \(-0.337157\pi\)
0.489560 + 0.871970i \(0.337157\pi\)
\(860\) 0 0
\(861\) −3.85836 2.80326i −0.131493 0.0955350i
\(862\) 0 0
\(863\) 3.79716 11.6865i 0.129257 0.397812i −0.865396 0.501089i \(-0.832933\pi\)
0.994653 + 0.103277i \(0.0329329\pi\)
\(864\) 0 0
\(865\) −43.3096 + 31.4663i −1.47257 + 1.06989i
\(866\) 0 0
\(867\) 0.976587 + 3.00562i 0.0331666 + 0.102076i
\(868\) 0 0
\(869\) 2.00015 + 22.9271i 0.0678504 + 0.777748i
\(870\) 0 0
\(871\) −0.893634 2.75032i −0.0302796 0.0931912i
\(872\) 0 0
\(873\) 10.3889 7.54801i 0.351613 0.255462i
\(874\) 0 0
\(875\) 47.6778 146.737i 1.61180 4.96062i
\(876\) 0 0
\(877\) 21.3017 + 15.4766i 0.719307 + 0.522607i 0.886163 0.463374i \(-0.153361\pi\)
−0.166855 + 0.985981i \(0.553361\pi\)
\(878\) 0 0
\(879\) 4.83531 0.163091
\(880\) 0 0
\(881\) 28.7853 0.969801 0.484900 0.874569i \(-0.338856\pi\)
0.484900 + 0.874569i \(0.338856\pi\)
\(882\) 0 0
\(883\) 6.42190 + 4.66579i 0.216114 + 0.157016i 0.690576 0.723260i \(-0.257357\pi\)
−0.474462 + 0.880276i \(0.657357\pi\)
\(884\) 0 0
\(885\) 2.90072 8.92749i 0.0975066 0.300094i
\(886\) 0 0
\(887\) 20.0127 14.5401i 0.671960 0.488207i −0.198721 0.980056i \(-0.563679\pi\)
0.870681 + 0.491849i \(0.163679\pi\)
\(888\) 0 0
\(889\) −23.7652 73.1417i −0.797059 2.45310i
\(890\) 0 0
\(891\) −26.1548 + 11.0944i −0.876218 + 0.371677i
\(892\) 0 0
\(893\) 14.9651 + 46.0578i 0.500788 + 1.54127i
\(894\) 0 0
\(895\) −5.69022 + 4.13419i −0.190203 + 0.138191i
\(896\) 0 0
\(897\) −0.273207 + 0.840844i −0.00912211 + 0.0280750i
\(898\) 0 0
\(899\) 5.29844 + 3.84954i 0.176713 + 0.128389i
\(900\) 0 0
\(901\) 15.6130 0.520146
\(902\) 0 0
\(903\) −2.11926 −0.0705246
\(904\) 0 0
\(905\) −32.7558 23.7985i −1.08884 0.791088i
\(906\) 0 0
\(907\) −5.18922 + 15.9708i −0.172305 + 0.530301i −0.999500 0.0316143i \(-0.989935\pi\)
0.827195 + 0.561915i \(0.189935\pi\)
\(908\) 0 0
\(909\) 46.5910 33.8503i 1.54533 1.12274i
\(910\) 0 0
\(911\) 0.656686 + 2.02107i 0.0217570 + 0.0669611i 0.961346 0.275345i \(-0.0887921\pi\)
−0.939589 + 0.342306i \(0.888792\pi\)
\(912\) 0 0
\(913\) 5.25071 8.73375i 0.173773 0.289045i
\(914\) 0 0
\(915\) 1.33122 + 4.09708i 0.0440089 + 0.135445i
\(916\) 0 0
\(917\) 23.4326 17.0248i 0.773813 0.562208i
\(918\) 0 0
\(919\) 15.9329 49.0364i 0.525578 1.61756i −0.237592 0.971365i \(-0.576358\pi\)
0.763170 0.646198i \(-0.223642\pi\)
\(920\) 0 0
\(921\) 3.01999 + 2.19415i 0.0995121 + 0.0722998i
\(922\) 0 0
\(923\) −12.8449 −0.422794
\(924\) 0 0
\(925\) −43.6654 −1.43571
\(926\) 0 0
\(927\) 8.54424 + 6.20775i 0.280630 + 0.203889i
\(928\) 0 0
\(929\) −1.16274 + 3.57855i −0.0381483 + 0.117409i −0.968317 0.249723i \(-0.919660\pi\)
0.930169 + 0.367132i \(0.119660\pi\)
\(930\) 0 0
\(931\) −31.7485 + 23.0667i −1.04052 + 0.755979i
\(932\) 0 0
\(933\) 1.18254 + 3.63949i 0.0387147 + 0.119152i
\(934\) 0 0
\(935\) −15.4628 17.7968i −0.505688 0.582018i
\(936\) 0 0
\(937\) −6.68970 20.5888i −0.218543 0.672606i −0.998883 0.0472506i \(-0.984954\pi\)
0.780340 0.625355i \(-0.215046\pi\)
\(938\) 0 0
\(939\) 2.67468 1.94327i 0.0872847 0.0634161i
\(940\) 0 0
\(941\) −9.14575 + 28.1477i −0.298143 + 0.917590i 0.684004 + 0.729478i \(0.260237\pi\)
−0.982148 + 0.188112i \(0.939763\pi\)
\(942\) 0 0
\(943\) −18.1371 13.1774i −0.590626 0.429115i
\(944\) 0 0
\(945\) 22.2192 0.722790
\(946\) 0 0
\(947\) −39.4193 −1.28095 −0.640477 0.767977i \(-0.721263\pi\)
−0.640477 + 0.767977i \(0.721263\pi\)
\(948\) 0 0
\(949\) −3.66478 2.66262i −0.118964 0.0864321i
\(950\) 0 0
\(951\) 0.484922 1.49244i 0.0157247 0.0483956i
\(952\) 0 0
\(953\) −28.5986 + 20.7781i −0.926399 + 0.673068i −0.945108 0.326757i \(-0.894044\pi\)
0.0187095 + 0.999825i \(0.494044\pi\)
\(954\) 0 0
\(955\) 7.69291 + 23.6763i 0.248937 + 0.766148i
\(956\) 0 0
\(957\) 4.07810 + 0.942565i 0.131826 + 0.0304688i
\(958\) 0 0
\(959\) −7.33605 22.5780i −0.236893 0.729083i
\(960\) 0 0
\(961\) 24.0234 17.4540i 0.774949 0.563033i
\(962\) 0 0
\(963\) 10.0896 31.0526i 0.325133 1.00066i
\(964\) 0 0
\(965\) −46.6210 33.8721i −1.50078 1.09038i
\(966\) 0 0
\(967\) −30.8195 −0.991089 −0.495545 0.868583i \(-0.665031\pi\)
−0.495545 + 0.868583i \(0.665031\pi\)
\(968\) 0 0
\(969\) −1.74453 −0.0560425
\(970\) 0 0
\(971\) −24.0997 17.5095i −0.773397 0.561905i 0.129593 0.991567i \(-0.458633\pi\)
−0.902990 + 0.429662i \(0.858633\pi\)
\(972\) 0 0
\(973\) −23.5348 + 72.4326i −0.754490 + 2.32208i
\(974\) 0 0
\(975\) −2.51122 + 1.82451i −0.0804233 + 0.0584309i
\(976\) 0 0
\(977\) −10.1623 31.2763i −0.325121 1.00062i −0.971386 0.237506i \(-0.923670\pi\)
0.646265 0.763113i \(-0.276330\pi\)
\(978\) 0 0
\(979\) 52.8025 + 12.2042i 1.68758 + 0.390047i
\(980\) 0 0
\(981\) −1.55305 4.77980i −0.0495851 0.152607i
\(982\) 0 0
\(983\) −13.3250 + 9.68119i −0.425002 + 0.308782i −0.779647 0.626219i \(-0.784602\pi\)
0.354645 + 0.935001i \(0.384602\pi\)
\(984\) 0 0
\(985\) −19.1829 + 59.0388i −0.611217 + 1.88113i
\(986\) 0 0
\(987\) 6.87051 + 4.99172i 0.218691 + 0.158888i
\(988\) 0 0
\(989\) −9.96207 −0.316776
\(990\) 0 0
\(991\) −45.4810 −1.44475 −0.722375 0.691501i \(-0.756950\pi\)
−0.722375 + 0.691501i \(0.756950\pi\)
\(992\) 0 0
\(993\) 4.95455 + 3.59969i 0.157228 + 0.114233i
\(994\) 0 0
\(995\) −5.72074 + 17.6066i −0.181360 + 0.558167i
\(996\) 0 0
\(997\) −4.62436 + 3.35979i −0.146455 + 0.106406i −0.658600 0.752493i \(-0.728851\pi\)
0.512145 + 0.858899i \(0.328851\pi\)
\(998\) 0 0
\(999\) −1.25405 3.85957i −0.0396764 0.122111i
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 572.2.n.b.313.5 yes 28
11.3 even 5 6292.2.a.z.1.6 14
11.8 odd 10 6292.2.a.y.1.6 14
11.9 even 5 inner 572.2.n.b.53.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.n.b.53.5 28 11.9 even 5 inner
572.2.n.b.313.5 yes 28 1.1 even 1 trivial
6292.2.a.y.1.6 14 11.8 odd 10
6292.2.a.z.1.6 14 11.3 even 5